HARMONY IN CHOPIN Chopin’s oeuvre holds a secure place in the repertoire, beloved by audiences, performers, and aesthetes. In Harmony in Chopin, David Damschroder offers a new way to examine and understand Chopin’s compositional style, integrating Schenkerian structural analyses with an innovative perspective on harmony and further developing ideas and methods put forward in his earlier books Thinking About Harmony, Harmony in Schubert, and Harmony in Haydn and Mozart. Reinvigorating and enhancing some of the central components of analytical practice, this study explores notions such as assertion, chordal evolution (surge), collision, dominant emulation, unfurling, and wobble through analyses of all forty-three mazurkas Chopin published during his lifetime. Damschroder also integrates analyses of eight major works by Chopin with detailed commentary on the contrasting perspectives of other prominent Chopin analysts. This provocative and richly detailed book will help transform readers’ own analytical approaches. D AV I D D A M S C H R O D E R is Professor of Music Theory at the University of Minnesota.
His current research focuses on harmony in tonal music, a project that began with a careful examination of historical analytical practices and was the basis for his book Thinking About Harmony: Historical Perspectives on Analysis (Cambridge, 2008). The project continues with focused studies on selected repertoires: Harmony in Schubert (Cambridge, 2010), Harmony in Haydn and Mozart (Cambridge, 2012), and the present book. He has written textbooks on music fundamentals and on ear-training and sightsinging and his articles and reviews have appeared in numerous journals. In addition, he is working on a textbook, Tonal Analysis: A Schenkerian Perspective (forthcoming). As a complement to his scholarly work, he occasionally performs on fortepiano and modern piano.
HARMONY IN CHOPIN David Damschroder The University of Minnesota
University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107108578 © David Damschroder 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United Kingdom by TJ International Ltd, Padstow Cornwall A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Damschroder, David, author. Harmony in Chopin / David Damschroder, the University of Minnesota. pages ; cm Includes bibliographical references and index. ISBN 978-1-107-10857-8 1. Chopin, Frédéric, 1810–1849 – Criticism and interpretation. 2. Harmony. I. Title. ML410.C54D25 2015 786.2092–dc23 2014046686 ISBN 978-1-107-10857-8 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents Preface Part I Methodological orientation: the mazurkas 1 The architecture of a tonic pillar: twenty-seven regular tonic pillars from the mazurkas 2 Between the tonic pillars: tonal trajectories in twenty-seven mazurkas 3 Irregular pillars in the mazurkas: alternatives to the perfect authentic cadence Part II Masterpieces 4 Étude in C Minor(op. 10, no. 12) in response to Graham H. Phipps 5 Nocturne in C Minor (op. 27, no. 1) in response to Felix Salzer 6 Preludes in E Major and E Minor (op. 28, nos. 9 and 4) in response to Fred Lerdahl 7 Prelude in G Minor (op. 28, no. 22) in response to Alison Hood 8 Prelude in C Minor (op. 45) in response to Jean-Jacques Eigeldinger and to Charles J. Smith 9 Ballade in F Minor (op. 52) in response to Edward Laufer 10 Barcarolle in F Major (op. 60) in response to John Rink Notes List of references to music examples Select bibliography Index of Chopin’s works Index of names and concepts
Preface Given my intention to explore harmony from Haydn through Debussy in depth, the decision to devote a volume to Chopin needs no special justification. Despite the narrow range of his compositional activities, Chopin’s oeuvre holds a secure place in the nineteenth-century repertoire, both beloved by audiences and admired by aesthetes. So, having recently published Harmony in Schubert and Harmony in Haydn and Mozart, I take a respite from Vienna (where I assume Beethoven and Brahms will wait patiently), following Chopin westward to Paris. My decades-long fascination with his mazurkas here reaches its culmination in the presentation of probing yet concise analyses of all fortythree mazurkas that Chopin published during his lifetime. (While at work on this project I also performed these compositions in fortepiano recitals and taught them in a graduate seminar.) Readers are invited to join me in exploring these wonderful creations over the course of this volume’s first three chapters. (As was the case in my seminar, a semester’s study of Schenkerian analysis should be regarded as a prerequisite.) The remainder of my offering (chapters 4 through 10) continues a practice I pursued in Schubert and Haydn/Mozart (note my abbreviations for those volumes): a focus on masterpieces by Chopin that have been addressed in print or online by at least one other analyst, so that the reader may juxtapose my interpretations with alternative viewpoints and, with my guidance, explore the differences. Though I provide numerous detailed Schenkerian graphs (crucial for creating hierarchy-sensitive harmonic analyses), the Roman numerals and other symbols below the music notation will be the principal focus of my attention. This study is intended for anyone who both especially enjoys listening to or performing Chopin’s music and concurrently possesses an interest and facility in the analysis of tonal music. Though one might suppose that such attributes would describe all musicians, clearly some are more inclined towards nineteenth-century repertoire and to analytical undertakings than are others. As both teacher and author, I endeavor to offer analyses that are both insightful and vibrantly presented, hoping that any initial resistance might eventually melt. That said, the rigorous pursuit of analysis requires dedication. This is not a book that can be digested quickly. Especially, chapters 1 through 3 should be read at a leisurely pace, ideally with time for repeated listening to each mazurka and (by those who are able) for making each work come alive at the keyboard.
Authors of studies in which harmony is a peripheral concern might reasonably elect to adopt the conventions for harmonic analysis that most readers already know and practice. My study of Chopin, on the other hand, is part of a broader harmony project that eventually will encompass the “long” nineteenth century: this is the fourth of a planned six volumes for the period up to 1850 (including Thinking About Harmony: Historical Perspectives on Analysis [abbreviated as TAH], the two analytical monographs mentioned above, and forthcoming studies on Beethoven and on Mendelssohn and Schumann), to be followed by another six volumes for developments after mid-century (TAH II plus monographs on Verdi, Brahms, Liszt and Wagner, Mahler, and Debussy). Consequently I have taken decisive steps to creatively transform the practice of scale-step (Roman numeral) harmonic analysis, integrating elements from historical harmony treatises, from Schenker’s writings, and from my own thoughts on such matters. Knowing that some readers will be encountering my perspective for the first time in this volume, in the initial chapters I offer especially detailed commentary that should assist in coming to terms with how my system differs from the current conventional practice. Readers already familiar with my analytical work are welcome to pursue the book’s chapters in any order. Concurrent with the creation of Harmony in Chopin I have been developing the textbook Tonal Analysis: A Schenkerian Perspective (to be published by W. W. Norton). Its existence might impact Chopin readers in three ways: anyone whose understanding of basic Schenkerian principles is shaky will have another convenient resource for remedying the situation; I occasionally reference that work in my discussion of specific concepts or to call attention to a particular passage by Chopin that I analyze there; and because of this pedagogical preoccupation my Schenkerian graphs within Chopin have become more disciplined and consistent in their notational deployments. At the heart of my perspective is the notion that imaginative thinking should play a vital role in analysis, since the notes in the score often do not fully convey a work’s structure. Consequently a major impediment to understanding will emerge if a rigid, literalist stance regarding what may come into play prevails when analyzing a composition. This dichotomy vividly struck me as I was viewing a painting depicting Christ in the Garden of Gethsemane, recently attributed to Adriaen Isenbrant, at the art museum in Strasbourg. In a small area above a hedge or wall off to the left, one can make out some illumination. What could it be? Isenbrant has painted it at a slant, as if the source
of the illumination were moving towards the right at a swift pace. Without adding something to what is literally presented in the painting, this passage must remain a mystery. For those who know the story, however, the illumination is central to the painting’s meaning: it comes, of course, from torches (hidden behind the hedge) carried by men, led by Judas, intent upon arresting Christ. Likewise, elements of a musical story may be hinted at though not explicitly stated in a composition. There is much about how music works that will remain a mystery if one is unwilling or unable to imaginatively extend beyond the printed score when analyzing music. By gaining a clear understanding of a composer’s practice when all requisite notes are present one becomes well equipped to make sense of more elusive passages. My close engagement with selected contributions by numerous other analysts gives my harmony project a unique panoramic perspective regarding tonal analysis in the current era. These commentaries (set off by shading in chapters 4 through 10) should not be regarded as neutral reviews such as one might find in a journal, but instead as documentation regarding how other ways of analyzing music appear from my distinctive vantage point. Consequently readers may engage with my perspective through an inviting mix of opportunities to assess my own analyses and to encounter my reactions to various alternative viewpoints (and eventually, in other publications, the reactions of others to my viewpoints). Because so many perspectives will be assessed over the course of my project, I have established some ground rules. First, though some analysts have been very prolific, I will devote only one chapter to each within my set of books about music before 1850. (Where warranted a second turn may be granted during the post-1850 phase of the project.) Second, only analysts whose outcomes significantly contrast mine (even if we share similar methodologies) will be the focus of a chapter. Third, I must hold a neutral relationship with another analyst in order to write candidly about his or her work: friends, mentors, and former students consequently are excluded. As a result, some authors one might expect to find in a monograph on Chopin are not featured in individual chapters. For example, one of the leading Chopin authorities of our time has published admirable analyses of profound insight; and, I occasionally share quarters with him at music theory conferences. Thus for reasons two and three, no chapter herein focuses on his work (though I do quote him on occasion in the endnotes to reinforce my points or to acknowledge alternative interpretations).
I appreciate the feedback on drafts of this work that I have received from various quarters. I also acknowledge the support of an Imagine Fund award from the University of Minnesota. As in the earlier volumes of my project, Peter Smucker has provided expert setting of the music examples. All analyses are based on the scores as printed in the recent National Edition (Cracow). In a few instances other editions and their editorial commentaries are drawn into the discussion. I am grateful to the New York Public Library, Astor, Lenox, and Tilden Foundations, for allowing me to purchase on microfilm and to make reference to the Oster Collection: Papers of Heinrich Schenker.
Conventions regarding note relations, chords, keys, and Roman numerals Pitch simultaneities (such as C-E-G) are indicated using hyphens (-), while pitch successions (such as C–E–G) are indicated using dashes (–). Direction may be indicated in melodic succession: ascending as C
E>C. A black arrow may be used to indicate a descending-fifth relationship that is or emulates a V(7)–I succession, whereas an outline arrow may be used to indicate a succession from a chord of the augmented-sixth type: for example, C➔F–D➔G➔C; C–A♭–D⇨G➔C. Keys and chords are distinguished as follows: C Major (with a capital M) is the key of C Major; C major (with a small m) is a C major chord. Unless another analyst’s methodology is being discussed, Roman numerals are presented in capital letters regardless of a chord’s quality, modified by one or more accidentals if the chord is altered. Thus C Major: I II V I and not I ii V I; and A Minor: I II V♯ I♯ (closing on a major tonic), not i ii° V I. An accidental to the left of the numeral corresponds to the chord’s root; one to the right corresponds to its third. If the chordal fifth, seventh, or ninth is altered, the analytical symbol will incorporate the corresponding Arabic numeral, as in C Minor:
. (Arrow notation – here II➔ – offers an attractive,
though less precise, alternative to the complete analytical symbol.) The bullet symbol (•) indicates an absent root. For example, B-D-F in C Major will be analyzed as V7• (or, with less precision, as V➔). Likewise a progression of chordal roots generally is presented in capital letters (C– D–G–C), though on occasions when quality is a factor in the discussion a capital letter may refer to major quality, a small letter to minor quality, and a small letter followed by a degree circle (°) to diminished quality: for example, C–a–F–d–b°–G–e–C. A bracket is used to connect the analytical notation for two musical events that normally would follow one another but that in the context under discussion occur at the same moment: for example,
when an F♯-A♯-C♯ chord sounds with,
rather than before, root B in a descending circle of fifths.
Parentheses around a pitch in an analytical example indicate that it is not actually present in the score, though it is understood. Parentheses around analytical notation may refer to the expansion of a deeper-level harmony (for example, when I is expanded by I IV V I) or to the harmonic assertion of a voice-leading phenomenon (for example, when the 6 phase of a I5–6, as in C-E-G to C-E-A, asserts the harmonic role of VI). Open parentheses designate a voice-leading transition between two harmonies. For example, I ( ) IV indicates that the chords between I and IV (perhaps a circular, parallel, or sequential progression) do not themselves participate in the harmonic progression, but instead serve to connect the harmonies I and IV. When a score’s chordal spellings do not coincide with the structurally appropriate spellings (for example, the substitution of easier-to-read F♯-A-C♯ for cumbersome G♭B♭♭-D♭), I generally will use the structurally appropriate spellings in my examples and commentaries, often placing the enharmonic spellings within square brackets to assist readers in locating the pitches in question within the score. I pay very close attention to hierarchies among pitches and chords. To alert readers to various hierarchical relationships I often will underline some pitch names to indicate their hierarchical prominence. For example, CB C above bass C–G–C conveys the relationship between two unfolded strands: a more prominent outer strand E>D>C, and a subordinate inner strand C>B
ant. anticipation CP chromatic passing note CV chromatic variant HC half cadence IAC imperfect authentic cadence IN incomplete neighboring note N neighboring note P passing note PAC perfect authentic cadence prg. progression
susp. suspension W wobble
Of course, the graphs often will incorporate Roman-numeral harmonic analyses, and in this regard I sometimes depart from Schenker’s practice. Because it is innovative, I document my Roman-numeral usage very carefully as the chapters unfold. Because measure numbers are a pervasive feature in my close analyses, I have developed an abbreviated style of reference, in the form measurebeat. For example, the symbol 23 indicates the third beat of measure 2. Generally the word “measure” will not precede the number. I regard measures in and as containing two beats. A measure designation such as 14/16 means that a given chord is prolonged from measure 14 through measure 16, with contrasting content occurring between statements of the chord, whereas the designation 14–16 indicates a continuous prolongation of a single chord without significant internal contrast. The symbol 15|16 indicates measure 16 along with its upbeat.
Part I ◈
Methodological orientation: the mazurkas
1
The architecture of a tonic pillar: twenty-seven regular tonic pillars from the mazurkas ◈ Chopin’s mazurkas are admired especially for their harmonic creativity. As Jim Samson suggests, “Chopin reserved for the mazurkas some of his most astonishing harmonic adventures, at times almost to the point of iconoclasm.”1 Our substantial investment of time and energy in these works over three chapters should offer the dividend of a striking and vivid perspective regarding Chopin’s harmonic practice over the course of his career as a composer. All of the forty-three mazurkas that Chopin published during his lifetime contain at least one regular tonic pillar, which is built from a phrase or group of phrases that concludes with a PAC in the mazurka’s tonic key. Though usually the tonic chord will occur at or near the beginning of a tonic pillar, a delayed initial tonic is a viable alternative, as long as I is established eventually and the progression then leads through V back to I for the cadence. The initial tonic might exceptionally occur during an introduction or only in the listener’s imagination (as will be explained in due course), in which cases the tonic pillar may be already engaged in the progression to the local dominant at its outset. The twenty-seven mazurkas that we explore in chapters 1 and 2 are distinguished from the sixteen that are deferred until chapter 3 by the fact that all of their tonic pillars (between two and four will occur within one mazurka) are regular. An irregular pillar will cadence on the tonic without a concurrent descent to (IAC) or on the dominant (HC) or the mediant, or it will be presented in a key other than the tonic. In all such cases a pillar later in the mazurka will conclude with a PAC in the tonic key and thus will be regular. Chapter 1 offers a detailed assessment of how twenty-seven regular tonic pillars are constructed. Five broad categories are proposed to account for Chopin’s range of
structures: uninterrupted third-progressions, uninterrupted fifth-progressions, interrupted third-progressions, interrupted fifth-progressions, and exceptional cases. How these pillars fit within the architecture of their respective mazurkas will be explored in chapter 2.
Uninterrupted third-progressions As is common in tonal music of this era, the projection of the tonic key in one of Chopin’s mazurkas often is accomplished through the stepwise filling-in of the tonic triad’s lower third – for example, E>D>C in C Major – supported by a harmonic progression that proceeds from I through V back to I. Though the ten tonic pillars explored in this section all convey these structural features, they nevertheless offer a considerable variety in terms of how these foundational chords are embellished and connected. Though II or IV often serves as an intermediary between I and V, in some cases Chopin proceeds directly from I to V or pursues a sequential trajectory rather than relying on one of those harmonic resources.
Opus 6/2 The Mazurka in C♯ Minor’s eight-measure introduction projects a B♯C♯ third, covered by G♯. The stemmed notes above the bass in 1.1 reveal the first-species foundation of A1’s linear strands: thirds and
converge upon the cadence’s unison C♯. An element from fourth species –
C♯’s delay in descending to B♯ – is here supported harmonically by II➔, enhancing the foundational I V♯ I progression. (Whereas the full inventory of an evolved harmony’s chromatic elements and added dissonances generally will be displayed beside its Roman numeral below the graph, a shorthand notation such as the solid arrow, which indicates that the harmony has taken on dominant-emulating characteristics, often will appear in the textual commentary. In this case Chopin has replaced C♯ Minor’s diatonic supertonic, D♯F♯-A, with a much more dynamic, dominant-targeting alternative, D♯-F -A♯-C♯. Whereas some analysts would elect to interpret this chord as diatonic in the context of the chord of its resolution –V7 of V♯ – it is interpreted here as a chromatic chord within C♯ Minor, with Roman II indicating that the second scale degree serves as the root.) The melody’s downward shift during V♯, restoring the register of the introduction, adds vitality to the presentation and motivates further registral fluctuation as the mazurka continues. The essence of the tonic pillar’s structure is not compromised by the presentation of its thirdprogression spread over a tenth or by the sounding of inner-strand pitches G♯ and E above the melodic descent’s C♯ goal. (Chopin emphasizes the C♯ by notating G♯ as a grace note and introducing E on beat two.) Because the mazurka continues beyond the tonic pillar, the third-progression (spread over a tenth) is interpreted as motion to the interior of the texture, consequently extending , which serves as the Kopfton (literally “head tone”), the pitch from which the mazurka’s deep structural descent – the ultimate tonic-confirming event – will emanate. Successors to at both the middleground and background levels emerge later (in measures 17 and 42), as we shall see in chapter 2.
Example 1.1 Analysis of Mazurka in C♯ Minor (op. 6/2), mm. 1–16.
Opus 6/5 [a.k.a. opus 7/5] The first-species framework that Chopin deploys during the tonic pillar of his Mazurka in C Major is identical to the one we noted in opus 6/2. Stemmed notes in 1.2 reveal the interaction between E>D>C above and C>BF>E descant in measures 7 and 8 hovers above the principal line, similar to G♯>F♯>E in measures 14 through 16 of opus 6/2 [1.1].2 That contrapuntal structure likewise prevails at the foreground level to project the pillar’s opening tonic harmony. (The Kopfton imagined at the outset is stated during the second local E>D>C descent, which extends from 53 through 63.) The repetition of the pillar, beginning in measure 9, both rescinds the upper-octave hoist of goal C (compare measures 8 and 12) and segues into the B section by destabilizing the goal tonic via a 5–6 shift (G to A in measure 12).3 As numerous later examples will confirm, the tonic’s fifth often will shift to its sixth as a means of segueing between the tonic and the supertonic, which in this case is realized as II➔ (D-F♯-A-C in measure 13, to be discussed in chapter 2).
Example 1.2 Analysis of Mazurka in C Major (op. 6/5), mm. 1–8. My assertion that the introduction conveys a tonic root and Kopfton (displayed within parentheses in 1.2) may be disconcerting. (Such bold assertions are a hallmark of imaginative analytical thinking, which contrasts a literalist perspective.4) Because an E (during 81) precedes the upper-strand D in the repetition beginning at 91, I retrospectively import that context to what precedes 51. In this case the initial tonic is unconventionally presented in position. Interpreting the solo G of measures 1 through 4 as a tonic harmony depends upon a careful assessment of the broader context. A comparison with another mazurka – opus 30/3 – reveals how Chopin will sometimes lead from a lone fifth scale degree into a robust tonic chord during an introduction. In opus 6/5 that evolution is elided. My proposed C and E project what I understand Chopin to have imagined as the opening chordal structure, represented meagerly by pitch G.5
Opus 7/1 The high spirits that Chopin conveys in his Mazurka in B♭ Major result in part from the persistent refusal of the melody to be confined by the line that traverses the pillar’s middleground
structural descent (depicted in 1.3). An upper third
coordinates with each of these elements, and even greater heights are attained as well. For example, the F of 23, already a third above the structural D, is embellished by neighbor G in measure 3, during a
expansion of the tonic. (The is unfurled, with E♭
sounding in the bass. An unfurling is defined as a chordal reconfiguration involving the substitution of a different bass note for the one that characteristically would occur.) This G is embellished by upper-third B♭ before F returns. Also, whereas an E♭ neighbor to Kopfton D sounds as a grace note at 51 before upper third G emerges, the corresponding spot in measure 9, during a varied repetition of the latter part of the phrase, attains greater heights by dispensing with the E♭. The persistent upward striving impacts even the close of the
descent: B♭ sounds an octave higher than expected in measure 8
(though not in measure 12).
Example 1.3 Analysis of Mazurka in B♭ Major (op. 7/1), mm. 1–12. A collision occurs when two successive syntactic entities are juxtaposed during the same moment in time, as in measure 6. Whereas the left hand persists in projecting the initial tonic, the E♮ that joins with B♭ and D in the right hand projects II➔ (here with omitted root: E♮-(G)-B♭-D is interpreted as a dominant-emulating evolution of the diatonic supertonic, C-E♭-G). The collision is conveyed in the harmonic analysis by placing a bracket above Roman numerals I and II. Whereas II➔ in opus 6/2 [1.1] is spelled as D♯F -A♯-C♯, in opus 7/1 the octave of the supertonic root C is displaced by ninth D, resulting in a chord spelled as E♮-(G)-B♭-D. (In the full inventory of chordal elements beside Roman numeral II in the graph, a bullet (•) indicates that the root has been omitted.) Chopin here takes advantage of the fact that B♭ and D are members of both the I and the II➔ harmonies in B♭ Major.
Opus 24/2 The Mazurka in C Major’s introduction provides the venue for the initial sounding of the tonic harmony. By the time A1 commences at 51, the progression has already proceeded to the tonic’s 6-phase chord within a local expansion of I-space [1.4]. Some imaginative thinking is called for in measure 5, since the upper E within an E
Example 1.4 Analysis of Mazurka in C Major (op. 24/2), mm. 1–20. Chopin divides the tonic pillar’s broad harmonic progression into two segments, each repeated. The initiating I5–6 transpires during the introduction and the first half of A1 (wherein the written-out repeat during measures 9 through 12 does not recapture the tonic’s initial 5-phase chord), whereas the continuation II V7 I transpires during the second half of A1. Observe in 1.4 how G and B at the downbeat of measure 13 function as accented passing notes that delay the full flowering of II, rather than asserting the arrival of V.6
Opus 24/3 An unfolded GC>B♭) than in the soprano. In fact, the soprano D♭>C over the bar line between measures 7 and 8 makes the perception of a PAC at that point doubtful.7 A modified traversal of the phrase’s second half (extending what might have been a normative eight-measure phrase to twelve measures) brings the D♭-toB♭ third into somewhat better focus (though note that D♭ appears within parentheses in 1.5 since it does not sound in the upper register in either traversal), with a more decisive landing on A♭ in measure 12. (Compare with 1.3, measure 12.)
Example 1.5 Analysis of Mazurka in A♭ Major (op. 24/3), mm. 0|1–12.
Opus 24/4 The extraordinary opening of the Mazurka in B♭ Minor involves the concurrent chromatic filling-in of two intervals from the F-A♮-C embellishing chord that precedes the initial tonic. Whereas the path from F to A♮ is traversed in the lower strand – five pitches in all – a chromatic descent from F to C in the upper strand encompasses six pitches, and so when A♮ arrives in measure 5 the upper strand has descended only as far as D♭, a half step shy of goal C. Chopin ingeniously employs this distinctive sonority (one that recurs often in his compositions) as a substitute for the intended one by treating downward-tending D♭ as an anticipation of the following tonic’s third, Kopfton D♭. Consequently the descending fourth’s goal C is elided, as conveyed by the parentheses around the C notehead in 1.6. Similar elisions and anticipations recur during the tonic pillar’s subsequent progression to V.
Example 1.6 Analysis of Mazurka in B♭ Minor (op. 24/4), mm. 0|1–12. The mediant, a common element in minor-key progressions, here lives up to its name by serving as the mediator between the tonic and the dominant harmonies (measures 6 through 10). Segments of the descending circle of fifths, pursuing an upward trajectory, provide the locomotion. The soprano follows this upward course as well, maintaining the interval of a tenth with the bass at the tonic, mediant, and dominant nodal points. Such voice leading places the normative stepwise descent from the Kopfton in jeopardy. The arrow at measure 11 in 1.6 reveals Chopin’s solution to the dilemma. Though A♮ (a transformation of diatonic A♭ into the leading tone) is introduced above the register of
Kopfton D♭, eventually it is transferred downward an octave, and a C emerges above it to link the Kopfton D♭ of measure 6 and the PAC’s B♭ of measure 12. (Though a C sounds at 113 in the accompaniment, its melodic statement is delayed until 121, at which point it takes on the role of a suspension.) Despite the bold path that connects the I and V♮
harmonies, first-species lines (here
) over a bass arpeggiation (B♭–F–B♭),
already noted in several other mazurkas, serve as the structural foundation.
Opus 30/2 Initially the Mazurka in F♯ Minor’s opening sixteen measures might seem to represent the tonic pillar for a “Mazurka in B Minor.”8 Yet the absence of a PAC should raise eyebrows among astute listeners. Noting that these measures do not recur later in the mazurka (and thus do not conform to the behavior of a tonic pillar), that the mazurka concludes in F♯ Minor (despite the score’s two-sharp key signature), and that the normative cadential and universal repetition characteristics of a tonic pillar are fulfilled instead by the material of measures 16|17 through 32, one may reasonably interpret the opening sixteen measures as an introduction on F♯ Minor’s subdominant [1.7]. Though two mazurkas (opus 30/4 [3.4] and opus 56/1 [1.9]) commence with the supertonic, in those cases the tonic is achieved in the context of the initial musical idea. Opus 30/2 is unique in the extent to which the tonic’s arrival is delayed. One might legitimately propose that Chopin has here gone too far – that the clash between the composition’s retrospectively wayward opening in B Minor and eventual settling down in F♯ Minor is something that cannot be fully reconciled by the listener.9 Nevertheless, 1.7 makes as strong a case as I can muster for tonal coherence.
Example 1.7 Analysis of Mazurka in F♯ Minor (op. 30/2), mm. 0|1–32. The melodic unfoldings during the introduction’s sequentially propelled progression contain a few holes. Two traversals of the succeeding upper and interior strands, which proceed in parallel thirds (with parentheses marking the absent pitches), occur during the opening sixteen measures: D
(C♯)
D
(C♯)
B
(A)
G♮
F♯
B
A♯ ,
B
A
G♮
F♯
E
D
Note that the initial opening is not pursued beyond measure 2 (a fresh start is offered in measure 3) and that the concluding melodic F♯ is delayed until after the written-out repeat
(at 163). That F♯ goal serves as the starting point for an ascent to the Kopfton, achieved at 182 by means of the reaching-over technique.10 The A1 prolongation of F♯ Minor coordinates ascending bass motion from the tonic through the mediant to the dominant with a rising melody, so that the normative descending second from Kopfton A to G♯ is presented as an ascending seventh. (Compare with the similar tonic pillar in opus 24/4 [1.6], where the lower register is retained.) Despite that anomaly, the line continues “downward” to F♯, so that a PAC is achieved within the phrase. The pillar’s repetition commences with an interesting variant on the IV of measure 16: D-G♯-B♯-F♯ at 243 is an evolved IV6 (=II⇨). (That is, diatonic IV – B-DF♯ – here is expanded through the incorporation of its sixth, G♯. With the assertion of G♯ as the chord’s root, diatonic G♯-B-D-F♯ further evolves through the raising of chordal third B to B♯. Since this chord correlates not to a “dominant seventh” sonority, which would be conveyed via the symbol II➔, but instead to what is often called an “augmented sixth” chord – here the “French” version – I deploy an outline arrow to the right of the Roman numeral: II⇨. All chords designated by arrows are surging: through added dissonance and/or chromaticism they target the chord with root a perfect fifth lower, here G♯⇨C♯.)
Opus 30/3 Many features of the Mazurka in D♭ Major’s tonic pillar, displayed in 1.8, correspond to structural elements from mazurkas we have explored above. The tonic harmony initiated by the fifth scale degree during an introduction relates to 1.2. The transfer of Kopfton to a higher register corresponds to 1.4. The embellishment of all three pitches of a thirdprogression by upper thirds recalls both 1.3 and 1.5. Its first-species foundation (F>E♭>D♭ against D♭>C
Example 1.8 Analysis of Mazurka in D♭ Major (op. 30/3), mm. 1–24.
Opus 56/1 Though the Mazurka in B Major’s tonic pillar will establish the key of B Major, the B major chord of measure 2 is not asserted as that tonic.11 It instead is an internal element within a connection between antipodal C♯ minor and G major chords, achieved via an obstinate circular progression that emphasizes descending whole steps, as shown in 1.9. Chopin here taps one of tonal music’s most astonishing properties: the antipode – the chord that seems to be the furthest possible tonal distance from an initiating chord – may in fact map back onto that initiating chord.12 One type of chordal evolution is denoted using a solid arrow (➔). For example, the C♯-E-G♯ at this mazurka’s outset could have evolved into C♯-E♯-G♯-B or E♯-G♯-B-D♮ to invigorate the succession to the F♯ dominant of measures 12 and 13. Another common evolution, especially prevalent with the II harmony, involves the lowering of the chordal fifth (or retaining that fifth in a minor-key context).13 An outline arrow (⇨) is used to denote such evolutions, which here might result in a chord spelled as C♯-E♯-G♮-B or E♯-G♮-B-D♮.14 Though the relationship is masked when a nickname such as “German augmented sixth” (which I eschew) is employed, observe that C♯ (a pitch that often will be omitted) serves as the root for a chord that incorporates the antipodal triad of pitches G♮, B, and D♮! Consequently Chopin’s seemingly wayward journey further and further from the initial C♯ chord in fact leads to pitches that, once E♯ emerges at 121, intensify the natural tendency of the C♯ supertonic to proceed to dominant F♯. As 1.9 reveals, this potent II expansion delays V until measures 12 and 13. The prolongation of V via a embellishing chord in measure 14 puts off the tonic arrival until measure 16.
Example 1.9 Analysis of Mazurka in B Major (op. 56/1), mm. 1–22. As the supertonic’s minor ninth, the pitch D♮ possesses a tendency to resolve downwards to the dominant’s fifth, C♯. In this case that resolution will be preceded by a embellishment (here presented uncharacteristically in a weak metrical position, at 123) that reverts to the major mode’s D♯. Consequently Chopin respells D♮ as C at 122, facilitating its upward continuation. Though the dominant’s seventh, E, sounds at 131, the voice leading should be understood as D♯>C♯, with E reaching over that strand, as shown in 1.9. Though no C♯ sounds in the upper register at measure 1, I imagine the broad chromatic filling-in of a C♯-to-E third (as slurred in 1.9) as a melodic trajectory within the opening thirteen measures. A reciprocal D♯-to-B third is pursued during the remainder of the pillar. Whereas an ascent in thirds connecting I and V, with the outer voices moving in parallel tenths, is a key feature of 1.6, a similar trajectory in the downward direction connects I and IV in 1.9.15 The melody’s subservience to the bass descent in thirds results in an empty space in the upper register during IV. I propose that, as was also the case in measures 5 through 11 of opus 24/3, the melody’s trajectory is more fully worked out in the interior of the texture, here as a connection of Kopfton D♯’s incomplete upper neighbor E through passing note D♯ to the dominant’s fifth, C♯ (at which point the action returns to the upper register). One way to support the E>D♯>C♯ span in a IV–V context is to utilize
IV’s upper-fifth chord as consonant support for IV’s passing seventh, D♯.16 This reading wins out against the hypothesis that the tonic is restored at 183, especially since Chopin’s modified repetition of the concluding measures retains the IV but dispenses with the upper-fifth chord.
Opus 56/2 A Polish folk spirit is especially pervasive in the Mazurka in C Major, with a
drone
sounding throughout the tonic pillar. The four-measure introduction’s G serves as the starting point for an ascending arpeggiation to Kopfton E [1.10]. Though a higher G sounds immediately thereafter, it replicates that in the tenor register, to which the A that follows G at 53 immediately transfers. (That line then continues upwards through B to C.) Consequently the F♯ and D during 61 serve as neighbors to the C and E of 51. (I admit that this reading may seem wayward. Yet compare with Chopin’s variant in measures 53 and 54, where F♯’s role as neighbor between two Es is more overtly stated.) Chromatic F♯ is a wobbly note (or wobble) – a note that temporarily takes on a chromatic inflection that eventually will be revoked – that soon reverts to diatonic F♮. The G initiates an upperoctave replication of the initiating GD>C descent that it supports taking precedence over the maintenance of E (thereby contrasting the emphasis upon E’s arrival an octave higher in measure 13, confirmed by the reiteration of E in the lower register at 161).
Example 1.10 Analysis of Mazurka in C Major (op. 56/2), mm. 1–28.
Uninterrupted fifth-progressions The four mazurkas in this section project the tonic harmony by means of an uninterrupted fifth-progression descending from the tonic triad’s fifth to its root. Several contrasting means of supporting
and
are deployed, distinguished principally by whether
sounds as a stable element in a tonic context or instead as an unstable element in a dominant context. (One could propose other options not encountered in this section as well.)
Opus 7/4 The determination that , rather than , serves as a composition’s Kopfton can be a difficult call, especially given that another potential reading – the embellishment of Kopfton with an upper third – occurs frequently. How the tonic pillar fits within the mazurka’s broader context sometimes provides useful data. For example, the chord at 363 in the Mazurka in A♭ Major, which I propose would be spelled correctly as G-B♭-D♭-F♭, features the dominant’s minor ninth F♭ [E♮] poised towards resolution to the tonic’s fifth, E♭, for the final statement of the tonic pillar.18 Note also that at 71 (during the initial phrase’s written-out repeat) D♭’s arrival from above is emphasized through the resolution of a suspended E♭ (the grace note). Consequently I propose that the preferred reading should be a fifth-progression from E♭, rather than a third-progression from C with upper neighbor D♭. Though challenging to comprehension, occasionally in music one initiative begins before a prior one concludes: here the bass descent from tonic root A♭ to subdominant third F gets underway before the soprano arpeggiation of the tonic – E♭
Example 1.11 Analysis of Mazurka in A♭ Major (op. 7/4), mm. 0|1–4. With the bass taking the lead, the downward trajectory in both outer voices coordinates with the harmonic progression from I through IV (inverted) to V, culminating in a PAC on I.19 Though the most rudimentary support for would be within IV-space (as
in the second-species model
), the unaccented passing note C often
is shifted to the following strong metrical position, thereby becoming an accented passing
note
. From this perspective it would be absurd to label the
chord at 32–3 as I, as once was common and still persists in some quarters.
Opus 33/1 Once Kopfton D♯ is established in measures 3 and 4 of the Mazurka in G♯ Minor, three pitches – A♯, C♯, and E – create a rich embellishing chord that at first extends Kopfton (highlighting a D♯D♯ neighboring motive that plays an important role at various points during the work, including the melody’s first three pitches) and then supports the descent through to [1.12]. As usual, the dominant supports before the PAC on . The D♯-to-G♯ descent is shadowed a third lower by B>A♯>G♯>F
Example 1.12 Analysis of Mazurka in G♯ Minor (op. 33/1), mm. 0|1–12. Chopin sets up a wondrous opportunity through the means by which he establishes the initiation point (pitch B) for that interior strand. Instead of rising swiftly to Kopfton ,20 he emphasizes the B at 12 by pursuing a descending third-progression to the tonic pitch. This emphasis on , with a fleshed-out descent, presages the closing segment of the phrase (measures 7 and 8). Such a coincidence of content offers a delicious opportunity: a two-measure overlap, wherein measures 7 and 8 might be regarded as the end of the phrase or the initiation of its repetition – or both!21 The measure-number grid that annotates 1.12, in which the numbers 6, 7, and 8 occur twice, reveals how this works. The hairpin symbol to the right of the number 9 signals a truncation of the I-space expansion
the second time. Through these means the tonic pillar’s footprint extends for twelve – rather than sixteen – measures. As has been the case in several other mazurkas, the structure of the opening depends upon imaginative thinking. (Note the parenthetical bass G♯ at the outset in 1.12.) Since the D♯ at 03 corresponds to that at 63, where bass G♯ supports a tonic chord, I do not think I have misrepresented Chopin by proposing a tonic context for the initial lone D♯. However, I have held my imagination in check during 12. Do these pitches assert themselves as II➔? 22 Or is this an instance (similar to that discussed above in the context of opus 7/4, 2
3) of
passing motion getting underway just as an emerging chordal structure takes shape (chromatic C against the tonic’s G♯ and B)? I have left some empty space below the staff (at measures 1 and 7) in 1.12 for readers more persuaded by the supertonic interpretation than I am to jot in a II numeral.
Opus 41/1 [a.k.a. opus 41/2] Parentheses in 1.13a surround an imagined initiating chord for the Mazurka in E Minor – a stable E minor tonic (related to that at 43, established before the varied second traversal of the phrase) to serve as an unheard predecessor of the mazurka’s already surging first chord. Granted, analysts who would label the pitches E-G♯-B-D as V7/IV are not in a position to appreciate the subtlety of Chopin’s writing here and might propose that the mazurka initially conveys the key of A Minor or celebrate Chopin as a master of tonal ambiguity.23 From my more imaginative perspective I counter such claims: having so often heard a diatonic tonic chord evolve into a surging, IV-seeking entity, I am not alarmed that the tonic’s foundational consonant state is here elided. (Just as II often evolves into II➔ in its approach to V, so also I evolves into I➔ in its approach to IV.) As analyst I reconstitute that unsounded initiating chord within parentheses in 1.13a, and in 1.13b I show how, during the varied repetition of the phrase, a diatonic tonic chord in fact precedes the surge.
Example 1.13 Mazurka in E Minor (op. 41/1) (a) Analysis of mm. 1–4; (b) Analysis of mm. 1–8. The subdominant of measure 2 supports
within a local descent from to . The
leap to F♯ at 31 likely will generate concerns regarding
. I propose that the
subdominant’s A extends into V-space (where it sounds an octave lower), during which the descent through G to F♯ transpires. This is a hard call, especially since the melody of measure 3 resembles that of measure 1. A viable alternative would be to propose an imagined G at the end of measure 2 (thus IV8–(7)), so that the G at 33 functions as a neighbor to an already established .24 In the phrase repetition Chopin extends IV by means of a shift to its 6 phase (a common occurrence between IV and V♯) in measure 7, here deploying chromatic Fnatural, attained through descent from 8 rather than the more common ascent from 5. (The pitch F♮ functions as a wobbly note, which one would expect to be revoked through the reinstatement of F♯ as the dominant’s diatonic fifth.) Alas, that initiative consumes two beats of the phrase’s third measure, which in the earlier phrase was devoted exclusively to the dominant. During the one beat remaining before the tonic arrival on the downbeat of measure 8, Chopin elects not to sound the dominant root or to convey the conventional melodic descent to scale degree 2, elements of the structure that were presented
straightforwardly during measure 3. Whereas literalist analysts likely would endeavor to make whatever sense they could of Chopin’s curious third beat, my imaginative interpretation takes two crucial factors into account: first, we have heard a dominant harmony in the corresponding location during the initial statement of the phrase, where the melodic G in fact descends to F♯; and second, the unfolded thirds A to F♮ followed by E to G would lead one to expect an unfolded D♯–F♯ third next. Though I anticipate considerable resistance from some readers, my graph asserts a dominant function at the end of measure 7 despite the absence of that Stufe’s root, third, and fifth.25
Opus 41/4 [a.k.a. opus 41/1] Rising motion in all voices connects the tonic and the dominant in the first seventeen measures of the Mazurka in C♯ Minor, in a manner that places the upper-register arrival of Kopfton G♯ against dominant root G♯, rather than the initial tonic C♯. (A diagonal line in 1.14 connects root C♯ and Kopfton G♯.) Embellishing chords, rather than a functional harmonic progression, support the intervening melody: D♮-F♯-A26 and F♯-A-C♯ within the realm of the tonic (measures 1 through 8); F -A♯-C♯-(E) within the realm of the mediant (measures 9 through 16); C♯-E♯-G♯ within the realm of the dominant (measures 17 through 19). When serves as the Kopfton, as here, the fifth-progression descending to the tonic root over the course of the tonic pillar may be supported by a double I–V♯–I arpeggiation, as noted by the prong at the bottom of bass C♯’s stem in 1.14, measure 20. (That symbol denotes the concurrent end of the first arpeggiation and beginning of the second.)
Example 1.14 Analysis of Mazurka in C♯ Minor (op. 41/4), mm. 1–32. Though the mazurka will end desolately in C♯ Minor, a significant part of the pillar’s structure (measures 17 through 24) shifts decisively towards C♯ Major. During the second I–V♯–I arpeggiation, which supports
, the tonic’s 6-phase chord (C♯-E♯-
A♯, unfurled) comes between the tonic and the supertonic, presented as II➔ at 223. In conjunction with this II➔, a melodic excursion extends upwards – from E♯ through F to
G♯ – substituting for the melody’s conventional descent to D♯, which sounds belatedly at the cadential downbeat (as a suspended ninth whose imagined D♯ preparation is displayed within parentheses in 1.14). (During the A2 statement of the tonic pillar – at measure 103, near the final cadence before the coda – the D♯ is straightforwardly presented during .) The segment of the pillar devoted to the descending fifth-progression is reprised, with variants, during measures 25 through 32.
Interrupted third-progressions Repetition occurs in many musical contexts, most obviously when a repeat sign instructs the performer to play a passage a second time. A more sophisticated deployment of repetition involves two related phrases in which the first fails to fully close while the second does in fact achieve closure. The term interruption and some related notation within graphs are deployed when in one phrase (the antecedent) the melodic descent proceeds from or from to (supported by V), and in the next (the consequent) a new try is inaugurated, this time achieving (supported by I). All of this section’s tonic pillars, from works with Kopfton , are constructed in this manner, thereby offering a more complex inner organization than prevails in the pillars we have explored already. Analysts display interruption using either of two distinct styles of graph notation. Though in this book I conform to the preference that developed during my extensive study of this topic while writing Tonal Analysis: A Schenkerian Perspective, I trust that readers who are accustomed to the other method, which maintains a greater visual distinction between the antecedent and consequent parts of a graph through separate beaming and separate Roman-numeral analyses, will be able to adapt to the method on display here for the duration of this study. Also note that analysts do not all concur with regard to how similar the two halves must be to one another for the notion of interruption to be viable. I am willing to allow a significant amount of variation between the two halves, so long as the deeper structure conforms to the principles of interruption.
Opus 6/4 The four-measure theme that transpires during the Mazurka in E♭ Minor’s tonic pillar is divided into two halves that are equal in length but not in structural content. (The entire theme is then repeated, with a few subtle alterations.) This inequality results from one of tonal music’s most prevalent and effective structural devices: the juxtaposition of similar phrases that cadence on the dominant and on the tonic, melodically realized through an interruption of the structural descent after . The mazurka’s Kopfton is (to be justified presently). The
of the antecedent does not continue directly to , but reaches that
goal only after a reiteration of
and its harmonic support. The two-beat dominant
at 22–3 is replaced by a dominant-to-tonic succession during measure 4. The analytical notation for interruption that I employ (here at the middleground level, since it is internal to the A1 section within an A1 B A2 ternary form) is displayed in 1.15.27 Note that the V♮ in measure 2 serves as the principal dominant, after which the reiteration portion of the consequent phrase does not move the structure along at all: only the final tonic root and the melodic that it supports hook up with the earlier components of the structural framework. Working in three dimensions would be ideal: one could place the second and behind the first ones, showing effectively how the final serves as the goal both for the broad descent from over the course of four measures and for the more local descent in measures 3 and 4. (Imagine putting some hinges into the middle beams so that one could physically move the second half of the graph behind the first half, aligning G♭ and F in the two phrases and allowing the E♭ to stick out at the right edge.)
Example 1.15 Analysis of Mazurka in E♭ Minor (op. 6/4), mm. 0|1–4. In that all three pitches of the tonic triad initiate melodic strands during the mazurka’s opening two beats, one may wonder which one serves as the Kopfton. Does the B♭ win out because it sounds first? Or does the E♭ because it is the highest? Following each strand through to its goal, one may be surprised to learn that neither of those lines is maintained in its initial register over the long haul. Though one hears B♭ proceeding to A♭ (at 21), the continuation to G♭ in measure 4 occurs only in the tenor register. And though an E♭>D♭>C♭>B♭ fourth transpires during the antecedent phrase, in the consequent phrase that line is more fully realized in the tenor register, though the concluding B♭ is absent and will be imagined during 43. Only the strand that proceeds from G♭ is maintained in register over the course of all four measures; and only that strand attains , by which point it in fact is the highest-sounding strand, which is how it is displayed in 1.15. (An incomplete neighbor occurs between and , as often is the case when IV serves as the intermediary between I and V♮.)
Opus 17/3 The Mazurka in A♭ Major’s sixteen-measure tonic pillar derives its binary shape from the interruption that occurs after the first phrase’s cadential dominant. Chopin’s prolongation of this dominant correlates motivically with the preceding tonic prolongations: whereas C>B♭>A♭ is heard repeatedly during I-space (measures 1 through 6), B♭>A♭>G is projected during V-space (measures 7 and 8) [1.16]. Another set of thirds plays an equally important motivic role: just as E♭ emerges above Kopfton C in measure 2, D♭ follows B♭ and C precedes A♭ during the pillar’s final two measures. (Compare with 1.3.)
Example 1.16 Analysis of Mazurka in A♭ Major (op. 17/3), mm. 0|1–16. Whereas in the context of an interruption the PAC of the second phrase will contrast the dominant close of the first, the two phrases may display other variances as well. Chopin offers a delectable sample in this mazurka. What are we to make of the pitch collection that sounds during 63? From a literalist perspective A♭-C♭-E♭-F might be regarded as a chromatic variant of the tonic’s 6-phase chord, here proceeding directly to the dominant. Yet during the consequent phrase one tiny shift makes a clarifying difference: Chopin lowers E♭ to D♮ (at 143), unleashing the chord’s vibrant II➔ potentiality. In 1.16 that interpretation is parenthetically supplied in the earlier presentation as well. Just as we can discern Michelangelo’s intentions even in his unfinished sculptures, so also a chordal function may be perceived even when
incompletely realized. I have chiseled away at the E♭ to reveal the D♮ that it conceals, using parentheses to acknowledge my participation.28 The phrase’s harmonic “defect,” like its failure to achieve a PAC on , is rectified during the second phrase.
Opus 33/2 [a.k.a. opus 33/3] A composition’s underlying structure and the presentation of that structure by a composer may not exactly match. Consequently pairs of parentheses are encountered frequently in graphs to indicate pitches that the analyst proposes an alert listener will imagine. In Chopin’s Mazurka in C Major, even the Kopfton E (= ) is an imagined note [1.17]. There is evidence of its influence: the E>D suspension/resolution pair in measure 7 depends on the conventional preparation by an E during the preceding I5–6, and the mazurka’s B section twice ascends to the imagined Kopfton’s wobbly displacement, E♭ (measures 20 and 28). The descending parallel sixths in the soprano and alto registers during measures 0 through 6 logically would begin with . Since no such E sounds, I have reconstituted the structure that I propose grounds Chopin’s mazurka. I admire – rather than condemn – Chopin’s free presentation.
Example 1.17 Analysis of Mazurka in C Major (op. 33/2), mm. 0|1–16. The antecedent phrase’s harmonic path conforms precisely to the normative convention for the supertonic’s use: the tonic first shifts to its 6 phase (here surging as VI➔, in measure 6), which leads effectively to the supertonic (also surging: II➔) followed by the dominant. For the consequent phrase, Chopin foregoes the tonic 6-phase chord to facilitate an earlier dominant arrival, leaving time for the tonic in the phrase’s concluding
measure. Not only is the surging VI➔ absent; II’s surge is retracted as well (so that the subtler diatonic II7 serves as herald of the dominant).
Opus 33/3 [a.k.a. opus 33/2] Whereas Kopfton is an imagined pitch in the Mazurka in C Major [1.17], is imagined in my analysis of the Mazurka in D Major [1.18]. Fortunately the redundancy of descent within an interruption structure means that a second opportunity for the sounding of exists. In this case measure 6 achieves what measure 4 neglects. As usual, the altered agenda of the consequent phrase results in revisions of the harmonic progression, geared towards achieving an earlier dominant arrival to make room for the cadential tonic. Here Chopin elects to dispense with his three-measure prolongation of I-space, leaving only the initial one-measure arpeggiation. This drastic cut permits an elective addition preceding the dominant arrival: namely the supertonic, which occupies measure 6.
Example 1.18 Analysis of Mazurka in D Major (op. 33/3), mm. 0|1–8.
Interrupted fifth-progressions Interruption is as useful in developing structures emanating from Kopfton as from Kopfton
. The examples explored in this section demonstrate some strategies for
supporting the descent from that did not emerge among the non-interrupted lines explored above.
Opus 7/2 The tonic pillar’s two phrases in the Mazurka in A Minor offer related yet contrasting harmonizations of the structural line descending from Kopfton . During the antecedent phrase the span from to transpires during an expansion of I-space, followed by II➔, which, with embellishment, serves as the initial support for before the HC dominant arrives [1.19]. During the consequent phrase a shift to I6 coincides with the arrival of . In a minor key I6 is innately suited for a dominant-emulating role, which may be enhanced through the addition of a minor seventh, propelling a surge (as VI➔) towards ♭II. Since Chopin realizes that potentiality here, the two phrases offer a strong contrast at this juncture: supported by II➔ versus ♭ supported by ♭II. (Compare 73 and 141 in 1.19.) Though ♭II is not innately inclined towards V♯, listeners have accustomed themselves to the ♭II–V♯ succession, which composers have promoted as a means of preventing their compositions from leading into the abyss. An extension beyond the diatonic pitch collection is held in check: B♭➔E♭ occurs rarely in A Minor, whereas the antipodal B♭-toE continuation has become the norm. (Here Chopin forgoes presenting ♭II in its first inversion, a common means of softening the effect of the antipodal root connection.) The melody’s B♭ wobble temporarily displaces diatonic B♮, which duly emerges during the dominant that follows – though not in the soprano register, where parentheses denote its imaginative presence within a descending fifth-progression in 1.19.
Example 1.19 Analysis of Mazurka in A Minor (op. 7/2), mm. 0|1–16.
Opus 17/2 During the Mazurka in E Minor’s tonic pillar, Chopin devotes equal time to the establishment of the initial I-space, with Kopfton , and to the fifth-progression that leads ultimately to a PAC. Both of the pillar’s phrases are twelve measures in length. Over the first six measures a dotted slur in 1.20 connects Kopfton B in its middle and upper registers. Both outer voices pursue arpeggiations of the tonic pitches: E
Example 1.20 Analysis of Mazurka in E Minor (op. 17/2), mm. 0|1–24. Once the upper-register B is secure, the descent towards E commences. The B>A>G segment of that fifth occurs over a tonic pedal from 63 through 83, embellished by A♯. (Compare with F♯ in 1.10, measure 6.) Chopin provocatively transfers G to an even higher register in measure 10. That act turns out to be of only local significance. Though residual high notes persist through measure 12, the structural
should be imagined in the
conventional soprano register beginning at 111, as shown by the parenthetical F♯ in 1.20.29 (The E and D♯ that follow in that register depend upon the imagined precedent of F♯. Note that the F♯ sounds belatedly during 113 and 121. No parentheses are required during the consequent phrase, since F♯ sounds during 231.) The consequent phrase, displayed in somewhat abbreviated form in 1.20, presents the six-measure opening tonic expansion once again, followed by a full fifth-progression to
the PAC. The II➔ that supported
before the dominant’s arrival during the antecedent
phrase is suppressed: the earlier II➔V♯ HC gives way to a V➔I PAC. Though most of the phrase’s content corresponds to what was presented earlier, Chopin offers a particularly delicious innovation between 231 and 241. Observe how, above F♯ (=
), some residual
upper-note activity based on chromatic lower neighbors and their resolutions emerges:
A♯
A♮
G♯
The underlined notes reiterate the chromatic line of measures 6 through 8 (and 18 through 20). There the B and A were components of the middleground structural descent; here they represent an interior strand hoisted to a position above the structural F♯. As the arrow in 1.20 indicates, dissonant A’s resolution pitch G sounds in the restored interior register, below the cadential .
Opus 17/4 As a preface to our exploration of the tonic pillar in the Mazurka in A Minor, a review of 1.11 is warranted. Observe how Chopin’s melody there accomplishes the upward transfer of Kopfton E♭ by means of arpeggiation. It is especially notable that the bass has already begun its descending trajectory from the tonic root A♭ before the upper E♭ is secured. Yet once that happens the soprano joins the bass in pursuing a downward trajectory. Three
consecutive sixths –
– occur within a broad I IV V I progression.
For the Mazurka in A Minor I depart from standard analytical notation to show the essence of Chopin’s writing in an overtly contrapuntal manner. In 1.21a the essential content of 1.11 is maintained, transposed into A Minor. The representation of soprano C in its foundational role as an unaccented passing note reveals the motivation – avoidance of parallel fifths – that would cause a composer such as Chopin to shift its presentation to the following accented beat. Several types of expansion are applied concurrently in the transformation of 1.21a into 1.21b. First, by leading the initiating soprano pitch E to its upper neighbor F, a series of 7–6 suspensions graces the descent. Second, a chromatic link connects the G-B-E passing chord and the F-A-D subdominant.30 Third, the dominant is expanded via a
voice exchange.
Example 1.21 Mazurka in A Minor (op. 17/4) (a) Contrapuntal model for the tonic pillar; (b) Analysis of mm. 1–20. The measure numbers annotating 1.21b assert that this model serves as the foundation for Chopin’s tonic pillar. Notably the Kopfton is omitted at the outset. The mazurka’s first sonority – an A-B-D-F embellishing chord that resolves into I6 (at 42 and 61) rather than I5 – syntactically follows the imagined moment of the initiating tonic.31 As in 1.11, an ascending transfer achieved via arpeggiation occurs in the opening measures, but in this instance that transferred pitch is not the Kopfton ( ), but instead its upper neighbor: F (presented during the introduction) through A (53) and C (61) to F (72). Throughout the melodic descent various substitutions occur: F♯ for E at 91, F for D♯/E♭ at 101, E for C at 111, and C for A at 121. The last two of these substitutions do not occur during the consequent phrase: the first because a C (an octave higher) actually sounds at 191 (justifying the omission of parentheses around that pitch in 1.21b); the second because the passing note is omitted when measures 11 and 12 are condensed for presentation in
measure 19. (Chopin’s abbreviation of the dominant makes room for the consequent phrase’s cadential tonic.)
Opus 63/2 The two halves of the tonic pillar in Chopin’s Mazurka in F Minor pursue contrasting harmonic trajectories [1.22]. Though both begin with a motion from a prolonged C➔ embellishing chord to the F Minor tonic, during the antecedent phrase a sequential progression connecting the tonic and the mediant supports the descent from through an imagined (above which a prolonged F serves as a substitute) to , while is delayed via a ♭ wobble, supported by ♭II. (Compare with 1.19, measures 14 and 15.) During the consequent phrase, in contrast, the initial minor tonic is elided, with I➔ in its place (measure 12). Consequently the progression proceeds to IV, which supports the surging tonic targets IV, measure 13 is aptly interpreted as
. (Because
rather than as an
inverted II7.) Each pitch in the consequent phrase’s fifth-progression is treated to embellishment by an upper fourth or third, extending the practice we first encountered in 1.3.32
Example 1.22 Analysis of Mazurka in F Minor (op. 63/2), mm. 1–16.
Some exceptional tonic pillars The five tonic pillars explored during the chapter’s final section distinguish themselves from those considered already either through their internal ternary form or through an initial statement that seems to lack forward momentum, a state of affairs that is corrected during a later phase of the pillar. Ultimately each proceeds to a PAC in the tonic key, justifying their inclusion within this chapter.
Opus 6/1 The two phrases that constitute the Mazurka in F♯ Minor’s tonic pillar do not conform to the interruption-generated antecedent/consequent structure of the two-phrase pillars we have explored above. In fact, the first phrase amounts to a false start: once tonic F♯ Minor and Kopfton are established (employing reaching-over during the initial ascent), the bass and soprano both lead upwards a third [1.23]. So far, so good! In most cases the bass would continue upwards from the mediant to an inverted II or ♭II or to IV, followed by V♯. (Compare with the first phrase in 1.22.) Here, however, the phrase unexpectedly loses its harmonic propulsion. Astonishingly, we waft gradually downwards through tonal space for four measures, maintaining outer-voice tenths while guided by the circle of fifths:
A
D♯
G♯
C♯
F♯
B
E
A
D
G♯
C♯
The C♯ chord upon which the descent lands is, of course, the same C♯ chord as that which occurred in measure 1.33 In this manner Chopin gives himself a second chance to make something of his promising opening.
Example 1.23 Analysis of Mazurka in F♯ Minor (op. 6/1), mm. 0|1–16. The inverted subdominant to which that progression leads in the second phrase is made distinctive through a wobbly fifth, F♮, that eventually reverts to F♯.34 As expected, V♯ follows.35 Yet one aspect of the structure near the cadence is highly unconventional. Soprano B in measures 13 through 15 is an incomplete upper neighbor to Kopfton A (= ). (Both A and B are embellished by an upper third: AB.) Generally the descent to from such a neighbor – either via a leap or filled in by a passing note – will sound
during V♯, facilitating a
melodic close to form the PAC. (Compare with the
normative contexts for an incomplete upper neighbor displayed in 1.9 and 1.15.) In this case, exceptionally, B extends into the domain of the goal tonic. As 1.23 reveals, a daring non-alignment of the soprano and bass elements of the structure occurs, with a belated G♯ (during 161), which “belongs” with the dominant chord of 153, serving as the thirdprogression’s .36
Without opus 42B The progression from the tonic to the dominant during the Mazurka in A Minor’s tonic pillar is expansively realized: Chopin devotes four measures each to the tonic and to the mediant, content that he repeats before proceeding through II➔ to V♯, which arrives at 201 [1.24].37 Though he could have produced a structure of equivalent dimensions to balance that opening, Chopin instead limits the tonic pillar to sixteen measures of content, expanded to thirty-two measures via written-out repeats, corresponding to
|:
a1
:|:
b
a2
:|
Consequently the a2 region must somehow balance what precedes it structurally, despite its comparatively modest dimensions. Chopin accomplishes this by sacrificing the mediant.
Example 1.24 Analysis of Mazurka in A Minor (without opus 42B), mm. 0|1–32. The mazurka’s Kopfton is a primordial entity that does not literally sound in the upper register at the outset. The melodic C>B from 22 through 31 (matching the preceding inner-strand A>G♯) functions as a suspension and resolution based on the assumption of a prior C preparation.38 An even bolder claim is required for the mediant expansion that follows: whereas Chopin provides a location (at 03) for an imaginative insertion of the tonic root A and Kopfton C, the corresponding location for imagining the mediant root and
its E (in the vicinity of 43) is elided. Fortunately both C and E are stated in measures 17 and 18 (after the repeat of the first eight measures), so that both ’s successor, (B), and the descant E>D♯
Opus 50/1 The half cadence characteristic of an interruption is not the only means by which a composer may express a sense of irresolution in music. In the Mazurka in G Major Chopin composes eight measures without proceeding beyond the initiating tonic, whose final iteration within the phrase by default serves as the “cadence.”39 (Beats 2 and 3 of measure 8 play a transitional role between the tonic pillar’s two phrases.) A structural departure from I-space emerges only after the fresh start in measure 9 [1.25].
Example 1.25 Analysis of Mazurka in G Major (op. 50/1), mm. 1–16. Not only is the first phrase lacking in substantive harmonic activity; it also leaves unresolved whether B or D will serve as the mazurka’s Kopfton. The upward arpeggiation DG>E>D (as in 71 through 81). Consequently the positioning of E>D an octave higher in measure 4 seems quirky. Is D the upper third of Kopfton B? Or is Chopin instead ascending in tiers, as C>B E>D? That question remains unanswered until measure 12, where the F♮ and G♯ that emerge against D set the downward trajectory of a fifth to G in motion. (Though initially G-B-D-F♮ may seem to convey I➔ surging towards IV, the evolution continues to G♯-B-D-F♮, a version of I6 that surges as VI➔ towards II.) A double G–D–G bass arpeggiation supports that fifth-progression. Chopin projects an inner strand a third below this line: note how the initial BA in measures 13 and 14 (with A reiterated during 151) and by A>F♯ in measures 15 and 16. This context helps one to understand that the melody’s G at 152 is a member of the inner strand, above which the outer strand’s third pitch, B, should be imagined. (The preceding downbeat B, though tempting, is not the structural B, but
instead an accented passing note connecting the preceding outer C and interior A: is an unfolded interval of V7.) Thus, though the structure is unevenly distributed, with almost all of the content falling within the second phrase, it eventually begins to resemble what we have come to expect of a tonic pillar with Kopfton .
Opus 50/2 Whereas the tonic pillar in 1.25 begins with a phrase that goes nowhere tonally, and that in 1.23 ascends a third, that in the Mazurka in A♭ Major descends a third [1.26]. Chopin’s timing is at first extraordinarily luxuriant: an eight-measure introduction arpeggiates E♭
).
Though the melody sounds both a C and an E♭ during measure 9, here the structural priority of C is emphasized through the linear descent of C>B♭>A♭ over four measures. (Compare with the less decisive situation in 1.25.) The tonic’s progression is then repeated a third lower during the following four measures. In sum, Chopin has devoted eight measures to a mere I5–6. Rather than continuing with this languorous trajectory, he chose to start afresh in the next phrase: the G-E♭-D♭ chord at the end of measure 16 functions in the role of the introduction’s chord, facilitating the restoration of the initiating tonic harmony in measure 17.
Example 1.26 Analysis of Mazurka in A♭ Major (op. 50/2), mm. 1–28. In stark contrast to what has preceded it, the twelve-measure phrase that follows is among the most densely packed with content to be found in any tonic pillar from the mazurkas. Considering first its deeper structure, note that tonic A♭ is prolonged from measure 17 through measure 26, during which an
voice exchange occurs in
the outer voices. (The parenthetical A♭ in the upper voice [1.26, measure 26] sounds an octave higher in the score.) A conventional I6 approach to II follows, though the II➔ and its successor, V7, collide. (That is, the supertonic sounds over the dominant root during 271–2, as indicated by the bracket placed above the II and V numerals in 1.26.)
Incorporating upper-third play (B♭A♭) reminiscent of that which embellishes the foreground C>B♭>A line of measures 9 through 12, Chopin achieves a PAC in measure 28. The tonic prolongation of measures 17 through 26 is based on a I III♮ V7 I progression, as displayed in 1.26. Note the wobbly E♮ above bass C and the presentation of V7 in its position. The connection between the tonic and the mediant is achieved via a circular progression: A♭ D♭ G C. The first link in that progression is filled in as A♭>F>D♭.40 At this foreground level one belatedly discovers how Chopin incorporates the A♭>F span, introduced during the a1 phrase, into a broader structure. With that succession now condensed into four measures through an elision (A♭>E♭F becomes A♭>E♭
Opus 63/3 An unusual occurrence in the Mazurka in C♯ Minor should induce some analytical speculation: whereas the initial tonic pillar employs four phrases, spread over thirty-two measures, its reprise near the end of the mazurka occupies only two phrases and sixteen measures (49 through 64), followed by a partial repeat incorporating variation. Clearly the initial pillar must contain some dispensable content. The second and third phrases pursue two common – though optional – features of minor-key compositions: an upward shift to the mediant during the second phrase, and an interruption during the third. Neither of those devices is employed in the condensed reprise of the pillar. However, 1.27 reveals how both devices contribute to the establishment of a ternary internal form for A1 reminiscent of that in 1.24. Whereas the second phrase’s extension to the mediant could have linked the initial I and an upward continuation to the dominant (again like 1.24), here Chopin devotes the first part of the third phrase (measures 17 through 22) to reestablishing the C♯ tonic.41
Example 1.27 Analysis of Mazurka in C♯ Minor (op. 63/3), mm. 0|1–32. Several features of this mazurka’s structure reprise constructions similar to those we have noted in other mazurkas. The EF >F♯>E recalls a similar line in 1.20 (there descending from Kopfton ). The circle-of-fifths connection between I and III resembles that in 1.26. The I II➔ V antecedent most closely resembles 1.24, which also shares the conversion from II➔ to II⇨ for the final phrase.
The analyses in this chapter provide compelling evidence that, despite the extraordinary richness and diversity on display in these tonic pillars, Chopin’s compositional style depends to a large extent upon mixing and matching a finite range of structural devices, all designed to perform specific roles within either broad or local traversals of harmonic progressions from the tonic through the dominant back to the tonic, as support for descending third- or fifth-progressions from the Kopfton to the tonic pitch. Whereas chapter 1 has focused on the tonic-to-tonic harmonic progressions characteristic of a regular tonic pillar, chapter 2 will place these pillars within the broader tonic-to-tonic trajectories of complete mazurkas.
2
Between the tonic pillars: tonal trajectories in twenty-seven mazurkas ◈ In the mazurkas that we explore in this chapter, repetitions of the tonic pillar alternate with episodes that pursue a wide range of tonal paths, usually diatonic though occasionally not. The most common trajectories are the maintenance of the tonic key (perhaps with a shift of mode) or proceeding to the dominant (perhaps tonicized). Around a third of the episodes pursue tonal paths, marked by shading in table 2.1, that extend beyond the tonic or the dominant. Table 2.1 Opus
Key
Examples
Pillars
First Non-Pillar Trajectory
Second Non-Pillar Trajectory
6/1
f♯
1.23, 2.18
3
V♯ prolonged
I to V♯
6/2
c♯
1.1, 2.19
3
V♯ tonicized
I to V♯
6/4
e♭
1.15, 2.1
2
I prolonged
––––
6/5
C
1.2, 2.2
2
I to tonicized V
––––
7/1
B♭
1.3, 2.20
3
V tonicized
I to V
7/2
a
1.19, 2.15
4
I prolonged
I♯ prolonged
7/4
A♭
1.11, 2.21
3
I to V
I to V
17/2
e
1.20, 2.3
2
I to V♯
––––
17/3
A♭
1.16, 2.16
4
I to V
lower third (CV♯2) tonicized
17/4
a
1.21, 2.22
3
V♯ prolonged
I♯ to V♯
24/2
C
1.4, 2.23
3
lower fifth tonicized
I to upper third
(CV♯1) 24/3
A♭
1.5, 2.4
2
I to upper third (CV♯1)
––––
24/4
b♭
1.6, 2.24
3
I to upper third’s V
I to upper third’s V
30/2
f♯
1.7, 2.5
2
I to upper third
––––
30/3
D♭
1.8, 2.6
2
I to lower third’s V♮
––––
33/1
g♯
1.12, 2.7
2
I to upper third
––––
33/2
C
1.17, 2.8
2
I to lower third (CV♯2)
––––
33/3
D
1.18, 2.17
4
V tonicized
I to V
41/1
e
1.13, 2.9
2
V♯ tonicized
––––
41/4
c♯
1.14, 2.10
2
I♯ prolonged
––––
42B
a
1.24, 2.11
2
I♯ prolonged
––––
50/1
G
1.25, 2.25
3
progression in tonic key
progression in tonic key
50/2
A♭
1.26, 2.26
3
upper third tonicized
lower fifth tonicized
56/1
B
1.9, 2.27
3
I to lower third (CV♯1)
I to lower third (CV♯2)
56/2
C
1.10, 2.12
2
lower third tonicized
––––
63/2
f
1.22, 2.13
2
I to V♮
––––
63/3
c♯
1.27, 2.14
2
I prolonged
––––
To conserve space the examples in this chapter present the tonic pillars in an abbreviated form. In each case a more detailed graph may be found in chapter 1. For the same reason a phrase pair defined by a local interruption may be abbreviated. Because
most of the mazurkas contain multiple episodes, it was not feasible to arrange the analyses in this chapter according to their various tonal trajectories. (The data in table 2.1 facilitates locating all the episodes that proceed along any given path.) Instead, we shall proceed by opus number in three groups, distinguished by the total number of tonic pillars: two, four, and then three. Exploring the four-pillar mazurkas before those with three pillars is warranted because in some cases the latter are conceived as abbreviations of the former. Though a coda generally will be displayed more compactly than will the mazurka’s nonpillar episode(s), it will be at least minimally acknowledged in the voice-leading graph when one occurs.
Two-pillar mazurkas
Opus 6/4 The Mazurka in E♭ Minor’s B section repeats the foundational structure of A1: middleground
over I V♮ I occurs in both contexts, without a change of
mode or key. (Compare 1.15 and 2.1.) Yet contrasting mechanisms are employed to
connect and
. In A1 an incomplete upper neighbor to the Kopfton and a harmonic
progression featuring IV occur, while a local interruption allows two measures of content to be spread over four measures. In B a circle of fifths is deployed as the means of connecting I and V♮. It is paced so as to spread the structural content over four measures. The confluence of dissonance and local chromaticism in the second and fourth chords of the circle creates surges that push towards the succeeding downbeats, thereby emphasizing the descent in tenths displayed in 2.1. Whereas the bass connects the E♭ and B♭ roots, an upper line traverses a G♭>D♮ diminished fourth.1 An F, emerging above that D♮ from a strand that transpires in the tenor register, helps to shape the third-progression (beamed in 2.1) that spans the four measures.
Example 2.1 Analysis of Mazurka in E♭ Minor (op. 6/4).
The essence of the mazurka’s form may be represented as | A1 |: B A2 :|, with an immediate, written-out repetition of each component. Though it would be more normative for this form to transpire as |: A1 :|: B A2 :| (a form that often is called rounded binary, though I prefer rounded ternary or simply ternary, due to the three letters required to depict it), here the repetition within A1 created by the interruption, followed by the written-out repetition (measures 5 through 8), followed by a repeat-sign repetition would lead to stagnation. Consequently Chopin elected to omit the conventional repeat sign after measure 8.
Opus 6/5 [a.k.a. opus 7/5] As chapter 2 unfolds we will have opportunities to observe how the non-pillar regions in Chopin’s mazurkas may either prolong the tonic (perhaps with a modal shift) or lead to the mediant, subdominant, dominant, or submediant. The dominant is by far the most common choice. It provides a context for the maintenance of or for an interruption of a descent (from or from ) at , as in the Mazurka in C Major [2.2]. The I-space of its A1 section (analyzed in 1.2) concludes with a brief yet significant sounding of the pitch A (at 123).2 As often is the case, here the 5–6 shift softens the potentially abrupt connection between I5 and II➔, on the path to V.
Example 2.2 Analysis of Mazurka in C Major (op. 6/5). In this mazurka the same thematic content (at two pitch levels) is employed in both the A and B sections. When this happens a background melodic connection between the two may seem doubtful.3 How can the pitches C, E, and G relate linearly with their counterparts a fourth lower? I propose that in this mazurka the tonic’s E and the dominant’s D form a background
connection, even if that interpretation requires
a note that in its tonic context serves as an “upper third” to the Kopfton to perform a deep structural role when transposed into the dominant key. The voice leading works as
follows:
Opus 17/2 The Mazurka in E Minor’s tonic key is established through the fifth-progression that transpires during the A1 tonic pillar [1.20]. The components of the extended B section that follows pursue a range of tonal goals. At first the tonic is prolonged, with a temporary modal shift to E Major in measures 31 and 32 [2.3]. Next E Minor’s mediant G-B-D is tonicized. Chopin extends this mediant through measure 49 using local embellishing chords infused with chromaticism. Finally an unusual realization of IV5–6 leads to the section’s tonal goal, V♯, which falls into place at the last possible moment – at 523, coinciding with the melody’s upbeat B that inaugurates A2. (Compare with 03.) By this point the background descent has reached
, and thus an interruption occurs. This
(which sounds first in the bass and then in the tenor register) is covered by B, the of A2’s initial tonic.
Example 2.3 Analysis of Mazurka in E Minor (op. 17/2). The ascending registral shift of Kopfton B during A1 is rescinded as the lower B is restored during measure 25, at the onset of the B section’s tonic prolongation, which mirrors A1 in traversing a complete fifth-progression, now without interruption. Soon thereafter the mediant emerges, unexpectedly. Whereas the tonic-prolonging phrase proceeds downwards in the bass from E to C via a G➔ embellishing chord (measures 24 through 28), the reprise of this content in measures 32 through 36 proceeds in a contrasting manner, projecting the root progression G–C–D–G as a tonicization of the mediant even though its initial chord is surging towards G’s subdominant C from the outset. Because the new context for measures 33 and 34 motivates a re-orientation of the local chordal hierarchy, the eventually rejected connection between E and C (displayed via
a slur placed within parentheses) and the ultimately triumphant G-to-D tonic-to-dominant motion are juxtaposed in 2.3. The background descent from through
to occurs
during this mediant tonicization. The soprano G (= ) that arrives imaginatively at 373 and literally at 391 does not budge through 491. Neighbors A♭ and A♮ embellish G without weakening its hold. The mediant is maintained throughout, after which the span from measure 49 through measure 52 completes the B section’s structural agenda in an unconventional way – namely, by placing the Urlinie’s descent from to
in the bass and the foundational bass’s ascent
from G through A to B in the soprano. This important activity may take listeners by surprise, since Chopin here converts melodic devices that had played embellishing roles during the mediant prolongation into the instigators of the harmonic motion to
.
This subdominant’s 6-phase chord surges as II➔ in the approach to V♯. Whereas on the one hand Chopin endeavors to make A2 less complex than A1 by rescinding the local interruption, on the other hand he postpones achieving the goal PAC: opportunities for a cadence in measures 64 and 66 are declined, delaying the PAC until measure 68.
Opus 24/3 When a mazurka’s B section leads to the dominant, a background descent from Kopfton or to
often occurs. That option not only provides a high level of contrast, but also
ideally prepares for the tonic’s return during A2 for a post-interruption descent to . Another option occasionally employed by Chopin is to proceed to the mediant, which offers neither the level of contrast nor the tonic-targeting characteristic of the dominant harmony. Because both and are components of the mediant, the Kopfton generally will be prolonged. The Mazurka in A♭ Major’s A1 and A2 sections open with a melodic unfolding of the third from A♭ to C [1.5]. That interval also guides the broad bass trajectory during the B section [2.4]. It appears that Chopin intends to traverse that span via a descending circle of fifths: A♭ D♭ G C. However, in his execution of that agenda the projection of the initial A♭>D♭ fifth as two thirds is abandoned after F is attained at 183. Observe how local upper thirds (reminiscent of the upper thirds that pervade the A1 section) embellish various points along the way. The initial bass A♭ is preceded by downward motion from a C minor chord. Likewise F emerges from upper third A♭. In my view the F minor chord at 192 should initially be perceived as the starting point for another descending third, this time from F to D♭. But Chopin, recognizing that his strategy might become tedious if pursued adamantly, elides this passage. (It appears within square brackets in 2.4.) Instead, a collision occurs: a D♭ indeed does emerge in the bass – sooner than expected and in coordination with an apposite though accelerated soprano A♭>G>F – but concurrently the following chord in the broad circular motion sounds.4 Because this collision does not allow diatonic D♭ to wobble to D♮, the G chord emerges as G⇨.5
Example 2.4 Analysis of Mazurka in A♭ Major (op. 24/3). The goal mediant chord at 201 incorporates a wobble (E♮). Consequently foundational major chords are juxtaposed in the mazurka’s A and B sections, a feature shared with major-key movements that proceed instead from I to V. This chord corresponds to what I call the mediant’s Chromatic Variant ♯1 (CV♯1), with one chromatic pitch.6 Since the preceding passage led the melodic line some distance downwards from Kopfton C (= ), Chopin quickly reconstitutes that register: a melodic C persists from 203 through 242. This C then hooks up with the C of A2, launched by the A♭
. Local melodic thirds persist during the extension that
transpires during measures 36b through 43. Though a structural close on is achieved in measure 36, residual echoes of the Kopfton persist.
Opus 30/2 In the Mazurka in F♯ Minor, the A1 tonic pillar’s initial IV (at 163) was preceded by the introduction’s prolonged subdominant [1.7]. In contrast, the A2 pillar (whose initial IV is embellished through the addition of 6-phase G♯ at 483) is preceded by the III that is attained during the B section [2.5]. As often is the case, a segment of the circle of fifths (F♯ B E A) serves as the means by which the tonic and the mediant are connected. Concurrently the melody within the B section focuses on C♯, which falls within a downward trajectory connecting A1’s cadential F♯ to A2’s reinstated Kopfton A.
Example 2.5 Analysis of Mazurka in F♯ Minor (op. 30/2). Though this mazurka’s tonic pillar, once it emerges, is in fact regular (with I V♯ I supporting
), its context is idiosyncratic because competing material (in a
key that conforms to Chopin’s misleading key signature of two sharps) seems at first to be performing the role of tonic pillar.
Opus 30/3 Chopin confronted options at every turn as he composed each mazurka. Whereas usually listeners hear only one out of several potential harmonic trajectories, in the Mazurka in D♭ Major Chopin makes a point of juxtaposing alternatives. “The road not taken” becomes instead one of two roads that he takes in succession. Earlier we noted how he alternates between retaining D♭ Major and moving into D♭ Minor during the tonic pillar. The accidentals within parentheses in 1.8 convey his “maybe yes, maybe no” attitude, which persists until the wobbly note F♭ reverts to F♮ in the mazurka’s final measure. Other sorts of options are juxtaposed during the B section. Note in 2.6 the connection between the pillar’s tonic root D♭ and the dominant root A♭ of measures 58 and 59. (This dominant resolves to I6 rather than to I5, a topic to be addressed later.) Bass G♭ (measure 57), which supports an inverted II, precedes A♭. Chopin well understood that two very common strategies for connecting the A1 section’s tonic root and measure 57’s supertonic bass are an ascent via the mediant (D♭
Example 2.6 Analysis of Mazurka in D♭ Major (op. 30/3).
We observed in 2.1 how a tonic prolongation might serve as a B section’s sole content, and in 2.3 how a tonic prolongation inaugurating a B section may precede further tonal activity. The structure through measure 60 could have been followed by bass E♭D♭ supporting a soprano descent to D♭ (resulting in a PAC in D♭ Major). In this case, however, Chopin’s progression instead tonicizes B♭ Minor (perhaps a factor in his decision not to persist with the B♭ chord of measure 32). An F-to-B♭ fifth-progression substitutes for the F-to-D♭ third-progression that we might have expected as a means of prolonging Kopfton F. Thereafter Chopin backtracks once again. Will he succeed this time in attaining a PAC in D♭? Succinctly the D♭ Major tonic of measure 10 recurs in measure 66, the dominant of measures 58 and 59 recurs in measure 67, and the 6-phase tonic of measure 60 recurs in measure 68. Note one significant difference: Chopin now fails to achieve a PAC in B♭ Minor, breaking off after the penultimate chord. Whereas an interruption on is a common goal for a B section, here Chopin closes a third lower – on
the
of B♭ Minor – thereby creating a novel juxtaposition at the juncture of B and A2.
In some especially creative writing, he slithers downwards chromatically from F (the root of B♭ Minor’s dominant) to D♭ (the root of D♭ Major’s tonic) during measures 70 through 79. The mazurka concludes with a reprise of the tonic pillar, this time with the cadential tonic shifting from minor to major quality at a breathtakingly late moment.
Opus 33/1 The melodic B>A♯>G♯ that played a prominent role during the Mazurka in G♯ Minor’s tonic pillar [1.12] guides the B section on its path from tonic G♯ to an inverted C♯ chord, initiating a circular progression to the diatonic mediant, B major [2.7]. Complementing the descending fifth-progression within A1 (D♯ to G♯), that C♯ chord supports the upward arpeggiation of a sixth (G♯D♯ neighboring motions within A1 (measures 0–1, 3–4, 5, etc.). Often the mediant will serve as an intermediary in a progression from the tonic to the dominant (as in 2.3 and 2.6).8 In this case it serves as an upper-third embellishment of the tonic (akin to the structure of 2.4). As was the case at 03, the lone D♯ at 363 signals the return of I-space.
Example 2.7 Analysis of Mazurka in G♯ Minor (op. 33/1).
Opus 33/2 [a.k.a. opus 33/3] Though the mediant and submediant chords may participate in harmonic progressions, they sometimes instead serve as terminal points within a contrasting section, contexts that may be interpreted as tonic embellishment. Several of the mazurkas explored above proceed from the tonic to the mediant and back over the course of A1 B A2. In the Mazurka in C Major Chopin deploys the submediant, which sounds (evolved as VI➔) in a harmonic context during the A1 section [1.17]. During the B section that follows, another chromatic variant – A♭-C-E♭ – is attained and even tonicized [2.8]. In this case the structure proceeds essentially from C-E-G to C-E♭-A♭ (unfurled as A♭-C-E♭) and then back to C-E-G: tonic C-E-G is extended via the concurrent pursuit of an embellishing chromatic neighbor (GG) and a wobble (E♮>E♭
Example 2.8 Analysis of Mazurka in C Major (op. 33/2). The chordal juxtaposition in measures 16 and 17 is extraordinary. In the context of the A♭ Major tonicization that is commencing, C-E♮-G (measure 16) is chromatic in the sharp direction, whereas D♭-F♭-A♭-B♭ (measure 17) is chromatic in the flat direction. Consequently a diatonic E♭
measure 21 might be interpreted as E♭E♭>D♭ over E♭ (third species), resolving to consonant
at the next downbeat. In conjunction with the insertion of chromatic E♮ and
the prolongation of the neighboring F, the unaccented passing note D♭ shifts to the following downbeat position. Similarly in measure 23, C>B♭ over cantus pitch E♭ (fourth species) is embellished by the chromatic lower neighbor B♮ and the upper neighbor D♭, so that the C suspension’s resolution pitch is delayed until 241, where it coincides with the tonic root. The foundational structure – without these local rhythmic shifts – is displayed in 2.8.
Opus 41/1 [a.k.a. opus 41/2] The descending fifth-progression B>A>G>F♯>E from the Mazurka in E Minor’s A1 section
[1.13]
is
complemented
by
an
ascending
sixth-progression
(D♯
prolongation
in measures 33 through 40.10 That descent brings the
melody close to the B section’s D♯ starting point, which is restored at 411, preceded by a retransitional embellishing chord featuring the diminished fifth
. A renewed ascent to
B, achieved at 451 and again covered by D♯, gives the B section a ternary internal form.
Example 2.9 Analysis of Mazurka in E Minor (op. 41/1). Another third-relationship (not graphed) warrants consideration as well. At a local level the connection between B and G♯ (the tonicized major dominant’s 5-phase and unfurled 6-phase chords, as in measures 30 and 33) may be invigorated through an internal D♯ chord (as in measures 31 and 32), which relates by perfect fifth to G♯. Chopin reaches D♯-F♯-A♯ early in the B section (measures 23 and 24), but there its potential to lead to G♯ is not tapped: instead it functions as an upper-third extension of B-D♯-F♯. Consequently measure 33’s G♯ chord is all the more satisfying, since it comes about through the realization of something that was at first denied. When D♯-F♯-A♯ is deployed again as the tonicized dominant’s upper-third extension in measures 55 and 56, it reveals its versatility
by proceeding neither back to B nor to G♯, but instead to the restored tonic E of A2. Outervoice parallel octaves are averted through the presentation of the surging tonic in position.
Opus 41/4 [a.k.a. opus 41/1] Already during the Mazurka in C♯ Minor’s A1 tonic pillar, the hold of the C♯ tonic’s minor modality wavers [1.14]. Though a conventional juxtaposition of C♯ minor and E major chords transpires during the opening measures, elements from C♯ Major are incorporated beginning in measure 17, affecting even the pitch content of the pillardefining fifth-progression (with E♯ substituting for E♮ during measure 20). Consequently the common form-defining juxtaposition of parallel keys (A1 in minor followed by B in major) is here subverted, since the shift to major precedes the formal division (at measures 32|33). Further confounding expectations, A2’s tonic pillar incorporates C♯ Major’s E♯ from the outset [2.10]. There is very little about this mazurka that reflects its foundational C♯ Minor tonality until the coda, where the minor tonic is restored and the work’s only fifth-progression utilizing diatonic E♮ is traversed. The mazurka ends in desolation, especially devastating given the presumed conquest of dark forces by C♯ Major.
Example 2.10 Analysis of Mazurka in C♯ Minor (op. 41/4). During the B section’s opening measures the voice leading projects an ascent through C♯ Major’s C♯
That D♯ is restored to the upper register during the following dominant harmony (assuming that the D♯ at 561 “belongs” in the preceding measure). The cadential C♯ (at 562) occurs in that register as well. As the measure numbers that annotate 2.10 indicate, a second traversal of this progression occurs immediately after that cadence. All goes well until the cadential moment (651), at which point Chopin substitutes C♯ Minor’s I6 for the expected C♯-E♯G♯ tonic. This insertion results in a second approach to the tonic goal, temporarily reminding listeners of the darker forces of C♯ Minor that underlie the mazurka. The progression transpires as m.
65
69 71
72
73
C♯ Minor:
I6
IV5———6♮
V⇨
I♯
This progression is especially noteworthy in that the pitches D♮, F♯, and A (measures 71 and 72) that emerge as IV’s “Neapolitan” 6 phase are retained as the fifth, seventh, and ninth of the dominant that follows.13 In this case, exceptionally, wobbly D♮ does not revert to diatonic D♯. Though some residual elements of C♯ Minor are retained from A1 (the use of A♮ in measures 73 through 79, as well as the employment of E in measures 81 through 88 as the divider between C♯ and G♯), the A2 section completes the background structure essentially in C♯ Major, as mentioned above. A more bravura close transpires during a repetition (measures 97 through 104). Chopin places an important element of the mazurka’s tonal plot within the coda: though it begins in C♯ Major (measure 105), the initial C♯ Minor tonic is restored at measure 119 and is retained through the end of the mazurka. Though its fifth-progression is displayed uniformly in the register just above Middle C in 2.10, in Chopin’s score its impact is enhanced by means of a gradual downward registral shift of two octaves: G♯ a twelfth above Middle C (measure 119), F♯ a fourth above Middle C (measure 127), and the remaining members of the descent sounding in the octave below Middle C.
Without opus 42B The internal harmonic progressions employed within the A and B sections of the Mazurka in A Minor proceed along similar routes. (Compare 1.24 and 2.11.) Both lead from the initial tonic to the diatonic mediant (A Minor’s C-E-G during the A sections, A Major’s C♯-E-G♯ during the B section). Both continue with a root-position II➔ that leads to V(♯), where a middleground third-progression is interrupted, followed by the post-interruption attainment of a PAC. The principal form-defining event within the mazurka is the wobble of the Kopfton from C to C♯ and back to C, as displayed on the top beam in 2.11. (C♯ is anticipated during A1’s cadential tonic in measure 32.)
Example 2.11 Analysis of Mazurka in A Minor (without opus 42B). The B section’s shape is ternary: x1 y x2. The binary x1 region’s antecedent half begins with an extension of I-space via a embellishment (unfurled as D-F♯-A) and an ascending arpeggiation from Kopfton C♯ through E to A, followed by II➔ V, where a local interruption occurs on
at 403. Though is restored during the consequent half, the
opening tonic is displaced by I6, with a restoration of I5 (at 443) only after the
embellishment. Concurrently the ascending arpeggiation attains greater heights, reaching the upper octave of the wobble-modified Kopfton C♯ at 461. Chopin employs arpeggiation to descend from that high C♯ to goal A in the lower octave during measures 46 through 48. Defying structural norms, no supported by V comes between C♯ and A. (I propose that Chopin projects the sense of a PAC in measure 48 nevertheless.) The B section’s y region opens with a robust prolongation of A Major’s mediant (C♯E-G♯), first stated in measures 49 through 51 along with a reinstatement of the raised Kopfton C♯. The sequential progression that emanates from that C♯ chord normally would pursue the following course: m.
49/51
52
53
54
55 57
58
C♯
B
A
G♯
F♯
E
C♯
G♯
A
E
F♯
C♯
In this instance Chopin allows the F♯ chord of measure 55 to evolve into F♯➔. Consequently a brief and wayward excursion to a targeted B chord occurs. It appears that Chopin is toying with an alternative means of proceeding from III to V, via a circular progression: C♯ ( ) F♯➔ B➔ (E). That alternative route is forsaken as he picks up again with the F♯ chord and proceeds, as initially expected, to C♯ in measure 58, followed by a repetition of the F♯ C♯ segment of the sequence, confirming the revised course. Only then – in measure 61 – does the broader progression continue with II➔ V. Because the sequence led the melody a significant distance downwards from the raised Kopfton, that register is temporarily vacant. (Note the B notehead inserted within parentheses at the top of the II♯ chord in 2.11.) The following V’s B (middleground ) occurs only at the end of a gradual filling-in of a G♯
Opus 56/2 The G
I cadence supports
the latter half of the fifth-progression from E, which is then repeated in full.
Example 2.12 Analysis of Mazurka in C Major (op. 56/2). What is the listener to make of the contents of measures 53 through 68? My proposed interpretation rests upon two crucial facts: (1) the filled-in ascending sixth of measure 53 relates both to G
not emphasize the E beyond its initial statement in his reformulated A2. Concurrently he invigorates another basic idea: the persistent F♯>F♮ that occurs six times during A1. Normally if one had to choose one of those two pitches to eliminate, it would be F♯, leaving F as a diatonic neighbor to Kopfton E. Chopin surprises us by retaining F♯ in place of F♮. (The latter will have its turn also, in measure 56 and its replicates.) Within this mazurka Chopin has created contexts for (measures 6 and 56), and
(measures 37–38),
(measure 54) in close proximity. The relationship between F or F♯ and E is a
significant factor in my reading of the work’s structure as emanating from Kopfton . The new material stalls temporarily in measures 67 and 68. Its melodic D in the lower register hooks up perfectly with the arrival of upper-register D at the onset of the continuation borrowed from A1. The mazurka concludes without a hitch. Its final tonic chord offers yet another registral juxtaposition.
Opus 63/2 During the Mazurka in F Minor’s tonic pillar, the antecedent phrase’s melodic descent from Kopfton C through imagined B♭ to A♭ transpired in the context of I proceeding to III [1.22]. The background
, which occurs early in the B section, is supported
in a similar way, though in this case III arrives before the descent begins [2.13]. The continuation to the supertonic is not surprising, since II➔ points toward the B section’s dominant goal, which will arrive after a repetition of what has been accomplished thus far within B. One pitch during that repetition is especially noteworthy: D♮ at 303. Whenever I and III are juxtaposed, the analyst should consider whether the III assumes a prominent position along the path to V♮, or whether it instead resides within a broader prolongation of I. The first of these interpretations is projected in 2.13, based on how measure 22 is structured: though the tonic pitch F sounds, it serves there as a passing note connecting III’s E♭ and II♮’s G. (Via chordal unfurling, F is doubled in the bass.) Chopin’s reconfiguration of this chord during the repetition (at 303) instead supports the second interpretation, since with D♮ the chord now represents a chromatic variant of I6♮ (F-A♭-CD♮), another common herald of II♮. Though it is a small point, Chopin’s subtle change reveals the richness of his thought on harmonic processes.
Example 2.13 Analysis of Mazurka in F Minor (op. 63/2). I developed the notion of peculiar juxtaposition in Schubert (chapter 1) to account for successive passages that one might think should be analyzed in equivalent ways due to their corresponding surface constructions but that, taking the broader context into account,
turn out to play contrasting roles. Chopin’s repeat of I6♮ II♮ (measures 30 through 32) in the more assertive form ♮VI➔ II♮ (measures 33 and 34) provides a strong incentive to interpret the next two measures as V➔ I. Yet in 2.13 the potential tonic chord is displayed instead as a passing within a prolongation of the dominant harmony. This passage parallels the mazurka’s first three measures: the tonic arrives in measure 4, not measure 2. Even when the is unfurled (as in measure 42 and measure 36), F is not asserted as the tonic root. Chopin goes even further in developing this construction. Whereas in measure 37 a D♭ is added to the embellishing chord as a neighbor, in measure 39 that D♭ is absorbed as a chord member, consequently lowering its resolution by a third, to an A♭ major chord. In the broader context this A♭ chord serves as an embellishment of the dominant (as conveyed by the figures and the abbreviations N and W in 2.13). The dominant function resumes at the onset of the A2 tonic pillar, followed by the reemergence of Kopfton C and tonic root F, setting the stage for the descent to the final PAC.15
Opus 63/3 The ascent from C♯ through D♯ to Kopfton E during the opening measures of the Mazurka in C♯ Minor’s A1 section provides the kernel that Chopin creatively expands during the B section [1.27 and 2.14]. An interior E that sounds inconspicuously at 322, during A1’s PAC, serves as the initiation point for a stepwise ascending line that traverses a full octave (filling out that from 03 through 42), leading to the restored upper-register Kopfton for the A2 section. (Though Chopin employs a D♭ Major key signature in his score, that of C♯ Minor is retained in 2.14.) At first the tonic is prolonged (from 343 through 442), taking on first the major third and later also the minor seventh of I➔. The long-extended E♯ results in a temporary conversion into C♯ Major. Consequently the subdominant that resolves I➔ is IV♯. Yet the ascending 5–6 sequence (with surging 6-phase chords) that leads to IV’s upper-third chord targets C♯ Minor’s A major (measure 49), rather than C♯ Major’s A♯ minor. The broader progression continues with IV’s 6-phase chord in its II⇨ incarnation (at 493).16 By this point the melodic content of the A2 tonic pillar is commencing, with a harmonization that at first contrasts that of the A1 presentation. Yet with the
of
measure 50 the correlation is restored. Though the tonic pillar within A2 is shortened and modified, a suitable PAC is achieved in measure 64. Those modifications are of special interest, in that they correlate with highlights of the B section: I➔ recurs in measure 60, IV♯ in measure 61, and II⇨ in measures 61–62. An imitation-enhanced repetition of most of the modified pillar concludes the mazurka.
Example 2.14 Analysis of Mazurka in C♯ Minor (op. 63/3).
Four-pillar mazurkas
Opus 7/2 The four presentations of the tonic pillar (a) within the Mazurka in A Minor are arranged as follows: A1
B
|: a1
:|: b
a2
A2
:|
A Minor —————
|: a1 A Major
:|: b
a2
:|
A Minor —————
Consequently the B section stands out more boldly than do the b regions. Whereas b resides within an internal rounded ternary form, B is a more independent entity – what musicians often call a trio. Given how often the tonic pillar recurs, it is not surprising that its internal binary structure (the antecedent and consequent phrases shown in 1.19) is truncated during the a2 statements, where only its consequent half is presented. The embellishing chord that occurs during the a region’s first measure influenced how Chopin shaped the b region. Whereas in its initial statement the chord might be imagined as deriving from concurrent neighboring motions – EE and (C)C – another common context for a would be 8
–
7
–
6
–
5
3♮
–
♯
–
4
–
3♮
Chopin devotes the entire b region to filling in the space between this device’s
and
components, deploying a hybrid circle of fifths. Whereas b’s first two measures present a viable start – from a1’s A through D (realized as F♯-A♭-C-E♭ = D⇨) to G, Chopin abandons that progression, backtracking to pursue a more novel route. From a reinstated D⇨ in measure 19 he drops down a third to B♭➔.17 The continuation of the circle of fifths proceeds along this lower trajectory, as shown by the letter names that annotate 2.15.18 A corresponding upper-third shift occurs as the circle draws to a close – in measure 24, where E-G-B♭-D arrives as if rooted on C, but is departed as if rooted on E. Over the
course of the b region the melody fills in the tonic’s E>A fifth, while the bass concurrently fills in its A>E fourth. (These expanses are slurred in 2.15.) The continuation in measure 25 (which corresponds to measure 1) is unfurled into position to accommodate the inverted A chord of 243.
Example 2.15 Analysis of Mazurka in A Minor (op. 7/2). The B section’s internal ternary form juxtaposes tonic prolongations during the outer parts (labeled x in 2.15) with a motion to the dominant (via a conventional I5–6 II➔ V harmonic progression) during the middle part (labeled y).19 I propose that whereas E (= ) serves as the Kopfton for the mazurka as a whole, the B section’s melodic focus is the third from C♯ to A (with interruption).20 Kopfton regains prominence with the onset of A2. The background descent from to occurs during that section’s a2 region, bringing the mazurka to a close [2.15].
Opus 17/3 During the Mazurka in A♭ Major’s tonic pillar the Kopfton C (= ) serves as the starting point for a descending third-progression to the tonic root [1.16]. In the context of the A1 section’s internal a1 b a2 form (in measures 0|1 through 40), that third-progression’s C leads through B♭ during b to the restored pillar’s endpoint A♭ during a2 [2.16]. (These pitches will constitute the background descent during the reprise after the mazurka’s B section.) The b region begins with six measures of strumming on II, focused melodically on the chromatic filling-in of II’s F>D♭ third, thereby prolonging the Kopfton’s upper neighbor, D♭. The next two measures feature an evolved dominant, during which the region’s melodic goal – (B♭) – is attained.21
Example 2.16 Analysis of Mazurka in A♭ Major (op. 17/3). The B section (likewise ternary) is in the key of F♭ Major (which Chopin presents as E Major), a chromatic variant of I6, as noted in 2.16.22 Consequently the Kopfton wobbles from C to C♭. Harmonically there are no surprises: the x regions proceed from the tonic to the dominant in their antecedent phrases (where a descending fifth-progression from C♭ is interrupted at G♭ [F♯]),23 and through the dominant to the tonic in their consequent phrases (where the fifth-progression is completed). The y region that intervenes proceeds from II➔ to V, supporting a prolonged C♭ in the upper line, here covered by E♭. The ascending C♭
also energizes measures 41|42 through 45|46, where the arpeggiated bass from the tonic root to the dominant root (F♭
Opus 33/3 [a.k.a. opus 33/2] The Mazurka in D Major offers an interesting study in contrasts. The outer A sections (first heard in measures 0|1 through 48) are uncommonly repetitive and uncomplicated in their harmonic fabric, whereas the interior B section is strikingly original, displaying chromatic writing that likely baffled many of Chopin’s contemporaries. Whereas the initial tonic pillar (a1 within A1) succeeds in establishing D Major via an interrupted thirdprogression (F♯>E>D) descending from Kopfton [1.18], the transfer of that material to a dominant context for the b region that follows offers no successor to : the C♯ of its C♯>B>A third-progression relates to the tonic’s interior D, rather than to F♯. Though some may find my parenthetical E in measures 17 and 89 of 2.17 dubious, it is consistent with my imaginative approach to analysis, which tolerates some discrepancies between the musical surface and a work’s foundational conception. In this case it even constitutes a “motivic” relationship, since a parenthetical E occurs in my reading of the tonic pillar as well.
Example 2.17 Analysis of Mazurka in D Major (op. 33/3). Recall that in 2.16 the relationship between the A♭-C-E♭ tonic (with Kopfton C) and a chromatic variant of its lower-third chord, F♭-A♭-C♭ (with wobbly note C♭) was at the heart of the move into and out of the B section. A corresponding shift emerges at the onset of the B section in 2.17: from tonic D-F♯-A to B♭-D-F♮. Yet in this case the progression
moves beyond the B♭ chord, ultimately to D Major’s dominant, A-C♯-E. Consequently the soprano F♮ here functions broadly as a chromatic passing note, rather than as a wobbly note, even if its successor E sounds in the bass (at 691) rather than in the soprano, where yet another appears within parentheses in my graph. Whereas II’s root E serves as the diatonic second scale degree in both D Major and D Minor, the diatonic sixth scale degrees are not identical. In D Major, B serves as , and in the context of I5–6 II the tonic’s 6-phase chord often evolves into a surging VI➔, targeting II. In a minor key, where B♭ serves as , one might instead encounter VI➔ targeting ♭II, wherein the supertonic’s lowering “fixes” the augmented fourth interval from diatonic up to diatonic (transferring the imperfect interval to the connection between ♭II and V). Observe that in this mazurka Chopin in fact proceeds from B♭-D-F♮ (the I6 from the parallel minor key) to E-G♯-B (II♯). How is this accomplished? Though B♭
Chopin deals with the task of enharmonic conversion at 651, where a dominantemulating evolved state of the D♭/C♯ chord targets F♯. Yet the F♯-A-C♯ chord does not take hold. Chopin backtracks, resolving the E♯-G♯-B♮-D♮ chord repeatedly. Only on the third try does its resolution endure and function within the broader harmonic progression. That chord is not F♯ minor, but instead A major (in measure 70). The accomplishment of the second +3 is sudden and unexpected, yet alert listeners would of course be aware of the special properties of the particular evolved chord that Chopin introduces in measure 65. Whereas C♯-E♯-G♯-B♮ would have targeted F♯ forthrightly, E♯-G♯-B♮-D♮ offers alternatives. Chopin demonstrates that its root might be C♯, or that it might be E. By measure 69 we come to understand that E♯-G♯-B♮-D♮ stands for G♯-B♮-D♮-F♮, an interpretation confirmed when ninth F♮ yields to root E♮. Having achieved II➔ (thereby completing the 3+3 ascent), the dominant goal is easily attained in measure 70. The mapping of A1’s structure into the A2 space rounds out the mazurka, as shown in 2.17. The background arrival on is followed by a tonic-focused coda.
Three-pillar mazurkas
Opus 6/1 The pitch C♯, the upper third to Kopfton A (= ), is prominently projected during the Mazurka in F♯ Minor’s a1 tonic pillar [1.23]. When A gives way to G♯ (supported by V♯) during the A1 section’s b region, C♯ serves as an upper fourth, repeated forcefully on the downbeat of every second measure.24 At first this buries G♯, though a forzando G♯ emerges in the upper register at 202 (still below the highest C♯). The dominant is prolonged without a tonicizing harmonic progression [2.18]. Instead, three concurrent descending lines connect chord members during the region’s eight measures: most prominently, the third from G♯ to E♯ (which serves as the dominant’s counterpart to a1’s A>F♯ third); the fourth from C♯ to G♯; and the fourth from E♯ to B, in parallel sixths below. G♯ is restored in the lower register as the terminus of the C♯>G♯ fourth (during 243). The return of the melody’s A during the a2 region that follows conforms to the structure of an interruption (here at the middleground level), as shown in 2.18. The goal of the melodic descent, F♯, arrives at 402.
Example 2.18 Analysis of Mazurka in F♯ Minor (op. 6/1). Because A1 is organized as a rounded ternary form (internal to the larger form of the movement), the mazurka’s B section comes across as a trio. Though it offers little variety either tonally or structurally, its playful (scherzoso) character leads to a considerable contrast nevertheless. The tonic pillar’s A>G♯>F♯ structural line is reconstituted as B>A>G♯>F♯ during measures 41 through 48, ending in a PAC. (This melody transpires in the textural interior, though the upper line doubles most of its pitches. Chopin’s accent marks, if observed by the performer, will help focus the listener’s attention on this line.) What at first appears to be a written-out repetition of those eight measures leads instead to
a ritenuto-enhanced HC, corresponding to the dominant of the earlier b section (though now at the background level), supporting background , as displayed in 2.18. Though listeners might expect to hear a da capo presentation of A1 – that is, a repetition of a1 b a2, perhaps omitting the repeats – as a conventional continuation after the trio, Chopin here abbreviates that structure, supplying only the tonic pillar. Even with that reduction in content, the B section’s interrupted concluding PAC.
connects with at the mazurka’s
Opus 6/2 Since serves as the Kopfton for the Mazurka in C♯ Minor [1.1], as it did also in opus 6/1, it is not surprising that the young Chopin created virtually identical foundational structures for the A1 sections of these two works. (Compare 2.18 and 2.19.) A descending line again prevails during the internal b region of opus 6/2, this time with more overt harmonic support than was the case in opus 6/1, as the G♯ Major tonicization displayed in 2.19 suggests. Whereas C , following its surge tendency (➔), might have led upwards to D♯ for the dominant harmony, followed by an 8–7 descending motion through C♯ to the melody’s B♯ goal, in this case that D♯ is elided, permitting a direct connection between C and C♯.25
Example 2.19 Analysis of Mazurka in C♯ Minor (op. 6/2). As in opus 6/1, the B section of opus 6/2 eventually attains background , supported by V♯. Chopin here calls upon III to mediate between I and V♯. Embellishment of the type (with an unfurling of the chords into position) pervades the mediant presentation. Its repetition is so persistent that we are relieved to hear an unexpected shift during measure 40. But what is the entity that Chopin so emphatically presents? As the section unfolds we come to understand that he has jumped the tracks, so to speak, by
juxtaposing the embellishment of mediant E and the embellishment of dominant G♯. (Note the temporary wobble of Kopfton E to E♯.) This dominant continues to the end of the B section, which segues into a reprise of the material from the introduction. Following the B section’s background
, the third-progression of A2 (where, as in opus 6/1, a
statement of the tonic pillar with written-out repeat substitutes for a full a1 b a2 reprise) achieves closure on .
Opus 7/1 The Mazurka in B♭ Major, whose tonic pillar projects Kopfton
[1.3], shares an
interruption-based middleground structure for its rounded ternary A1 section with opus 6/1 and opus 6/2, with modest variations in the detail. (Compare 2.18, 2.19, and 2.20.) An F sounds above both the D (= ) of the a1 tonic pillar [1.3] and the C (= ) of the b region, and in both cases upper neighbor G embellishes this F. A structurally deep interruption occurs at the close of the B section (again matching opus 6/1 and opus 6/2), here achieved via a chromatic D>D♭>C descent (completed in the tenor register), supported by I II➔ V. The restoration of the tonic and the post-interruption descent to occur within A2, which abbreviates the full reprise of the initial A1. Chopin instead inserts repeat signs requesting a second pass through the B and A2 sections (reminiscent of the once common, though by Chopin’s day often neglected, repeat of the development and recapitulation sections within a likewise ternary sonata-form movement). That feature is not shared with opus 6/1 or opus 6/2.
Example 2.20 Analysis of Mazurka in B♭ Major (op. 7/1).
Opus 7/4 Though serves as the Mazurka in A♭ Major’s Kopfton [1.11], the structural agenda of its A1 section (divided into a1, b, and a2 regions) still corresponds to those of the three mazurkas with Kopfton that we have just explored: namely, a local descent to (here prolonging rather than ) during a1, an interruption on
during b (achieved here by
means of a middleground descent through and ), and a descent to during a2 [2.21]. Since the B and A2 sections lie ahead, that descent is a middleground rather than a background event. Kopfton is embellished by upper neighbor F during the B section, followed by the background descent from to during A2.
Example 2.21 Analysis of Mazurka in A♭ Major (op. 7/4). Though Kopfton E♭ is not literally stated as the b region begins, its prolongation during A1 makes it available as the starting point for linear initiatives as the mazurka continues. The E♮C of 103–111 continues that line (wherein F serves as an incomplete upper neighbor) in the first of several descents of a third from Kopfton E♭, here within the tonal context of the tonicized mediant, C Minor. Though initially one might suspect that the A♭ chord at 111 represents a restoration of the original A♭ Major tonic, the broader context of
measures 9 through 14 projects a I5–6 ♭II V♮ I progression in the key of C Minor, wherein A♭-C-E♭ serves as C’s 6-phase chord. Chopin cleverly moves beyond III using the ♭II of its tonicization as IV within the broader A♭ Major progression connecting I and V over the course of the entire b region.26 (Compare D♭-F-A♭ at 132 and at 152.) The chromaticism in the tenor register during measures 15 and 16 (C
Opus 17/4 Kopfton (E), prolonged via a local fifth-progression during the Mazurka in A Minor’s tonic pillar [1.21b], is the starting point for a middleground descent commencing during the ensuing b region [2.22]. Note how Chopin auditions two alternative harmonizations for C (E-A-C in measures 38 and 42 and D♯-F♯-A-C in measure 40) before proceeding to B. (Some upper neighbors embellish E-A-C, as shown in 2.22.) Since the descent is interrupted at , the A1 section’s middleground fifth-progression is completed during its a2 region.
Example 2.22 Analysis of Mazurka in A Minor (op. 17/4). The B section’s first eight measures conform to the standard disposition of an antecedent phrase, with a descent from Kopfton E interrupted at B. Chopin presents this material in the parallel key, A Major. The second phrase (not graphed) does not so well conform to what we might expect. No descent to A (= ) occurs, and thus the interrupted of the antecedent has no successor within the melody. During the repeat of the two phrases, the situation deteriorates even further. Whereas at least a D occurs in measure 76 as a token inauguration of descent during the first “consequent” phrase, in measures 91 and 92 Chopin ascends to F♮. The motivation for this turn of events can be found in the structure presented in 1.21b, where an F plays a crucial role in energizing the soprano line. Here that process is already under way during the latter portion of the B section and continues through A2 to the background close on in measure 108.
This mazurka’s coda is extraordinary. The reading in 2.22 depends upon two potentially controversial assertions.27 First, I suggest that the II➔ harmony spelled as D♯F♯-A-C in measure 109 is prolonged through measure 114 (where Chopin spells D♯ enharmonically as E♭). A parallel progression of diminished seventh chords (embellished by two anticipations, F♮ and B♭) connects those two supertonic statements.28 The melody’s unfolded D♯>C is complemented by B
Opus 24/2 The relationship between G-B-D and D-F-A in measure 13 of the Mazurka in C Major is interpreted in 1.4 as a embellishment (unfurled) leading into the harmonically asserted supertonic . A similar , now both unfurled and tonicized, is prolonged throughout the work’s B section of this five-section (A1 B A2 C A3) mazurka [2.23]. This tonicization offers a surprise. Normally if the pitch F is established as a temporary tonic in C Major, the diatonic pitch collection of F Major will be employed. However, in this case the C Major pitches are retained (B♮ instead of B♭), despite the fact that a I II➔ V I harmonic progression clearly establishes F as a local tonic. Whereas the B♮ of measure 22 occurs often as a chromatic pitch in F Major (as the third of II➔), the B♮ in the melody at the end of measure 27 – projecting V7 as a chord with a major seventh – is not characteristic of that key. Consequently the mode of the F tonicization is not major, but instead Lydian.
Example 2.23 Analysis of Mazurka in C Major (op. 24/2). The B section’s melody acrobatically jumps between two registers during the F Lydian theme. Upward and downward stems in 2.23 segregate the two principal strands, both of which descend a third (A>F and C>A). The melody’s F at the cadence serves as an upper neighbor to the mazurka’s Kopfton, E. The C section following A2 offers an alternative to what occurred during the introduction. Recall from chapter 1 that between the 5 and 6 phases of the initial tonic harmony, a G-B-D chord occurs [1.4]. That is an idiomatic choice within tonal practice. An equally viable and more dynamic option is E➔, which leads to A via a surge. Chopin devotes the entirety of the C section to a traversal of the path between the tonic C and this
surging E chord, a strategy motivated by the fact that this mazurka’s A sections commence on I6. An idiosyncratic ascending 5–6 sequence serves as the means of locomotion. Whereas a diatonic sequence with evolved 6-phase chords might proceed as C5————6
D5————6
E5
C A➔
D B➔
E
Chopin here charts a chromatic course, as C5————6
D♭5———–6
E♭5————6
E5
C A♭➔
D♭ B♭➔
E♭ C♭[B]⇨
E
When a linear pattern works in units smaller than the diatonic steps, some enharmonic conversions will be required, as here – an inevitable consequence of using notation designed for diatonic modulo 7 tonality to convey what is essentially a chromatic modulo 12 conception (here with the cycle targeting D elided). One detail of Chopin’s writing during the sequence is astonishing. Note that measures 73–74 and 85–86 are identical in pitch content. Yet one precedes an E♭ chord and the other an E chord. How can this be? In the former, Chopin treats the E♭ as an upper neighbor to chord member D♮, so that
targeting the E♭ chord of measure 84. In the latter, Chopin treats A♭ as an anticipation of the following E chord’s third (alas, occurring at the same moment as an enharmonic shift), so that
targeting the E chord of measure 88. The A3 section’s restored tonic arrives at 903. The tonic pillar continues along its normative course from there, supporting the descending third-progression that at this late point in the mazurka is interpreted as the background descent to . The coda deploys
embellishments freely over the course of a I IV V I harmonic progression, bringing the mazurka to its close.
Opus 24/4 In a minor-key composition the mediant often emerges on the path between the tonic and the dominant (as is the case during this mazurka’s tonic pillar [1.6]). Yet it may serve instead as a sort of major-key oasis: from the tonic to its upper-third chord and back again. The Mazurka in B♭ Minor deploys such an oasis twice: during A1’s b region, and again during the B section. Though Chopin uses contrasting means to attain the mediant in these two cases, they both conclude with the same strategy for tonic restoration, designed to accommodate the specific manner in which the tonic pillar opens. As often happens in a minor-key context, a segment of the descending circle of fifths connects I and III at the onset of A1’s b region in conjunction with a stepwise ascent from Kopfton D♭ to A♭ [2.24]. When serves as a movement’s Kopfton, it generally will appear at the bottom of a third- or fifth-progression during the tonicization of the mediant key. The harmonic progression that transpires through measure 28 supports not only the melodic descending fifth from A♭ to D♭, but also an interior strand that descends by step from D♭ to F. The mediant oasis continues with a repetition of the structure (not graphed).30 Yet a surprising turn of events emerges in measure 35, where the progression’s penultimate chord, V7 in D♭, loses its will to continue and quickly veers downwards in half steps, landing on the V7 of the mazurka’s B♭ Minor home key (retaining the “wrong” note D♭ in place of C, as was also the case during the initial statement of the tonic pillar [1.4]). Squiggly lines in 2.24, like those in 1.23 and 2.6, indicate the free fall through tonal space.
Example 2.24 Analysis of Mazurka in B♭ Minor (op. 24/4).
Chopin’s strategy for accomplishing the B♭-to-D♭ shift during the B section contrasts the earlier circular strategy, yet it is closely allied to the D♭-to-B♭ shift that closes both of these contrasts to the tonic pillar. We noted above that two dominants are juxtaposed at the end of A1’s b region: D♭ Major:
D♭
A♭
B♭ Minor:
F➔
B♭
Chopin employs the same principle in reverse during measures 53 through 64: B♭ Minor: D♭ Major:
B♭
F A♭➔
D♭
In this case there is no free fall (in part because the bass ascends from F to A♭), but instead a harmonic trajectory is pursued in the context of D♭ Major, noted in 2.24. While attaining the mediant, Chopin also transfers Kopfton D♭ down an octave. Above and beyond the contrasting melodic and harmonic frameworks, two features of the B section’s D♭ tonicization differ from what occurred during A1’s b region. First, despite the apparent intent to contrast the minor-mode tonic, D♭ Major soon takes on features of D♭ Minor. Second, the phrase that establishes D♭ as a local tonic ends in a half cadence at both measures 76 and 92 (extended). Consequently the dominant harmony that Chopin calls upon in his strategy to get back to B♭ Minor is already established as a goal and does not need to be removed from its context, as was the case with the A♭ dominant in measure 35. Chopin adds a further element of excitement during this second traversal: his free fall begins not with the dominant’s fifth (E♭) in the melody, but with its seventh. The third G♭>F>E♮>E♭ (measures 95 through 97) precedes the E♭>D♮>D♭ that occurs in A1’s b region. The mazurka’s background structural descent transpires during A2. Though the preceding B section dwarfs the A2 phrase’s eight measures, Chopin elected not to reprise the entire A1 rounded ternary predecessor as A2. Instead, after stating the tonic pillar a second time (as was the case during A1’s a1 region as well) he proceeds immediately to a substantial coda, where a poignant surprise emerges: at the end of a second pass through
an extended and evolving embellishing chord, the tonic re-emerges with major third D♮ (at 1282), which is retained through the end of the mazurka.
Opus 50/1 The D-F♯-A-C chord that precedes I at the opening of the Mazurka in G Major does not participate in a substantive harmonic progression [1.25]. However, in both the B and C sections of the five-part form, Chopin creates a vibrant tonic-prolonging harmonic progression that calls upon this chord (at the onset of the second and third statements of the tonic pillar) to take on a more assertive harmonic role, as V7 within a I5–6 II(➔) V➔ I progression [2.25]. The B section proceeds only so far as II➔, pointing to A2’s initiating V➔ I. During C, V➔ (initially with both ninth and seventh) is attained and then reiterated once the tonic pillar (A3) begins. In the former, II surges towards V, whereas in the latter the tonic’s 6-phase chord surges (as VI➔) towards II.
Example 2.25 Analysis of Mazurka in G Major (op. 50/1). The deluge of chords during the C section dwarfs the B section’s modest dimensions. Yet most of those chords are deployed in the context of two circular progressions that connect hierarchically deeper chords. Chopin calls upon the versatility of the descending circle of fifths to pursue both ascending and descending trajectories. Emphasizing every third chord, he ascends two thirds (GC>B in measures 50 through 52). Whereas a local G D➔ G progression would be an ideal means of prolonging I5, when instead a I5–6 succession is being pursued (measures 42 through 53), an internal B➔ embellishing chord often occurs instead of or after a D➔ chord.31 The circular progression in measures 50 through 52 accomplishes a downward migration of the surge tendency, from D➔ through C➔ to B➔. The I6 to which B➔ resolves is asserted as VI➔.32 In its final statement, as A3, the tonic pillar’s fifth-progression serves as the mazurka’s background descent. A coda projects that fifth again, as outlined in 2.25.
Opus 50/2 Recall that a C major chord (C minor with a wobbly E♮) crops up during the Mazurka in A♭ Major’s tonic pillar [1.26, measures 22 through 24]. Later, a C Minor tonicization extends through the B section within the mazurka’s five-part form [2.26]. Its initial C chord likewise incorporates E♮, propelling (in conjunction with the seventh, B♭) a surge towards C Minor’s IV at the outset.33 (The chord’s diatonic C-E♭-G state is elided.) In fact, since the section ends with a Picardy third, a minor tonic never sounds. It is sensed through the pitches A♭, B♭, and D♭ that occur during the phrase interiors. The two phrases (measures 29–32 and 33–36, which are integrated in 2.26) differ in two principal respects. First, the second phrase is more overt in its harmonic orientation, with the bass potently projected as C>FC is transferred to the top of the texture).
Example 2.26 Analysis of Mazurka in A♭ Major (op. 50/2). Another sixth, FE♭>D♭ third-progression whose concluding D♭ serves as the upper neighbor of the movement’s Kopfton, C. Chopin
deploys a familiar tonal trajectory during the middle part (y) of the section’s three-part form: from the tonic’s 6-phase chord through II to V7. The II harmony is enlivened by the pitch C, an anticipation of the following dominant’s third. (The C results from Chopin’s maintenance of measure 70’s melodic contour despite the contrasting harmonic trajectory.) A final statement of the tonic pillar brings the mazurka to a close, with a background descent to coordinating with the PAC.
Opus 56/1 The Mazurka in B Major’s tonic pillar is unusual in that it begins with an extended II to V7 harmonic succession, preceding the tonic arrival at 161 [1.9]. Consequently the tonal design of the B1 and B2 sections must be compatible with having II as an immediate successor, a situation not encountered in any of the other mazurkas we have explored. Chopin’s instinct to use the tonic’s 6-phase chord as the B1 section’s goal (measures 69ff.) reflects the prominence of I5–6 II V7 I progressions in the music he knew and composed [2.27a]. In this case I6, unfurled as diatonic G♯-B-D♯, sounds initially in its first chromatic variant, G♯-B♯-D♯, which Chopin spells enharmonically as A♭-C-E♭. Because a D♯ [E♭] region (a tonicized expansion of G♯’s upper-fifth embellishing chord that eventually targets G♯ as D♯➔) precedes the G♯ [A♭] chord’s arrival in measure 69, an E♭ Major key signature is employed. As is often the case in ascending a third from the tonic (here B to D♯ [E♭]), a segment of the descending circle of fifths is deployed (B E♯⇨ A♯➔ D♯). Whereas D♯ arrives during the fourth measure of the B1 material’s first statement (measure 48), it is present from the onset of the second statement (measure 61). In the first statement a G♯ [A♭] chord (measure 53) functions as IV within the local tonicization of D♯ Major, whereas at measure 69 it takes on the role of I6 in the connection of B Major’s I and II. Despite the potential for this prolonged G♯ chord to surge as VI➔, targeting the C♯ supertonic that begins A2, Chopin here restores diatonic G♯-B-D♯ at measure 79, just before the continuation to C♯. Though that event often would signal that B♮ will be absorbed by the C♯ chord as its minor seventh, here that is not literally the case, though one might easily prolong the B imaginatively through beats 1 and 2 of measure 81, with resolution to A♯ on beat 3.
Example 2.27 Mazurka in B Major (op. 56/1) (a) Analysis of the work; (b) The sequence of measures 181 through 189. Chopin’s tonal plan during the B2 section concludes with an astonishing passage. Recall that the essence of the B1 section was to proceed from D♯➔ to G♯, with time devoted to attaining and then tonicizing the D♯ chord before its ➔ surge reached full force. At the onset of the B2 section (measures 102–103), a variant of that trajectory, D♮➔ G♮, occurs swiftly. Whereas the B1 section’s G♯-B♯-D♯ is the unfurled first chromatic variant of the B Major tonic’s 6-phase chord, the B2 section’s G♮-B-D♮ is the second. Due to its immediate arrival, more time is available for a G Major tonicization. As 2.27a shows, it appears that a fifth-progression descending from D♮ (a wobble from Kopfton D♯) is in the works. An antecedent phrase proceeds as far as G Major’s dominant, supporting A♮, the penultimate note in that fifth-progression. Will the consequent phrase that begins in measure 119 succeed in attaining a PAC in G Major? Whereas the B1 section’s G♯ chord leads effectively to the C♯ supertonic that initiates the tonic pillar, the B2 section’s G♮ chord does not. Might the pillar begin a half step lower (a “Neapolitan” transformation) during its A3 presentation to accommodate the G major variant of I6? Or might the G chord somehow be raised by a half step to lead effectively to the diatonic supertonic? Chopin chose the latter alternative, which he realizes in a flamboyant manner. In both phrases a D♮ emerges at the top of the dominant chord that
might lead to the PAC tonic. (In the graph this is condensed into a single presentation, labeled with measure numbers 112/132.) Over the course of measures 136 through 142 Chopin deploys arpeggiated
chords (beginning with F♯-A-D♮) to float gently
downwards through tonal space from that dominant to a tonic that happens to be one half step higher than the expected one. That half-step elevation is the very correction that will allow the B2 section to proceed effortlessly to the supertonic that begins the A3 tonic pillar, repeating the trajectory that led from B1 into A2.35 The coda confirms B Major through two consecutive statements of a magnificent hybrid circle of fifths (measures 181–189 and 189–197). Though Chopin incorporates a number of minor deviations, such as anticipations and suppressed melodic pitches, the normative contour displayed in 2.27b guides its course. Whereas the circle might have proceeded in an alternation of 8 and 5 in the outer voices throughout, its first half transpires with the bass lowered by a third, so that the 8 5 alternation is replaced by 10 7 (thereby charged with dissonance).36 Of course, this lowering from B to G♯ replicates the tonal course of the mazurka’s B1 section. In this case an ascending third restores the normative bass for the second half of the progression.37 The two boxes below the staff in 2.27b denote the sites of the lowering and raising by a third.
3
Irregular pillars in the mazurkas: alternatives to the perfect authentic cadence ◈ The projection of a mazurka’s tonic key is sometimes accomplished via a tonic pillar that does not conclude in a PAC on the tonic. Closes on the dominant, on the mediant, or with an IAC on the tonic are viable alternatives to a regular tonic pillar. For example, irregular and regular tonic pillars may serve successively in shaping the A sections of a broad A1 B A2 form. An irregular pillar that concludes in a half cadence may be referred to as a I–V tonic pillar, while one that leads to the mediant may be referred to as a I–III tonic pillar. These situations, as well as some more unusual designs, are explored in this chapter, which brings our exploration of all the mazurkas that Chopin published during his lifetime to a close.
A tonic pillar concluding with an IAC
Opus 17/1 The Mazurka in B♭ Major’s enigmatic tonic pillar might elicit several potential structural interpretations. Does the principal line connect and , and , or and ? Is the line traversed in four measures and then repeated, or instead spread over eight measures?1 The prominence of F’s upper neighbor G in the mazurka’s B section (sounding first in measure 29) is a factor in choosing F rather than D as the Kopfton. The model for a1 displayed in 3.1a seems to me the most apposite. Kopfton F is prolonged during I-space, where an embellishing facilitates the local descent of a third (F>E♭>D). The V that follows supports
and likewise incorporates a descending third (E♭>D>C), preceding a tonic
close on , where, this time, the motivic third (D>B♭) lacks an internal C. The entire phrase is then repeated in measures 5 through 8, with modest variants (such as the 4–3 suspension in measure 7).
Example 3.1 Mazurka in B♭ Major (op. 17/1) (a) Analysis of mm. 0|1–29; (b) Analysis of the work.
Chopin alters the tonic pillar in important ways during its a2 presentation (measures 17 through 24), following the b region. The A♭ that enlivens I-space from the outset results in a surging approach to the embellishment (here with minor-hued G♭ substituting for G♮) from above: (elided B♭)>A♭>G♭>F connects the boundaries of I-space during measures 17 and 18. The presentation of the tonic chord in its second inversion at 183 allows for a stepwise connection to bass G♭ for the inverted
(again with a
borrowing from the parallel minor key) that now shares duties with V in supporting .2 In the phrase reiteration that follows in measures 21 through 24, Chopin further develops the supertonic, both through its evolution into II➔ and through the expansion of the preceding
I-space into I5–6, a characteristic means of leading into II. (Observe that I6 is here asserted as VI➔, pointing dynamically toward the supertonic.) Note also how measure 24 differs from the similar measures 4, 8, and 20 (all of which sound D on their third beat, supporting my reading of within linear descents from at those points). In that the tonic pillars as yet have presented only the upper half of the F>B♭ fifth, measure 24 is the day of reckoning: will the line achieve its B♭ goal, resulting in a PAC; or will we have to settle for an IAC as the structural close? Whereas earlier the b region (to be explored presently) introduced the second scale degree, now the descent through
to occurs
quickly just as the section (or, during A2, the entire work) comes to a close. The b region that comes between a1 and a2 to shape the mazurka’s A1 section deploys II➔ V to succinctly achieve its dominant goal. Though the that serves as ’s successor in the linear descent is presented forzando in the low and middle registers at 91, its sounding at the top of the texture is delayed until 151 (at the end of a crescendo). The structural content is presented in four measures (9 through 12) followed by a varied repetition, thereby matching the format introduced during the a1 region. Chopin indulges in a flamboyant flourish during that repetition, with a rapid traversal of a circle of fifths supporting a stepwise descent through the dominant’s C>F fifth. The B section is structured as an autonomous trio [3.1b]. The B♭ tonic’s embellishing chord (first heard in measure 2) is here unfurled and asserted as the key of E♭ Major. Though the chordal progressions at various structural levels remain uncommonly simple, the embedding of one interrupted progression within a broader one is sophisticated. Chopin undertakes excursions above the melody’s fundamental structure. The third from C to A♭, filled in chromatically between 343 and 363 and between 431 and 433, is especially intriguing. In fact, given that in both contexts the motion continues downwards (by leap) to F, a reference to measures 15 and 16 may be discerned, despite the contrasting tonal contexts (fifth to root of dominant F in B♭ Major versus ninth to fifth of dominant B♭ in E♭ Major). The that is restored along with the resumption of the B♭ Major tonic for the onset of A2 again serves as the starting point for a descending fifth-progression. Because the A2
section concludes the work, this time that descent corresponds to the Urlinie.
The immediate restoration of I after a I–V tonic pillar
Opus 7/3 In a mazurka whose A1 section closes with a PAC in the tonic key, the B section may initially extend that tonic and then pursue a dominant goal. (As an example, see 2.3.) That strategy may prevail even if A1 ends in a vibrant HC. In 3.2, which displays an analysis of Chopin’s Mazurka in F Minor, observe how the melodic A♭>G that transpires over the course of A1 (with written-out repeat) is followed by the quick reaching-over of B♭, which resolves to a restored Kopfton A♭ early in the B section. Consequently the background tonic extends into measure 28, despite the HC in measures 16 and 24.
Example 3.2 Analysis of Mazurka in F Minor (op. 7/3). The mysterious introduction is grounded on lower-neighbor embellishment of the tonic’s root and third (imagining a G to go along with C and E♮, as occurs literally in measures 77ff.). The potential assertion of the introduction’s C-E♮-(G) as V♮ and F-(A♭)B♮-D♭ as II⇨ will be discussed later, in the context of this material’s recurrence at the juncture of B and A2.3 The initial tonic pillar that follows is simply constructed: the tonic is solidly established by means of upper-neighbor embellishment of its third and fifth in measure 11 (complementing the lower neighbors of the introduction), followed by a progression through II➔ to V♮. The harmonic trajectory that prevails during the B section follows a conventional course, though with one notable omission. Most of the section is devoted to the connection of the F tonic’s 5- and 6-phase chords: F-A♭-C and D♭-F-A♭. One of two intermediary chords often occurs between those points: either C-E♮-G (as
C, an embellishing chord
of the preceding F tonic) or A♭-C-E♭, which likewise possesses a natural dominantemulating tendency (as A♭➔, which embellishes the 6-phase D♭-F-A♭, here abetted by the addition of G♭ at 613). Chopin pursues the latter course, first attaining the A♭ chord via a segment of the descending circle of fifths (measures 26 through 30) and then tonicizing it until it surges towards D♭. The proposal of an omission, mentioned above, stems from the fact that I6 often leads to II, which in turn targets V♮. In a minor key, a very special relationship exists between I6 and II⇨: the former (D♭-F-A♭ in Chopin’s mazurka) may be a subset of the latter (D♭-F-A♭-B♮).4 Yet instead of adding B♮ in the vicinity of measure 73, Chopin allows the three pitches of the unfurled I6 each to descend a half step in turn, in a direct approach to V♮.5 This memorable and unusual voice leading heightens the emotional impact that Chopin seeks to attain also through the pianissimo dynamic indication and the ritenuto, sotto voce, and smorzando markings. Rewarding those listeners who noted the II⇨ omission, the following dominant prolongation (which reprises the mysterious introduction) uses the very notes of II⇨ – D♭-F-A♭-B♮ – in an embellishing context. Though V♮’s arrival concludes the B section’s harmonic progression, the embellishing chords that follow uncannily project the unsounded harmonic predecessor of V♮. The A2 section is constructed as a regular tonic pillar. Though its first phrase again ends on V♮, the phrase that follows is no mere repeat of the preceding one (as are measures 17 through 24). It instead serves as a conventional consequent phrase, concluding in a PAC that supports background . Ultimately the A1 section’s irregular close is of only local significance. The circle of fifths that leads out of I-space soon after the onset of the B section would transpire just the same regardless of what cadence occurs in measure 24.
Opus 30/1 Several features of the Mazurka in C Minor [3.3] echo those of the Mazurka in F Minor [3.2]. The A1 sections of both works present a I–V♮ tonic pillar, employing II➔ to lead to V♮. Likewise, a restoration of the tonic function occurs at or near the beginning of both B sections, followed by a segment of the descending circle of fifths that leads to the mediant. In the Mazurka in C Minor that restored tonic (at 163) is surging, already targeting the next chord in the circle of fifths. Both mazurkas tonicize the mediant, and both reach V♮ by the end of the B section. During A2 suitable revisions convert what was an irregular pillar during A1 into a regular one.
Example 3.3 Analysis of Mazurka in C Minor (op. 30/1). The chief difference between the two mazurkas’ structures concerns the manner in which the background V♮ is attained. Whereas the mediant in the Mazurka in F Minor ultimately leads to the diatonic I6, which could have proceeded (but does not) to II before V♮, in the Mazurka in C Minor the mediant is followed by a chromatic variant of I6 at 283. This chord in fact does lead through II➔ to V♮.6 Yet Chopin’s conception is even richer. As the two tiers of measure numbers in 3.2 and 3.3 suggest, both mazurkas make extensive use of repetition. For a few measures of the Mazurka in C Minor, Chopin eschews that practice and composes distinctive content, so that the connection between the mediant and dominant in measures 22 through 24 (not graphed) does not match that which occurs between measures 28 and 30. (Note also that the mediant is expanded – measures 20 through 22 – during the former phrase, while the dominant is extended – measures 30 through 36 – during the latter.) The former leads from III through IV to V♮. (The stepwise connection between III and IV is facilitated by the shift to III’s 6-phase chord at 232.)
Because of the persistent repetition during the A1 and B sections, the two dominant arrivals should be understood as equivalent. Chopin achieves his goal; then he backtracks and presents another pathway to the same goal. To enhance clarity the graph integrates those trajectories as much as possible, favoring the latter when they diverge. One way or another, the irregular tonic pillar of A1 must be transformed into a regular one during A2. The latter’s opening phrase reprises the full content of A1’s I–V♮ progression. What follows starting at 451 – which one might even resist calling a phrase – attains tonic closure in an unusual way. Instead of proceeding through the dominant to the expected PAC, it merely prolongs its initiating tonic. Consequently the local E♭>D>C descent of measures 46 through 48 serves as a motion to background , the endpoint of descending lines from at three distinct structural levels, as indicated by the multiple beams in 3.3.
Op. 30/4 The chords of the Mazurka in C♯ Minor’s introduction precede not only the tonic harmony that opens the A1 section, but also, through their recurrence at the end of the B section, the initial tonic of A2 as well. Their structural implications will be discussed below in terms of the latter context, which the introduction replicates only in part. Once the tonic harmony and Kopfton E emerge in measure 5, a broad tonic expansion ensues. F♯’s roles as both neighboring note to E and passing note to upper-third G♯ are on display in 3.4. The ♮II harmony serves as the principal connector between I and V♯ during the expansion of . Though the arrival of the pillar’s cadential dominant is placed at measure 31 in 3.4, Chopin’s writing in measures 28 through 31 teases listeners: should the passage be interpreted as repetitions of V➔ I followed by V♯, or instead as repetitions of V (with the chords unfurled)?
Example 3.4 Analysis of Mazurka in C♯ Minor (op. 30/4). As in the other mazurkas explored in this segment of the chapter, the tonic harmony and the Kopfton are restored early in the B section. Initially the C♯ minor chord is fortified through motion to its upper fifth, G♯ (measures 39ff.). The broad melodic descent E>D♯>C♯ over measures 34 through 65 shifts from representing the third to root of the C♯ tonic chord to the seventh to fifth of an F♯ chord. Whereas Chopin utilizes the descending circle of fifths in the B sections displayed in 3.2 and 3.3 to connect the tonic and the mediant, here the circle extends only to its third chord: C♯ F♯ B. This B chord is tonicized
between measures 66 and 95 (parts of which are displayed in 3.4). Chopin’s tonal plan involves a conversion from subtonic B to dominant G♯.7 The harmonic analysis in 3.4 displays the B chord as a not yet fully formed dominant: the pitch B is the wobbly third of the G♯ major dominant, with the arrival of root G♯ delayed until measure 99. The B-D♯F♯ tonicization is an upper-third substitution for the rightful G♯-B♯-D♯ dominant tonicization. Chopin negotiates the transition between B and G♯ by juxtaposing embellishing chords targeting each: F♯➔ in measures 94 through 96 and D♯➔ in measures 97 and 98. By the time the G♯ chord arrives, it is too late for further tonicization. Its minor seventh F♯ is already in place, and so instead of content extending its role as I in tonicized G♯, it asserts its background role as
, announcing the restoration of the C♯ tonic for
the A2 section. As mentioned above, the D♯➔ and G♯➔ chords were first encountered within the mazurka’s introduction. The A2 section offers an intriguing reprise of the dominant–subtonic relationship. Certainly a PAC must be attained at the close of A2. The dominant at measure 128 is where the precedent harmonic trajectory of A1 concludes. How will Chopin achieve a tonic cadence? His extraordinary response involves a plan to proceed from the already attained dominant to its subtonic upper-third chord and then back again. Both of those moves are accomplished through an inspired yet unconventional construction. Whereas the subtonic–dominant connection within the B section was negotiated via a shift of embellishing chords, in these final measures Chopin instead deploys a linear progression to connect the G♯ and B chords themselves: a wondrous application of the descending circle of fifths, filled with altered pitches, added dissonances, and enharmonic spellings, which transpires as m.
128
G♯
129
C♯
F♯
130
B
E
131
A
D♮
132
G♮
C♮
In this interpretation, a collision at beat 3 of measure 132 involves two adjacent chords within the circle – F♮ (which in a familiar evolved state would be correctly spelled as AC♭-E♭-G♭) and B (spelled as B-D♯-F♯-A) – that are enharmonic equivalents of one another. The passage in fact comes across as a parallel progression of major-minor seventh
chords – as a temporary transfer from diatonic modulo 7 tonal space into the modulo 12 realm, where spans such as this G♯>B may be traversed by unconventional means, in this case through a descent in half steps: 8 (7) 6 5 4 3 2 1 0 11 (with C = 0).8 The dominant restoration is likewise inventive. Whereas B♯-D♯-F♯-A would be a suitable successor of the subtonic chord, projecting a conventional intensification of the dominant function, in this case leading tone B♯ is displaced by an anticipation of its resolution: C♯-D♯-F♯-A is prolonged during measures 133 through 138.9 At the cadence F♯ resolves to E and A resolves to G♯ above tonic root C♯. The soprano tonic , anticipated during the dominant harmony, sounds only in the bass at the cadence. Consequently the C♯ that concludes the background
melodic descent is displayed within parentheses in 3.4.
Without opus 42A A prominent feature of the irregular tonic pillar that serves as A1 for the Mazurka in A Minor is its array of
descents [3.5a]. Most are local manifestations, within their
own four-measure phrases. Some are preceded by their upper thirds. (The descending third E>D♯>D♮>C beginning in measure 9 inverts the ascending sixth E
Example 3.5 Mazurka in A Minor (Without opus 42A) (a) Analysis of mm. 1–40; (b) Analysis of the work.
The mazurka’s B section is a binary construction [3.5b]. Both halves begin with an unhurried attainment of the major tonic (measures 44 and 60), which is then extended via a I IV5–6 V7 I progression. During the x1 half, the progression continues thereafter to the mediant’s first chromatic variant, of major quality. (Whereas during A1, tonic A-C-E proceeds to C-E-G, the x1 half of B proceeds from tonic A-C♯-E to C♯-E♯-G♯.) Though the opening of x2 is modified harmonically to accommodate the continuation after the mediant (as opposed to the dominant, as was the case at the juncture of A1 and B), the tonic re-emerges as expected in measure 60. Prolonged through measure 68, the progression then continues with Passing motion to
, which supports C♯’s incomplete upper neighbor.
coordinates with the dominant’s arrival. Given its location at the
divide between B and A2, this dominant functions at the background level, supporting the Urlinie’s . As is often the case, an interruption of that line’s descent coincides with the A2 tonic restoration, which here also re-engages the diatonic Kopfton C♮, rescinding the B
section’s C♯ wobble. The tonic pillar that ensues within A2 is regular: is attained in the context of a PAC in measure 110. Numerous reiterations, which complement the local that pervade the initial portion of A2, extend this close.
descents
Op. 63/1 The eight-measure phrase that opens the Mazurka in B Major proceeds in a conventional fashion: from I5–6 through II➔ to V [3.6a]. (An unfurled embellishing chord in measure 3 extends the initial tonic.) The next phrase is not a consequent ending in a PAC, but instead a repetition of the progression to the HC, with the melody presented an octave higher. Consequently the tonic pillar is irregular.
Example 3.6 Mazurka in B Major (op. 63/1) (a) Analysis of the work; (b) Analysis of mm. 31–61. As in the four mazurkas explored earlier in this section, the tonic is restored soon after the B section begins. (Like measure 24 in 3.3, the tonic in measure 21 of this
mazurka is surging – as B➔ – upon its return, setting in motion a descending circle of fifths.) Unlike those four mazurkas, here the B section broadly extends the tonic. Observe in 3.6a how the harmonic progression at the onset of B is a variant of that in A1, the most crucial difference being its close in a PAC in measure 28. Immediately thereafter the latter part of the phrase is reiterated: from II➔ in measures 29 and 30 to V7 in measures 31 and 32. Though eventually that dominant will find its tonic, closing the B section (as shown in 3.6a), an extended episode that tonicizes F♯ Major intervenes. Before we explore that passage, note how the fact that the B section prolongs I results in a modest revision in the chordal content at the onset of A2, where the succeeding root F♯ (compare with measure 5) occurs already against the Kopfton (measures 69–70).11 In contrast to the A1 statement of the tonic pillar, this time the pillar’s second phrase, which is expanded, leads to a PAC. At its most basic level, the prolongation of the F♯ dominant during the latter part of the B section does what most tonicizations do: it proceeds from the tonicized pitch (F♯) to its dominant (C♯) and back [3.6b]. In this instance the F♯
Other contexts for I–V tonic pillars
Opus 6/3 The establishment of the tonic harmony and of Kopfton at the outset of the Mazurka in E Major integrates multiple layers of arpeggiation, with some filling-in by passing notes. The melodic pitch B is emphasized during the eight introductory measures not only through its repeated sounding in the left hand but also through the descending arpeggiation B>G♯>E. (The initial C♯ neighbor recurs in the upper register at 121.) Further local arpeggiation transpires to hoist B up an octave during measure 9, followed by a deeper level of arpeggiation traversing the tonic’s remaining pitches E in measure 10 and Kopfton G♯ in measure 12 [3.7]. Some playful embellishing arpeggiation occurs between passing note F♯ and goal G♯ in measures 11 and 12. The tonic expanse is followed by II➔ V, accomplished in such a way that the EE>D♯. (The accented B>B octave during measure 16, corresponding to the B
Example 3.7 Analysis of Mazurka in E Major (op. 6/3). As with the other I–V pillars explored in this chapter, the tonic is restored during the B section before further tonal adventures ensue. Yet whereas in those other mazurkas the tonic restoration occurred quickly, so that one sensed the tonic to be an initiating entity
within the section, in this case A1’s middleground
is complemented by a full
eight-measure presentation of . Within that expanse Chopin deploys a double dose of embellishing chord. Whereas the B-D♯-F♯ dominant may be embellished by two concurrent lower neighbors (A-C♯-F♯), here the unfurled F♯-A-C♯ chord likewise is embellished by two lower neighbors (E-G♯-C♯, not graphed). Observe that one of the neighbors does not return to its starting point: though A in measure 34 could have ascended back to B in measure 38, it instead is retained as the dominant’s seventh. This phase of the B section concludes with the tonic, achieving a PAC in measures 39 and 40. The pitch B, which sounds above Kopfton G♯ in measure 12, recurs in measure 41. During the ensuing eight measures, which extend the tonic, B is transferred down an octave, so that the C♯>A third (complementing G♯
The chord, which arrives unfurled in measure 50, is tonicized: a descending thirdprogression (C♯>B>A) in A Major transpires over the course of eight measures [3.7]. During a repetition of this passage beginning in measure 58, Chopin creatively modifies the harmonization so that a fully chromatic filling-in of a descending seventh connects the tonic root A at 581 and the supertonic root B at 631. The chromatic line takes on the character of a stupefying feat, enhancing the mazurka’s robust character.
The restoration of the tonic in measure 69 coincides with the onset of a fresh B
regular tonic pillar. Because the B section features the Kopfton’s upper neighbor, A (flagged in 3.7), the third-progression from to (interrupted) during the A2 section serves as the background descent.
Opus 24/1 A recurring formula for Chopin’s irregular pillar usage may be observed in the Mazurka in G Minor. The first sixteen and the last sixteen measures of the composition are equivalent except at their endpoints: II➔ V♯ (= HC) in the former is replaced by V➔ I (= PAC) in the latter. Chopin’s large-scale tonal plan takes advantage of the fact that the pitches of V7 occur during the pillar’s opening measure. Whereas in that context they serve locally as an embellishment of measure 2’s initiating tonic, the broad tonal trajectory extending through A1 and B leads to this chord as an asserted member of a middleground harmonic progression – I5–6 II⇨
– that culminates in the restoration of I during the second
measure of A2 [3.8].
Example 3.8 Analysis of Mazurka in G Minor (op. 24/1). Chopin offers a liberal sprinkling of colorful chords during the pillar: the tonic’s embellishing chord – G-C-E♭ – sounds at the beginning of measure 3 but evolves into a more intense F♯-A-C-E♭ over tonic pedal G before the tonic restoration on the following downbeat. Likewise II➔ sounds as C♯-E♮-G-B♭ over a dominant pedal (from sixteenthnote C♯ during 63 into measure 7). Eventually the dominant’s root D is joined by third F♯ (at 73), concurrent with II➔’s root A displacing ninth B♭, thereby creating a potent collision of II➔ and V♯.
In mazurkas explored earlier in this chapter the initial I–V tonic pillar has been followed – after variable amounts of delay – by a tonic restoration before the B section’s agenda continues. Consequently listeners might expect minor seventh C to emerge soon after the D-F♯-A chord of measure 16, so that D➔ targets a G tonic. Yet in this case Chopin skips the tonic restoration, instead proceeding to the tonic’s closely allied upperthird chord. Consequently the addition of dissonance is integrated with an upward hoist of a minor third during measures 17 through 20, where F-A-C-E♭ (= F➔) targets B♭-D-F. This B♭ chord persists through the cadence of measure 32. (The first ending at that point incorporates a transition back to the G tonic for a repeat of A1 and the first part of B.) Relief from the emotionally distraught mood projected during A1 is offered not only by the shift of mode to major during the B section, but also by the absence of such features as the melodic augmented seconds of measures 3 and 6|7 and the chordal collision during measure 7. Instead one is treated to some luscious chromaticism, for example during the descent in parallel sixths from 223 through 242. (Note how Chopin seamlessly increases the chromatic density during the repetition of that passage, where not only the D>C and F>E♭ seconds are filled in, but also the upper line’s concluding C>B♭ and the FG thirds and B♭
at 491. The upward resolution
of C♯ to D is elided. Instead, the dominant’s seventh C♮ sounds during all of measure 49. As mentioned above, the mazurka’s second tonic pillar is regular. Because no interruption occurs during the B section, Kopfton B♭ is still in force at the onset of the A2 section. An interrupted third-progression leads through background A at measure 56 to goal G in the final measure.
Opus 50/3 Though by definition a regular tonic pillar is intended to project I-space, that which Chopin created for the Mazurka in C♯ Minor is disproportionately devoted to the dominant: the G♯-B♯-D♯-F♯ embellishing chord of the first four measures will be deployed in an abbreviated form later as a dominant extension (measures 32|33–34), whereas a long internal dominant prolongation (measures 9 through 15) nearly overwhelms the pillar’s initiating and closing tonics (measures 5 and 16) [3.9a]. The irregular pillar that occurs within this mazurka (the second of four, in measures 32|33 through 44) results from simply not following through to the conclusion of the regular pillar, as presented in measures 0|1 through 16. In fact, with such potent dominants on both edges – as well as an internal dominant pedal point – one might doubt whether the tonic chord of measure 35 (repeated in measure 39) can overpower the dominant hegemony in that region. In the fourth pillar, which repeats the content of the second, only the freshly composed continuation after the dominant of measure 133 (leading to a cadence on the tonic in measure 157) tips the scale decisively in favor of the tonic. Though the initial a2 pillar reprises (in abbreviated form) the I II➔ V♯ portion of the preceding a1 pillar, at best it represents a mere reiteration of the approach to the dominant attained during the b region (akin to what is displayed in measures 37 through 40 of 3.5a). Its supposed tonic chord might even be interpreted as an unfurled embellishment of the dominant (expanding upon the content of measure 3, as graphed in 3.9a).
Example 3.9 Mazurka in C♯ Minor (op. 50/3) (a) Analysis of mm. 0|1–92; (b) Analysis of the work.
A no-nonsense fifth-progression from G♯ to C♯ provides the melodic shape for the mazurka’s opening five measures [3.9a]. Here Chopin’s contrapuntal proclivity is overtly realized, with a tenor line that imitates the soprano. Only after goal C♯ is attained at 51 does Kopfton E emerge (embellished by D♯ and F♯). Early in measure 6 the tonic absorbs the 6-phase pitch A♯, preceding the arrival of II➔, at which point another fifthprogression (from D♯ to G♯, whose goal we expect will be achieved at 91) begins. Though the dominant in fact arrives as expected, Chopin withholds the melodic G♯ for several measures, placing an embellishing minor ninth A at the top of the texture. The resolution to G♯ and restoration an octave lower (measure 13) occur before the dominant’s D♯ descends to the tonic-supported C♯, completing a conventional third-progression from the Kopfton.
A tonal trajectory connecting the tonic and the dominant is an attractive option during the b region of a ternary A1 section. (Compare with 2.16.) The fact that the middleground interruption at the end of b will not be resolved during the upcoming irregular a2 pillar has no effect upon how the b region transpires. In this instance the tonic is extended through measure 24 via a sequential connection between two tonic chords. Whereas normally the sequence employed would proceed with bass C♯>G♯EC♯ supporting a descending sixth-progression from Kopfton E, in this case the G♯ chord is internal to a1 and thus resolves to tonic C♯ before the A chord emerges in measure 17. During the II➔ that follows after the sequence, the melody gradually builds back upwards to the D♯ (measure 27) that succeeds Kopfton E at the middleground level and connects with the D♯ of V♯ (measure 32). As indicated above, a2’s tonal plan demotes the impact of the tonic restoration, instead favoring dominant prolongation. Consequently the b region’s
ultimately is left
dangling at the end of the a2 region. Chopin’s re-engagement with the thematic content of a1 here involves contraction: the essence of measures 0|1 through 9 is stated in measures 32|33 through 37 and is then repeated even more succinctly. The region closes with a fourmeasure melodic arpeggiation of the pitches of V♯, segueing into the B section, which begins in measure 45. Though the V♯ that concludes the A1 section – unexpectedly lacking a tonic resolution – is a middleground event and the V♯ that ends the B section (measures 89–92) is a background event, the uncommon dominant density at this juncture makes a conventional I-to-V♯ trajectory ill suited for B. Chopin therefore has elected instead to tonicize a chromatic variant of the dominant’s upper-third chord. Because dissonant B♯D♯-F♯ cannot be tonicized, Chopin allows B♯ to wobble to B♮. That lowering, introduced in measure 45, is not rescinded until measure 89. Because B Major is in a sense the “wrong” key, the trajectory that Chopin sets in motion for its tonicization – a local ternary form divided by an interruption after the
that arrives at measure 70 [3.9a] – is not
fully realized (and thus resonates with the unresolved ternary interruption during A1). In this case the y region is extensively developed, with a surging I leading through IV5–6 to V, while the x2 region that follows proceeds only through its initial pre-surge I phase.
One foreground detail (not graphed) plays an important role in the realization of Chopin’s tonal plan for the B section: namely, the incorporation of the B tonic’s 6-phase chord as a substitute for the dominant during the repeat of x1 (measures 53 through 60). The basic idea, which extends into the onset of the y region, is I8–7♮, the conversion of the stable B-major tonic into a surging chord targeting IV. That tonic is expanded via a local B>F♯C♯, covered by F♯>E. Concurrent with the background close on , this E opens the tonal space that will be traversed – as a reprise of the E>D♯>C♯ descent – during the coda.13) The magnificent coda deploys the lowered supertonic (measures 165 and 171) as the principal intermediary between the tonic and the dominant [3.9b]. Though usually that chord’s wobble (here D♮) would be rectified by the dominant’s D♯, in this case a supertonic evolution during measure 173 results in a D♯-rooted version of II occurring prior to the onset of V.14 (I have displayed the chord as F -A-C♯-(E) in 3.9b, though D♯ might be imagined instead of E: both convey the function II⇨.) Chopin’s means of connecting the tonic and the lowered supertonic incorporates an obstinate circular progression that I propose resides outside of conventional modulo 7 tonal space. Instead, once it gets on track modulo 12 chromatic tonal space subdivides into four equal segments. Using the numbers from 0 through 11 (with C = 0), the progression proceeds as m.
157
158
159
160
161
162
163
164 170
165
166
167
168
169
melody:
1
1
3
4
6
7
9
10
0
1
3
bass:
1
6➔
11
9➔
2
0➔
5
3➔
8
6➔
11
The conversion of this lucid and elegant circular progression into modulo 7 music notation inevitably results in some enharmonic inelegance, requiring a mix of minor third and augmented second intervals. (Though Chopin chose to notate the bass as B
Contexts for the I–III tonic pillar
Opus 41/2 [a.k.a. opus 41/3] Though the Mazurka in B Major’s diatonic mediant is D♯-F♯-A♯, that chord’s first and second chromatic variants – D♯-F -A♯ (spelled by Chopin as E♭-G-B♭) and D♮-F♯-A♮, both of major quality – emerge at corresponding locations (measures 17 and 37) within the initial presentation of A1 and what at first appears to be A1’s exact written-out repetition [3.10]. The D♯ major chord’s F is a wobble that reverts to F♯ with the arrival of the dominant in measure 20, while the D major chord comes about as a result of Chopin’s elective shift to B Major’s parallel minor key (in which D-F♯-A is the diatonic mediant) starting in measure 35.
Example 3.10 Analysis of Mazurka in B Major (op. 41/2). The eight-measure phrase that opens the A1 section’s a1 region is conventionally constructed: after a tonic that is extended via neighboring-note embellishments and an upward registral shift of Kopfton D♯ (at 71), II➔ V provides an appropriate close. The second phrase begins like the first, but instead of again proceeding via C♯➔ to F♯, A♯➔ D♯ (spelled by Chopin as B♭➔ E♭) transpires, concluding a tonic-to-mediant connection propelled by a descending circle of fifths – B E♯ A♯ D♯. (The E♯ chord, with root omitted, is realized by adding G , spelled as A♮ during 151, to the tonic’s B-D♯-F♯. The chord functions as E♯⇨.) The lavish attention devoted to the mediant arrival, including a repetition of A♯➔ D♯, extends the phrase beyond eight measures. Yet Chopin persists in his agenda until the dominant is attained in measure 20, not only closing with a half cadence (more definitively than in measure 8) but also – an important point for understanding what happens later – creating a phrase that divides into groups of four measures (a hypermetrical organization boldly introduced by the repetitive measures 1–4 and 9–12). Instead of proceeding directly to the mazurka’s B section, Chopin begins over
again in measure 21. What will happen this time: a tonic-closing consequent phrase (the most normative realization of the a1 and a2 form markings in 3.10), resulting in a regular tonic pillar; an exact repetition, resulting in a I–V irregular tonic pillar; or something else? In a sense, listeners never learn the answer, because that phrase’s conclusion is preempted by the B section’s unexpected onset in measure 39. Measure 38 (which corresponds to measure 18) is the tenth of what we should expect will be a twelvemeasure phrase that could conclude over the next two measures either with a PAC (D♮ F♯ | B) or with another HC (D♮ | F♯). Chopin diverts the D♮ chord from its apparent role as divider between tonic B and dominant F♯, which would transpire if the initial a1 region’s B–D♯–F♯ arpeggiation were again deployed, now in a minor-mode context. (Note especially how a circle of fifths again links the tonic and the mediant.) Surprisingly, the D chord serves instead within a broad sequential descent in thirds:
B
D♮➔
G♮
B➔
E
(marked in 3.10). One may confirm the extraordinary nature of what ensues in measure 39 by counting four-measure units through the end of the B section: 39–42, 43–46, 47–50, and 51–54. From what precedes it, measure 39 should function as an internal element of a four-bar hypermeasure; yet based upon what follows (and fostered by Chopin’s forte and accent markings), the listener must undertake a metrical recalibration so that measure 39 is interpreted as a hypermetric downbeat. The sequential descent’s goal E chord (at 493) serves as IV within a broad harmonic progression in B Minor. The dominant and then the tonic bring that progression and the B section to a close in a PAC, with soprano B belatedly making good on the intention to complete the descending third-progression that was interrupted at measure 20. Because the B section does not close on the dominant, the background structure is no further along at the onset of A2 than it was during A1. We should expect that a regular tonic pillar – incorporating background
will be presented as the content
of A2. Chopin achieves this through truncation, not proceeding to (or, at this point, beyond) the mediant that was the final structural event within A1. Consequently there is no opportunity for a post-interruption descent to complete the background third-progression,
following the of measure 66. In this context the D♯ in measure 69 does not correspond to a reinstatement of . Instead, as 3.10 shows, the B of measure 67 – which was not so emphasized during A1 – serves as the arrival of background , directly after . The D♯s that follow may be interpreted as upper-third extensions, echoes of the Kopfton that persist in multiple registers through the final chord. Brief glimmers of a minor-mode resurgence (G♮ in measures 72 and 74) do not ignite. The mazurka concludes as it began, with repeated iterations of an embellished major tonic chord.
Opus 41/3 [a.k.a. opus 41/4] The Mazurka in A♭ Major projects a straightforward structure in a daringly incomplete manner. The listener’s ability – or willingness – to engage in imaginative musical thinking is tested. If one’s internal ear does not perform structure-completing operations to make up for lacunae at both the end of the B section and the end of the A2 section, the mazurka’s structure likely will seem defective. The broad tonal plan supports an Urlinie descending by step from Kopfton , with an interruption after
. The
span occurs during the A1 section, in
conjunction with a straightforward I➔ IV5–6 V7 I harmonic progression [3.11a]. The continuation to occurs at 522, the final measure of the B section. Despite the absence of audible harmonic support, this B♭ and its upper third, D♭, certainly project the dominant harmony, whose root E♭ and third G have been inserted parenthetically in 3.11a. Under normal circumstances, the remainder of the work (the A2 section) would be devoted to completing the structure interrupted after the B section’s
. All begins well, with a
restoration of along with tonic root A♭. Yet sooner or later Chopin must confront the fact that the tonic pillar he deployed during A1 is irregular. He cannot simply reprise A1, since the descent would not reach , nor would the tonic harmony end the work. The and III that conclude A1 effectively precede the emergence of
and V during the B
section. Yet that state of affairs may not likewise conclude A2. What to do?15
Example 3.11 Mazurka in A♭ Major (op. 41/3) (a) Analysis of the work; (b) Hypothetical measures 83 and 84. What Chopin does is both elegant and mysterious. Taking advantage of the fact that both halves of the tonic pillar are repeated during A1, he plays with fire by again moving from the A♭ tonic to the mediant during the first statement of the pillar’s second half during A2 (measures 74 through 76, corresponding to measures 22 through 24). The final phrase begins in measure 77. Chopin “needs” to replace the circular progression’s G➔ C of measures 31 and 32 (likewise measures 75 and 76), supporting soprano D♮ to C, with a harmonically asserted E♭➔ A♭, supporting soprano B♭ to A♭ (= ). He proceeds just to the point where that shift would come into play. Then he simply stops, mid-phrase! Though two measures that might suitably complete the final eight-measure phrase are offered in 3.11b, they do not sound within the composition. Chopin’s fermata gives time for the imaginative generation of such an ending, leading to the Urlinie’s concluding pitch, . It is as if the diminuendo that has been in progress since measure 78 succeeds to the extent that the concluding measures of the composition become inaudible. Consequently Chopin did not write them down.16
Opus 59/2 The Mazurka in A♭ Major’s background events are all normatively positioned within the form: A1 begins with , B ends with , and A2 ends with [3.12a]. Chopin complicates matters by proceeding to the mediant at the end of A1, resulting in an irregular pillar that will require modification for presentation during A2. In this case that necessity leads to an astonishingly inventive alternative ending involving the juxtaposition of two contrasting means of achieving the supertonic, and with II⇨ replacing II➔.
Example 3.12 Mazurka in A♭ Major (op. 59/2) (a) Analysis of mm. 1–89; (b) Analysis of mm. 89–101. The A1 section’s first phrase is a model of elegant harmonic writing. The opening tonic is prolonged via an unfurled embellishing chord in measure 3. Its 6-phase F emerges in measure 6, perfectly setting up measure 7’s II➔, which leads to a half cadence on V in measure 8. Were a regular tonic pillar in the making, the next phrase would conclude with V7 I. Instead Chopin allows the 6-phase chord of measure 14 (related to that of measure 6) to be subjected to its own 6-phase extension, thereby lowering the continuation by a third: instead of the antecedent’s B♭➔ E♭, Chopin leads via G➔ to a
cadence on mediant C. Rather than moving directly to the written-out repeat of what has occurred thus far, Chopin allows time for the listener to savor the mediant attainment (measures 17 through 22). One might imagine a local
during 223 (meagerly
represented by F) as a means of directing the progression back to the opening tonic. The progression from the tonic to the mediant is then repeated. As is also the case after several of Chopin’s irregular I–V tonic pillars (explored earlier in this chapter), a tonic restoration follows after this irregular I–III tonic pillar (via II7 V7 I in measures 45 through 52) to initiate the B section. Yet that is only the first of two alternative continuations ensuing from the D♭-F-A♭-B♭ chord of measure 45. Since that chord is reinstated in measure 53, and since the latter scenario turns out to lead into the further stages of the composition, the tonic-restoring material is displayed as a parenthetical passage in 3.12a. Beginning in measure 53, D♭-F-A♭-B♭ serves as an embellishing chord of the mediant, evolving into D♭-F-G-B♮ before resolution, at which point the mediant’s third wobbles to E♮. Though the C mediant chord might have taken on further surge characteristics, targeting I6 (= F minor), the E♭ dominant emerges instead in measure 68, bringing the B section to a close. The mediant’s wobbly third (E♮) and the dominant’s minor ninth (F♭) are juxtaposed during 681–2. The A2 section’s first phrase reiterates the I5–6 II➔ V progression of its A1 counterpart. Thus far I6 has not been asserted as VI➔. Since some revision of content during A2’s second phrase is required in any event (so that a regular pillar cadencing on I – rather than on III – is achieved), Chopin elects to go all out, expanding the phrase to thirteen measures. The first sign of this is his connection of the tonic’s 5- and 6-phase chords via an ascending 5–6 sequence, proceeding as follows in measures 81 through 84:
A♭5(–6
B♭5–6
C5)–6
D♭5–6
E♭5–6
F
(As often is the case in this context, Chopin here abbreviates the ascent by omitting the chords within parentheses, made possible by the fact that A♭5 and C6 both are composed using the pitch classes A♭, C, and E♭. Note also that the 6-phase chords all evolve into surging entities.) Some rambunctiousness at 841 displaces F’s 5-phase C with the premature arrival of 6-phase D♮. Yet it turns out that at that moment the sequence is
breaking up, and so the D♮ is understood in retrospect to function as a passing note connecting the F chord’s elided fifth C and minor seventh E♭ (enharmonically spelled as D♯). The VI➔ at 843 potentially could lead (as do, without surging, the several I6 chords of earlier phrases) to II➔. Chopin does not pursue that trajectory. Recall that the A♭ major tonic chord possesses, in all, four consonant 6-phase chords – the diatonic version and three chromatic variants. Three of these four chords are employed within this mazurka: diatonic A♭-C-F (measure 6 and its replicates); the first chromatic variant, A♮-C-F (measure 84, to which E♭ [D♯] has been added); and the second chromatic variant, A♭-C♭-F♭ (measures 85/88.) Any of these choices may lead effectively to some form of supertonic. As explained in the context of the Mazurka in F Minor, op. 7/3 (see page 96, above), the addition of D♮ to F♭A♭-C♭ results in II⇨. It turns out that Chopin makes use of that strategy during this phrase. The abandoned F➔ chord consequently is displaced by an alternative 6-phase chord a half step lower, achieved by tapping the potential for F➔ (= F-A♮-C-E♭) to function as a B⇨ chord (= D♯-F-A♮-C, confirmed by the shift of ninth C to root B♮ during 843). Though Chopin proceeds through the circle of fifths (F B♮ E♮ from 843 through 851), the E♮ functions as ♭ rather than as ♮ . (In fact, Chopin spells the chord as F♭-A♭-C♭ just before resolving to II⇨ during 881.) Adding further interest to an already abundantly fertile region, the F♭ chord is prolonged via a modulo 12 circular progression that divides the octave into three equal (parts (4 0 8 4, spelled as E♮ C A♭ F♭) in measures 85 through 88.17 Once that cycle has concluded and the D♮ has been added to instill the II⇨ function, the V7–I cadence occurs without incident between 882 and 891. The coda expands upon an idea from measures 1 through 4. In that earlier context, A♭-D♭-F serves as an embellishing chord of the tonic. During the coda it is twice asserted as IV (above a tonic pedal point), each time followed by V7 and I [3.12b]. (The second of the two phrases contains several borrowings from the parallel minor key, including IV’s minor third, F♭.) Two sonorities are particularly vivid and unusual. In measure 91 the chromatic passing note F♭ (which Chopin spelled as E♮) sounds simultaneously with anticipations G♮ and C (not graphed), creating a memorable sonority against pedal point A♭. The momentum stalls during the second phrase as the local fifth-progression descends through to
. Cadential chords with both minor- and major-key inflections are
auditioned. The descent continues downwards to for a PAC only on the third try, during which the minor-key (C♭, spelled as B♮) is supported by the dominant’s third G and the chromatic passing note E♭ (spelled as D♮) connects the dominant’s root E♭ (imagined) and seventh D♭.18 The remaining measures of the coda provide echoes of Kopfton (at 1041, 1081, and 110–111) and restore the embellishing role of A♭-D♭-F (at 1073–1081).19
Opus 59/3 Pillar closure is of special interest in the Mazurka in F♯ Minor. Because the irregular pillar of the a1 region concludes on the mediant (measure 16), Chopin restructures the a2 region’s second phrase, with the apparent intent to achieve a PAC [3.13a]. However, measure 44 does not offer the expected tonic resolution. Instead, the dominant is extended, embellished by pitches from F♯ Major. The a2 region’s tonic goal (with melodic F♯ concluding a middleground fifth-progression descending from Kopfton C♯) merges with the B section’s initiating F♯ Major tonic (with melodic C♯ reinstating the mazurka’s Kopfton) in measures 45 and 46. Since neither of the preceding pillars offers a normative PAC, Chopin has no precedent for building the mazurka’s final tonic pillar (A2), where he electively inserts an extended cadenza-like passage between the second phrase’s seventh and eighth measures (115 and 134). As we shall see, the initiation of the pillar during A2 likewise departs from a conventional formulation. Example 3.13 Mazurka in F♯ Minor (op. 59/3) (a) Analysis of the work; (b) Analysis of mm. 64–70; (c) Analysis of mm. 80–134; (d) Analysis of mm. 115–134.
The a1 tonic pillar opens with a robust projection of Kopfton C♯ in two registers: C♯B>A third (with unfolded upper thirds), presented in the context of a mediant prolongation. The region’s one new – and vital – structural element occurs during the final beat of measure 24: the middleground progression’s and its dominant support. This event occurs at the precise moment when one would have expected instead to hear the initial C♯ of a2 (as in 03). In this case the C♯
replaced by IV5–6), so that measure 43 counts as the phrase’s
seventh measure. The dominant of that measure “should” resolve to an F♯-A-C♯-F♯ tonic in measure 44. As mentioned above, Chopin instead extends the dominant, postponing the tonic attainment until the onset of the B section. Coinciding with a shift to F♯ Major, the B section’s opening phrase shares several features with the tonic pillar’s first phrase. In both contexts the phrase’s third measure presents a embellishment of the tonic. (That is unfurled during the a1 region’s second phrase and during the B section, and both of those realizations are preceded by a surging F♯-A♯-C♯-E.) Both phrases likewise achieve their dominant goals via a tonic 6-phase chord (in measures 6 and 50) leading to II➔.
The return to tonic F♯ Major that we expect after the B section’s first phrase and its repetition is magnificently expanded in measures 64 through 70 [3.13b]. Whereas melodically the Kopfton C♯ might have proceeded directly to the dominant’s seventh B before resolution to A♯, here an upward melodic excursion through E♯ (at 523, repeated at 643) to G♯ (at 651, repeated at 751) occurs.20 As with the upward C♯B sixth between measures 65 and 70, is stepwise – in this case chromatic. Supporting that descent is a chord progression that begins as a tonicization of the C♯ dominant (I5–6 II➔ V7 I) but that then continues unabated as a circle of fifths (continuing the tonicizing progression’s chain of fifths: A♯➔ D♯➔ G♯➔ C♯➔ leading to F♯➔ and beyond). As always in such a circle, if the initiating chord is to return as the eighth chord, one of the fifths must be imperfect. Observe that the A♮ chord at 683 lacks a minor seventh and thus does not strongly project the sense of A➔, targeting D♮. That is where Chopin inserts the corrective diminished fifth, A♮>D♯. The juncture of the B and A2 sections (measures 96|97) is the site for a creative structural variant. In most cases the return of the so-called “tonic” pillar will project the tonic harmony at or near its outset. In this case, however, the B section’s closing measures proceed to a dominant harmony at that location. (See 3.13c, to be discussed below.) Things are out of kilter here: though one background dominant has occurred during the B section, guiding the Urlinie’s to , another dominant generally would occur to support , which, interrupted, would resolve to after the A2 section’s post-interruption downward fifth-progression from a restored
. All of these features are displayed in
3.13a, though with one curious shift: the background dominant is delayed until the first phrase of A2. What had been a local dominant in measures 8 and 32 now functions at the background level. To accomplish this, Chopin places the dominant root C♯ at the bottom of the phrase’s initial chord (which earlier had served as the tonic), thereby converting it into a embellishment of the dominant. In this context the G♯➔ chord of measure 103 (matching that of measure 7) serves as an embellishing chord inserted before the ’s resolution to
.
Given the highly idiosyncratic start of A2, the preceding B section must conclude atypically with a chord that will lead effectively to V♯. There is no better choice than II⇨. Yet Chopin first auditions another trajectory following the internal tonic of measure 70: he leads to the mediant via a circle of fifths (F♯ B E♯ A♯ in measures 73–74), reminiscent of measures 9 through 16 (here converted to a major-mode context). As the earlier b region reminds us, III (here represented by the parallel major key’s major mediant, A♯-C -E♯) may lead directly to V♯. Yet Chopin instead backtracks, repeating the background (measure 80) and then restoring F♯ Minor (measure 87), followed by an alternative circle of fifths (displayed in 3.13c) that leads not to the mediant, but instead to the supertonic (II⇨). This is accomplished in an ingenious way. From tonic F♯, B➔ E➔ A➔ D➔ transpires without a hitch. At that point, Chopin takes advantage of a wondrous enharmonic equivalence: D-F♯-A-C♮, which we might expect will lead to a chord rooted on G♮, instead takes on an alternative meaning as B♯-D-F♯-A, a chord rooted on G♯. Since at one point a half-step shift is required to keep the circle of fifths on track (as we noted above in the context of the D♯ chord in measure 69), Chopin astonishingly brings about that shift by doing nothing! Upon arrival D-F♯-A-C♮ is A➔’s rightful successor, D➔; upon departure B♯-D-F♯-A serves as G♯⇨, C♯’s rightful predecessor.21 (In 3.13c the chord is written twice – juxtaposing its alternative spellings – and analyzed first as a chord rooted on D and then as a chord rooted on G♯.) From II⇨’s resolution to V♯ (with extended embellishment), the progression continues as described above. In that measure 115 corresponds to measure 43, listeners should sense that the moment of closure is close at hand – potentially as early as measure 116. Chopin delays that resolution until measure 134 by proceeding through a cadenza-like passage (indicated by open brackets in 3.13a and presented in detail in 3.13d). Initially the C♯ dominant is tonicized, with an idiosyncratic ascending 5–6 sequence leading from C♯ to its dominant G♯ (measure 119) and back.22 The melodic connection of G♯>B in measures 119 through 121 is reminiscent of the same interval in a similar context in measures 65 through 70. At measure 122 an internal IAC occurs, consequently postponing the deeper closure (with background ). The harmonic progression that begins thereafter has the promise of bringing about a PAC due to the melodic G♯ that arrives in measure 127, but yet another
G♯>B sixth transpires, so that the tonic of measure 131 likewise is not “the” closing tonic. The lowered supertonic chord that follows finally breaks the spell: as 3.13d shows, the dominant of measure 133 does succeed in bringing about a PAC.23 A coda follows. (Its essential features are graphed in 3.13a.) Given that a Picardy third occurs at the preceding PAC, the coda traverses the major-key fifth-progression C♯>B>A♯>G♯>F♯.
Idiosyncratic tonic pillar contexts
Opus 33/4 The opening tonic pillar in Chopin’s Mazurka in B Minor (measures 0|1 through 24, followed by a written-out repeat) is classified as irregular because it cadences on the dominant. This is a conventional sort of irregularity, like several we encountered earlier in this chapter. Chopin makes a predictable adjustment during the pillar’s final presentation, where the second phrase concludes with a PAC (measure 200).24 Such a construction justifies the mazurka’s placement within this chapter, though not within this section, which is devoted to idiosyncratic pillars. That categorization results from Chopin’s extraordinary continuation after the HC of measure 24: the a1 pillar is repeated, but with a remarkable, strange, and unexpected turn of events at its cadence. The lowered supertonic (“Neapolitan”) chord arises naturally in a minor key: a diatonic presentation of I5–6 (here B-D-F♯ to B-D-G) produces a chord that (especially when enhanced by the addition of the pitch F♮ to B-(D)-G, as at 171) inherently leads towards ♮II. In accordance with an unwritten covenant among composers pertaining to the use of the lowered supertonic, the key’s foundational B
Example 3.14 Analysis of Mazurka in B Minor (op. 33/4).
Through 482 it will seem to listeners that a routine repeat of the entire opening tonic pillar is being presented. Yet the performer will note, perhaps with some alarm, that the expected goal root F♯ (as in measure 24) is notated as G♭ in measure 48. Chopin indeed fulfills the implications of that spelling: the line ultimately proceeds as G>G♭>F♮, with G♭ serving as a chromatic passing note. Whereas II➔ generally proceeds to V (as in measures 5 and 6), the lowered supertonic’s inherent dominant-emulating tendency generally will not be tapped by composers, since ♮II➔ leads into the abyss: it points towards the tonic’s antipode, in this case F♮. Consequently the meek F♮ at the end of measure 48, which in
fact introduces that antipode, is an astonishing event. It causes the b region, which commences in measure 49, to open in the highly unusual key of ♭I. Ultimately the mazurka’s tonal course will be corrected: by the end of the b region the conventional F♯ dominant is attained. Yet a half-step depression within tonal space prevails from 483 through measure 63. How is this accomplished? Whereas F♯ is expected in measure 48, F♮ occurs instead (as explained above); and whereas F♮ is expected after what should initially be interpreted as a C chord in measure 63, that chord is enharmonically transformed into an F♯ chord. Observe in 3.14 how ♮II in B Minor is reinterpreted as II in B♭ Major, leading to V in that key. Given that build-up, it is not surprising that the b region robustly asserts a B♭ Major tonic. In fact, a standard progression prevails in that key through measure 63: I is followed by IV, and IV undergoes a 5–6 shift in which the 6-phase E♭-G-C sounds in its evolved state E♮-G♭-B♭-D♭ (= II⇨). Without the visual clues that Chopin provides in the score, listeners should reasonably expect this chord to resolve to V in B♭ Major. Yet Chopin (as also most readers of this book) certainly had learned that this particular variant of II (often referred to as the “German” augmented sixth) may be enharmonically transformed into a dominant seventh. It so happens that this C⇨ chord’s enharmonic equivalent is the very F♯➔ chord that would lead the progression back to B Minor. Under normal circumstances the mazurka might continue with a2 (concluding the A1 section) followed by B, after which a concluding A2 would offer the final PAC. Yet in this case there are two contrasting a1 models from which the content of a2 might be derived: either the conventional irregular version of measure 0|1 through 24, which ends on V♯, or instead the key-shifting irregular version of measures 25 through 48, with its half-step depression. By choosing the latter for a2, Chopin arrives at a tonal juncture (at the end of measure 88) not well suited to precede a normative B section (which in this case will begin in the initial tonic’s parallel key, B Major). Rather than grapple with that juxtaposition, Chopin takes the unusual step of inserting a full statement of the b region, thereby putting his tonal house in order before the onset of the B section. Though b content is employed, Chopin achieves the same tonal goal as if a2 had instead proceeded as in the initial a1 model. This is the only instance of a direct succession from a b region to a B section within Chopin’s published mazurkas: the b designation in 3.14 truly deserves the exclamation point that annotates it.
The B section opens in measure 105 with two eight-measure phrases, each proceeding from the tonic to the dominant in the key of B Major. Both phrases are shaped by the traversal of a descending fourth from Kopfton F♯, thereby matching the contour of the original a1, though with alternative harmonic routes between the initial I and goal V. The next sixteen measures repeat these phrases with modest adjustments and one significant change: the second phrase concludes without achieving its dominant goal. The dominant instead serves as the initial chord of the following phrase, where it supports background , which is followed by ♯ at the tonic resolution. After several repetitions, the passage breaks off at background , supported by V♯, in measure 151. A written-out cadenza that expands the dominant (and recalls content from the preceding measures) transpires during the next seventeen measures. As mentioned above, the original tonic pillar is constructed in such a way that a PAC may be attained with minimal modification. Yet Chopin’s tonal plot thickened during the initial a1’s repetition: due to the extraordinary C♮G♭>F♮ again lead away from the B Minor dominant? No! Aroused afresh, Chopin instead uses C♮, the other of the two pitches he has been dangling before the listener, as the initiation point for a similar descent in half steps: C♮>B>A♯ introduces the B Minor dominant’s leading tone. The measure (200).
and I that conclude the mazurka sound within a single
Opus 56/3 Chopin’s Mazurka in C Minor contains one of the most astonishing constructions in his entire oeuvre. To understand it, imagine a keyboard mechanism placed on rollers, so that it may move freely to the left or right, consequently hitting different piano strings and thereby facilitating transpositions. Whereas normally such a mechanism would be in the locked position, imagine a pianist performing a mazurka with it accidentally unlocked while several earthquake tremors occur, moving the keyboard a total of seven times to the right, each resulting in either a half-step or a whole-step shift. Despite these seismic shifts, the performer maintains the integrity of the tonal plan according to what the fingers are doing instead of according to the sounds that the strings are emitting.25 It so happens that these seven seismic shifts add up to twelve half steps, so that, despite the extraordinary sonic output, the mazurka ends in the key in which it began. The mazurka’s basic tonal plan incorporates an irregular tonic pillar – I II V♮ – during its A1 section and prolongational I II V I progressions in the dominant key during both the A1 and B sections. The chordal roots are displayed in the context of C Minor at the top of 3.15a, with much of the content in that line shaded to indicate where seismic shifts ensue, resulting in alternative sonic output, as displayed below the shaded regions. The A1 section opens with a progression that broadly extends from I to V♮, incorporating an evolved tonic 6-phase chord and a minor supertonic [3.15b]. Chopin proceeds with a written-out repeat, during which a seismic shift raises supertonic D to E♭ in measure 49. Whereas the minor D chord might have undergone chordal evolution so as to result in a D➔ surge directed towards dominant G, now instead E♭➔ targets “dominant” A♭, which arrives in measure 52. Another seismic shift affects a repetition of that passage: F➔ B♭ occurs in measures 53 through 56. This B♭ chord represents C Minor’s dominant even if by now the seismic activity has moved it three half steps higher. The tonic pillar concludes with a prolongation of this “dominant,” engaging a fifth-progression in the melody during measures 56 through 72 (with the normative D>G dominant span raised to F>B♭). Though at first the chord introduced in measure 57 may seem to be yet another II➔ (a third seismic shift: E♭➔, F➔, F♯➔), the progression ultimately incorporates that chord within the B♭ “dominant” prolongation. Consequently the chord spelled by Chopin as if its root were F♯ functions as a C-rooted chord (initially II⇨ in tonicized B♭ Major, shifting to II➔ during measure 68), as clarified by the modified spelling in 3.15b.
Example 3.15 Mazurka in C Minor (op. 56/3) (a) Tonal content of mm. 2–136; (b) Analysis of mm. 0|1–136; (c) Analysis of mm. 137–220. Onset measure
Seismic shift (in half steps)
2
C Minor:
Foundational progression
C
D
(= G Major:
G
––––––––––––
–––––––––
G
A
G )
D
49
+1
E♭
A♭
53
+2
F
B♭
134
+2
D
G
135
+2
E
A
135
+2
F♯
B
136
+2
G♯
C♯
136
+1 ____ +12 = octave!
C
G
The key of B♭ Major prevails during most of the B section (from measure 73 until the renewed seismic activity beginning in measure 134). That choice conveniently allows the composition to retain the pitch D as : though normally D would be the fifth of dominant G Minor, here it instead serves as the third of the seismically achieved “dominant” B♭ Major. The ternary B section opens with an x1 region (measures 73 through 88) that pursues the tonicizing I II V I harmonic progression that will be subjected to numerous seismic shifts during the x2 region. (Note how the B♭ tonic extends through the end of measure 77, where elements of its embellishing chord – F and C – and its surging third and minor seventh – D and A♭ – collide.) The B section continues with a y region that, after adopting the hue of B♭ Minor, leads conventionally via II➔ to the dominant in measure 105 (extended through measure 120). Though a middleground interruption of the melody on
typically would be
resolved by during the x2 region, the intended DC>B♭ melody that is initiated in measure 121 is jolted by repeated seismic shifts that move the goal B♭ up a major sixth to G (in the bass at 1363). Examining the phrase that begins with melodic pitch D at 1291, note how upper-neighbor E♭ is supported by II at 1341. This C-G-E♭ chord might evolve to surging B♭-E♮-D♭ (= II➔) before dominant A♮-F-C (whose C would be
within the
local melodic descent) arrives. Yet at that very moment a new wave of seismic shifts begins, so that B♭-E♮-D♭ is jolted upwards to C-F♯-E♭ (thereby being distinguished from the preceding diatonic II only by the half-step descent of G to F♯). The dominant’s thus is represented by D – rather than by C – at the end of measure 134. Each of three repetitions of II➔ V coordinates with another whole-step seismic shift, so that V within
the dominant prolongation, represented by an F chord during most of the B section, is raised not only to root G, but also to A♮, B♮, and C♯. Whereas the G♯-B♮-D-F chord at 1362 might initially be interpreted as yet another whole-step shift (as C -E♯-G♯-B♮, functioning as II➔ in G♯), the bass instead descends as G♯[A♭]>G, and therefore the goal I of the dominant-tonicizing progression is achieved. Whereas the “dominant” C♯ chord of 1361 normally would resolve to F♯, one final seismic shift – this time the shift of a half step – leads to goal G, completing the trajectory presented in 3.15a. The tonic pillar of A1 is doubly irregular: not only does it conclude on V♮, but that V♮ has shifted seismically upwards a minor third. During A2 we expect that such irregularities will be foresworn and that the tonic pillar will conclude regularly – with a PAC on tonic C (to which Chopin applies a Picardy third, E♮, in measure 189). The decisive swerve away from the precedent of A1 occurs at measure 173. The ensuing progression begins as if Chopin intends to pursue a conventional harmonic course: I IV5–6♭
in measures 171
through 176. Yet the chord with bass B♮ in measure 176 eventually evolves into the chord with bass C♭ in measure 180. From that point, the bass moves chromatically downwards to F (at 1871). As 3.15c shows, an idiosyncratic descending circle of fifths that connects IV’s 5-phase F-A♭-C and chromatic 6-phase F-A♭-D♭ chords propels this line.26 This extended IV yields to
in measure 188, followed by goal I♮ in measure 189.
The coda, which commences in measure 189, contains a double CC bass arpeggiation, supporting
and
. Each half is repeated, as
is conveyed by the measure numbers annotating 3.15c. Chopin’s treatment of ♭ is of special interest. When D♭ occurs below
, it at first reverts to D♮ (at 1963) before V♮’s
resolution. Yet during the repetition of that segment the wobbly note does not yield to the diatonic pitch: D♭ holds out at 2043. However, during the span from wobble yields to D♮ in both traversals, at 2083 and at 2123.
to the D♭
Opus 59/1 The Mazurka in A Minor is constructed in the most extended of Chopin’s mazurka forms, with four tonic pillars in all: A1 and A2 sections (both with a ternary division into a1, b, and a2 regions) surrounding an internal B section (where the parallel key – A Major – prevails). Chopin defies his own conventions by presenting the third of the tonic pillars (at the onset of A2) not in A Minor, but instead in G♯ Minor. As we shall see, he begins preparations for this unusual event as early as A1’s b region. The mazurka’s inaugurating tonic pillar opens with a three-measure prolongation of the tonic’s E-G♯-B-D embellishing chord. (A local embellishment in measure 1, before E sounds at the bottom of the texture, should not be confused with the arrival of tonic A.) This chord will be asserted as a relatively deep structural V♯ at the onset of a2 (measures 25–27), following a b region that proceeds only as far as an evolved IV6. (See 3.16a.) The juxtaposition of surging B➔, E➔, and A➔ chords during measures 9 and 10 and the weak metrical placement of the A➔ chord might call into question the deep structural role assigned to that A chord in 3.16a. Yet an elision occurs: instead of a conventional expansion of the broader I-space (via a local supertonic and dominant) followed by a transformation of the goal I to surge towards IV, the tonic reinstatement at 103 is already surging. Perhaps compensating for this fleeting A-chord restoration, an expanded version of the progression during the b region extends the equivalent tonic harmony for five measures (17 through 21) before proceeding to IV♯.
Example 3.16 Mazurka in A Minor (op. 59/1) (a) Analysis of mm. 1–36; (b) Analysis of mm. 37–130.
The Kopfton E is the first pitch heard in the mazurka. Extended via upper-third G (in conjunction with the local shift to tonic A Minor’s upper-third chord – C-E-G – in measures 5 through 8), a middleground descent – E>D>C – over the course of the pillar likewise incorporates an upper-third embellishment of D (F>D in measure 11) before goal C, presented as an anticipation at the end of measure 11, sounds. The descent only as far as during the initial tonic pillars (a1 and a2) will affect how Chopin proceeds during the B section (measures 37 through 50) and will be rectified during A2’s a2 region, to be explored below.
The b region draws upon a1’s establishment of the A Minor tonic and of Kopfton to launch its tonal trajectory, which is similar to that which inaugurates a1: the II➔ of measure 13 replicates much of what occurred in measure 9, leading to V♯ in measure 14 (as in measure 10). What follows is unusual, an instance of a seismic shift. Instead of proceeding directly to I➔, Chopin repeats the II➔ V♯ succession in a transposition down a half step (measures 15 and 16), consequently achieving tonic A not via its normative E dominant predecessor, but instead via E♭ – its antipode! This half-step depression is displayed within a box in 3.16a. While the ear may succeed in making the broad connection between roots E (measure 14) and A (measure 17), the passage sets the stage for a more remarkable deviation that will occur later, at the onset of A2. Though a b region often will conclude on V♯, here the dominant function is already built into the initial measures of the tonic pillar, as mentioned above. Consequently the prolonged I➔ of measures 17 through 21 proceeds only to IV♯ and its evolved 6-phase chord (D♯-F♯-A-C) before the pillar theme enters in the left hand at 251. The a2 tonic pillar’s progression is similar to that of a1, with the structural melody again descending E>D>C. The goal C is transferred down an octave and wobbles to C♯ for the onset of the B section (in A Major) in measure 37. Indeed the fact that the linear progressions descend only a third from during the initial two tonic pillars results in some unfinished business that Chopin addresses at the onset of the B section, where the major-hued C♯ yields to B and then A in measures 37 through 42 [3.16b]. Only upon that line’s completion is Kopfton E freshly stated, with a full descent of the E>A fifth transpiring during measures 42 through 50. The E>D>C♯ component of that fifth is complemented by ascending motion in the bass, in an A5–6 B5–6 C5♯ sequential trajectory. A C♯➔ chord is, of course, a common predecessor of the tonic’s 6-phase chord. The next round of tonic prolongation (measures 49 through 82) is extraordinary. Note the extended prolongation of the E minor chord first sounded in measure 56. Chopin explores several possible continuations before proceeding through F♯➔ to B➔ in measures 71 and 72 (the version displayed in 3.16b). That B chord “should” lead to dominant E. (Compare with the B chord of measure 13.) Yet at that point an extended half-step depression (another seismic shift) begins. Now with augmented fifth, B-D♯-F
leads not as expected to E-G♯-B (to inaugurate the third statement of the tonic pillar, as in measures 25 and 26), but instead to D♯-F -A♯, which shares two common tones with the preceding II➔. This D♯ “dominant” sets A2 in motion, resolving to “tonic” G♯ in measure 82. The entire a1 region maintains this half-step depression. Fortunately Chopin has already devised a means of re-establishing the rightful tonal center. The depressed chords of measures 15 and 16 (displayed within a box in 3.16a) are the same as the last two depressed chords displayed within a box in 3.16b. Chopin simply persists along the course of a1 and b until those chords emerge (stating them twice so as to maintain the dimensions of the b region from A1), and then does exactly what he did during the earlier b region to emerge out of the depression. (Compare measures 16–17 and 94–95.) The remainder of b and the onset of a1 correspond to their counterparts within A1. Whereas both the a1 and a2 tonic pillars within A1 traverse the linear progression of a third descending from Kopfton , during the final pillar (the a2 of A2), a revision of the harmonization in measure 114 prevents the occurrence of an unsuitable IAC. (See 3.16b.) The pitch C (background ) is supported by an embellishing chord (D♯-F♯-A-C, which later evolves into D♯-F♮-A-C) that comes between presentations of the dominant supporting (at 1133) and (at measures 123 through 129). The PAC in the work’s final measure coordinates with the descent from B to A (= ) in conjunction with the tonic’s arrival. Despite the irregularities of cadence and tonal center that have characterized the earlier statements, a regular tonic pillar – in A Minor throughout and with a full descent from to – finally prevails.
Part II ◈
Masterpieces
4
Étude in C Minor (op. 10, no. 12) ◈ in response to Graham H. Phipps Graham H. Phipps, drawing upon precepts of the eminent Austrian theorists Simon Sechter and Arnold Schoenberg, offers a robust study of Chopin’s Étude in C Minor in an article from 1983.1 That composition was selected with good reason: Phipps was keen to explore Schenker’s extensive and detailed graphs of the work and to reveal ways in which his own Sechterian/Schoenbergian perspective offers contrasting and, in his view, superior insights, just as my taking up the work again now offers an opportunity to assess Phipps’s perspective. I, too, am uncomfortable with aspects of Schenker’s reading, but so as not to complicate the presentation or distract from my focus on Phipps’s analysis, my comments relating to Schenker’s graphs will be relegated to the notes, for the most part. Phipps contends that Schenker’s theory is “restrictive in a manner which prevents him from perceiving significant musical relationships” (p. 544) and that it is at fault by (as Schoenberg contends) “ignoring the musical facts” (p. 545). He does not attempt to build upon Schenker’s insights, as I do.
The introduction and the A1 section, part 1
The introduction and the A1 section, part 1 (measures 1–18) Charged with preparing the C Minor tonic arrival at 91, the introduction projects two variants of the tonic’s most characteristic embellishing chord: G-B♮-D-F and its more potent variant, B♮-D-F-A♭. Whereas the A♭>G appoggiatura of 11 is reiterated con forza at the top of the texture during 51 (embellishing the pitch G, which will emerge as the work’s Kopfton), that motive is raised a step – to B♭>A♭ – during 73 to assert the chordal ninth, which reverts to G during 83 as a G>E♭>C arpeggiation of the tonic triad commences. (Make special note at this point that I underline the pitch names G and A♭. My contention that the work’s Kopfton is G – rather than E♭ – likely will be controversial, and so my attentiveness to how G is deployed throughout will warrant the reader’s attentive consideration.) Through this means the A1 theme’s GG neighboring-note motive is adumbrated during the introduction. (See 4.1.) That tonic arpeggiation also provides the unfolded E♭>C resolution of the introduction’s pervasive
diminished fifth. (Thus
advocates of Kopfton may also find supportive evidence in Chopin’s introduction.) This third (ascending from C to E♭ and filled in by passing note D) likewise is incorporated within the A1 theme.
Example 4.1 Analysis of Étude in C Minor (op. 10/12), mm. 1–18.
The descending triadic arpeggiation leading into 91 is complemented by the A1 theme’s ascending arpeggiation during measures 10 and 11: C
subservient role: B♮ and D belong to the prolonged embellishing chord, whereas C does not. As the introduction progresses the underlying arpeggiated chord intensifies, evolving from B♮-D-F-G to B♮-D-F-A♭. Consequently the A♭>G second of 11 (and numerous other statements through 63) is elevated to B♭>A♭ during 73. Phipps does not make that association. Instead he proposes that this B♭ serves as a chord member: the dominant root in a potential shift of the tonal center to E♭ Major (p. 554 and ex. 2, systems 2 and 3). Whereas I perceive an unwavering presence of B♮ (against which B♭ clashes) from its sounding during 73 to its sounding during 82, Phipps places the B♭ on a higher plane, with a B♭>A♭>F>D arpeggiation of V7 in E♭ Major potentially resolving to its tonic during 81. That interpretation requires some curious hierarchical shifts: in a context in which the first and third sixteenth notes of a beat embellish the second and fourth, exceptionally the B♭ during 73 and the E♭ during 81 must counter that trend.3 Phipps proposes that the introduction serves as the Schoenbergian Grundgestalt for the Étude. If that is the case, then it seems to me he has overlooked an important feature of its shape: the neighboring motion from G to A♭, then back to G (as displayed in 4.1), conveying an intensification and then retreat prior to the tonic resolution. That process is then mapped onto the tonic, with the A♭ at 121 embellishing Kopfton G. It is heartening to know that Phipps (in alignment with Sechter’s view) concurs with my reading of the F♯-A♮-C-E♭ chord’s root as D (measure 14), though my II➔ label (or II with numbers, accidentals, and a bullet symbol, as in 4.1) conveys something slightly different from his “dominant of G” terminology (p. 556). Phipps suggests that the emergence of this chord will come as a surprise: focusing on the right-hand A♮-C-E♭, he proposes that root F♮ is “expected” in the left hand. I hold a more neutral perspective on what might happen after a phrase’s initial tonic, regarding II (in which A♮, C, and E♭ serve as the fifth, seventh, and ninth) and IV (in which those pitches serve as the third, fifth, and seventh) as equally viable successors. In this case Chopin employs F♯-A-C-E♭, initiating an exploration of the chord’s mehrdeutig character.4 Here it leads to G, whereas, reinterpreted as A-C-E♭-G♭ (which Chopin presents in its F-A-C-E♭ variant), it
leads to B♭ in measures 24 and 25, and, reinterpreted as C-E♭-G♭-B , to D♭ in measures 64 and 65. Phipps and I propose opposing hierarchies for the chords of measure 15. Whereas he regards the first-inversion G major chord at 151 as the onset of a “four-measure resolution” – extending through measure 18 – of the F♯-A-C-E♭ “dominant” (p. 556), I instead regard all that has transpired within the phrase thus far as contributing to the establishment of the phrase’s initial I-space, culminating in a potent I➔ at 153–4. (Phipps and I agree that this chord functions as a tonic, as a comparison of his ex. 6 and my 4.1 confirms.5 We disagree regarding its hierarchical depth.) Consequently the IV at measure 16, which supports the the melodic path between and
on
, resides deeper within the structure in my
reading than in Phipps’s. A consistent descending half-step motive transpires within many of the phrase’s measures: from the melody’s signature A♭>G in measure 12 to the bass’s B♮>B♭ and A♮>A♭ (measures 15 and 16) to the melody’s E♮>E♭ and E♭>D (measures 17 and 18). Though Phipps’s ex. 6 displays most of these seconds, for the most part he does not propose any hierarchical relationships among them. Had he done so, the contradiction between the B♮>B♭ pitch hierarchy and the V (I) analytical hierarchy in measure 15 would have stood out glaringly.
The A1 section, part 2 (measures 19–48)
The A1 section, part 2 (measures 19–48) After a two-measure allowance for the C Minor tonic chord to settle in (measures 9 and 10), the A1 section proceeds with eight measures – 10|11 through 18 – during which Chopin traverses a conventional I-to-V♮ harmonic progression, supporting the descending melodic fourth from Kopfton G to D. That content is reprised in a more definitive and much expanded statement during measures 21 through 41, which are organized as 8 + 8 + 5 measures. (The five-measure unit dovetails with a reprise of the introduction material. The tonic re-emerges in measure 49 to inaugurate A2.) Whereas in the first phrase the bass trajectory from C through B♭ and A♭ to G coordinates with the harmonic progression I ➔ IV V♮, for the expanded version Chopin instead pursues a circular progression that incorporates C, B♭, and A♭ as roots (C F B♭ E♭ A♭ … ), thereby providing an alternative means of support for the stepwise descent from Kopfton G. The circle’s component chords are delineated in 4.2, in which two alternative conclusions for the passage are juxtaposed. (These measures are displayed in graph notation in 4.3, which will be introduced during our consideration of the A2 section but which may be consulted now.) Chopin in fact jumps off the circle’s tracks in an unexpected development over the course of measures 33 through 35. How does he initiate the circular progression, and why does he elect to abandon it?
Example 4.2 Analysis of Étude in C Minor (op. 10/12), mm. 21–41.
Example 4.3 Analysis of Étude in C Minor (op. 10/12). The two parts of A1 begin along the same course: measures 10|11 through 13 map onto measures 20|21 through 23. Even the melody’s A♮ at 241 stems from the earlier passage. Yet the upward drive initiated by that pitch now persists for three measures, in coordination with a crescendo and even a stretto. Though numerous combinations of pitches sound during these measures, I propose that they are guided by an evolutionary process that may be expressed in symbols as C ➔ ⇨: that is, in targeting the circle’s second chord (F during measure 27), the C minor tonic chord first becomes dominantemulating (C-E♮-G-B♭ during 261–2) and then takes on an augmented-sixth character (E♮G♭-B♭-(D♭) during 264). The augmented sixth (which most often occurs in the context of a supertonic), in coordination with the embellishment of the following major F chord, gives a strong sense of a B♭ Major tonicization (II⇨ V I) to the passage from 264 through 281, though from a broader perspective this trajectory remains bounded by C Minor’s C tonic and potential G dominant. With that internal B♭ Major tonicization in mind, the A♮ of measure 24 serves as a diatonic component of a sequential connection between the C supertonic’s root position and surging first inversion: m.
(=
23
24
x
25
C5–
–6
(D5–)
–6
26 E♭5
E♮6
C ———————————————————)
This sequence is somewhat rambunctious, in that the D5 component is elided. The addition of the pitch F to C6 fosters the direct link to D6, as F➔B♭.6 Drawing upon the momentum
generated thus far, Chopin extends further during measure 26, from C to E♮ in the top voice and from E♮ to G♭ in the bass. Root C finally yields to root F at 271. Chopin begins a shift from notation in flats to notation in sharps during measure 28. The curiously juxtaposed G♯ and B♭ during 284 should be regarded as components of a B♭7 chord, targeting the circle’s next component, E♭ [D♯].7 Chopin complicates matters by employing an unfurled embellishment to precede that E♭ arrival (measures 29 and 30), as displayed in 4.2.8 Consequently the B♭ chord’s dissonant A♭ [G♯] at 284 is suspended for a full measure before resolution to G♭ [F♯] at 301. Though the similarity in how the F chord in measure 27 and the E♭ chord in measures 29 and 30 are embellished might have created a parallelism within the circle, the E♭ chord’s minor quality prevents it from imparting a dominant function. (Thus a potential tonicization of A♭ Major following that of B♭ Major is declined.) Yet the minor quality of the E♭ [D♯] chord followed (after some linear connection) by an A♭ [G♯] chord of dominant character (measure 33) constitutes the onset of an alternative and quite striking tonicization: that of the lowered supertonic (Neapolitan) key, D♭ Major. The continuation marked as “Alternative 1” in 4.2 realizes that potentiality and proceeds onward to the G goal. However, Chopin abruptly changes course after the A♭ [G♯] chord. If left unattended, a descending circle of (perfect) fifths does not chart a course from the tonic to the dominant. Instead, C would lead through F, B♭, E♭, A♭, and D♭ to G♭, the tonic’s antipode. Composers are left with two options (unless they are willing to take the long route – reaching G [A ] at the circle’s twelfth chord): either they can modify one of the perfect fifths by a half step (generally at F–B♮, at A♭–D, or at D♭–G); or they can abandon the circular progression before the dominant arrives. The two alternatives displayed in 4.2 reveal how these options might be realized. In the first, the melodic descent overshoots the mark, requiring a corrective shift from D♭ to diatonic D♮ in coordination with a D♭–G diminished fifth in the bass. This is a common occurrence in music, one that Chopin in fact will call upon later in the Étude (as the measure numbers 72 and 75 in 4.2 indicate). Yet he here elects instead to pursue the second of the two options, deploying two seismic shifts to hoist the A♭➔ [G♯➔] chord targeting D♭ upwards first to B♭➔ (measure 34) and then to C➔ (measure 35).9 Perhaps a factor in Chopin’s choice was the desire to realign this part of A1 harmonically with the I ➔ IV V♮ trajectory of the section’s first part, despite the altered relationship with the melody’s descent from Kopfton
G to D. Or perhaps he wanted to reserve the Neapolitan chord, which will be featured during A2 (measure 72).10 In any event, the section’s melodic goal , supported by V♮, is achieved at 411.11 Though both Phipps and I are drawn to the F➔ B♭ succession of measures 27 and 28, we contextualize it in contrasting ways. Whereas he singles out the F chord of measure 24 as “the means for movement to the B♭-major cadence” (p. 558), therefore apparently proposing a four-measure extension of F➔ (though no further details are provided), I instead interpret that initial F➔ within the expansion of an evolving C chord, with the C-to-F succession occurring over the bar line between measures 26 and 27. (Though he acknowledges a cadence in measure 28, Phipps calls the F-B♭-D chord at 271–3 a “tonic harmony in B♭ major” (p. 558), further distinguishing his interpretation of the broad C–F–B♭ circular trajectory from mine.) Equally problematic, in my view, is his assertion that this B♭ Major cadence marks a sectional close (p. 558), thereby relegating measures 29 through 40 to the status of a “retransition” (p. 564). I instead regard root B♭ as internal to a dynamic circular trajectory whose continuation to E♭ is already under way by the end of measure 28, with the arrival of B♭’s minor seventh, A♭ [G♯]. (Phipps’s detailed harmonic reduction of measures 28 through 36 – his ex. 10 – omits that A♭.) Phipps’s ex. 10 (p. 560) is rich in information. I commend his interpretation of the hierarchical relationship between the chords of measures 29 and 30, and of measures 31 and 32. (He displays IV I successions in E♭ Minor and in C♯ Minor. Schenker, on the other hand, binds the A♭ chords of measures 29 and 33, thereby reversing the hierarchy that both Phipps and I propose.12) Though I go one step
further, interpreting Phipps’s G♯-to-D♯ motion as E♭[D♯]
, and though I
do not regard this brief flourish on E♭ as a tonicization, I acknowledge that, within the context of his perspective, the analysis is exemplary. That said, the interpretation of measure 29’s content as IV (in E♭ Minor) causes syntactic difficulties, since the preceding B♭ dominant chord would be
leading to an A♭ chord. This infelicitous succession is spirited away through Phipps’s insertion of a “silent interdominant” (p. 559), which he labels as I within parentheses in his ex. 10 (between the V and IV numerals). Though I am a vigorous advocate of imaginative analysis in general, in this context – in which the B♭ dominant’s seventh, A♭ [G♯], arrives at 284 and is then retained within the following measure – the tactic’s viability becomes doubtful. (As mentioned above, Phipps avoids that issue by omitting the A♭ from his example.) I propose instead a broader, hierarchically differentiated trajectory: from B♭ (the first chord in Phipps’s example) to E♭ [D♯] (the third chord) and then onward to A♭ [G♯] (the sixth chord). Chopin’s writing in measures 33 through 37 has elicited quite different responses from Schenker, from Phipps, and from me. Schenker inserts a parenthetical D♭ chord to resolve the surging A♭➔, and a parenthetical E♭ chord to resolve B♭➔.13 Phipps, on the other hand, inserts a parenthetical F chord (presumably surging) between A♭ and B♭ and a parenthetical G chord between B♭ and C in his ex. 10 to justify Chopin’s “deceptive resolutions of dominant harmony” (p. 559). I propose a more radical interpretation, in which only the third of these chords actually resolves: the tendency inherent in the surging A♭➔ chord is simply raised two notches, first to B♭➔ and then to C➔, in the double application of a seismic shift (a strategy introduced on page 133, above). By this means the progress of the broad progression (C to A♭➔) in measures 21 through 33 is retracted through the reinstatement of the tonic chord (now surging), so that IV becomes the principal intermediary between the perimeter I and V♮ harmonies, as it was also in measures 9 through 18.
The A2 section and coda (measures 49–84)
The A2 section and coda (measures 49–84) The recurrence of the A1 section’s opening part at the onset of A2 helps to define the form as binary. (See 4.3.) Indeed, Chopin might have proceeded in a parallel construction until the vicinity of the A2 cadence, where a PAC would replace A1’s HC. He instead chose to compose fresh material that in several ways expands upon constructions already set forth. The chord of measure 14 proves to be a source from which diverse continuations flow. It was of course no secret during Chopin’s formative years that diminished seventh chords are susceptible to multiple enharmonic interpretations. In its spelling as F♯-A-C-E♭ in measure 14, it serves as II➔, leading to V♮ in a local tonic-prolonging progression (displayed in 4.1). In its spelling as A-C-E♭-G♭, it would lead to a B♭ chord. Resolving the chord’s ninth G♭ (an incidental dissonance) to F, that is what Chopin accomplishes in measures 24 and 25, as explained above. At the outset of A2 the II➔ function of measure 14 is reprised in measure 54. That leaves one remaining opportunity for a novel resolution, which Chopin fulfills with aplomb. Though the chord of measure 64 is spelled like that in measure 54, it targets ♭II, and thus its “correct” spelling would be C-E♭-G♭-B (as shown in 4.3). The downward-resolving B displaces the chordal root A♭. Yet the D♭-F-A♭ resolution that might have occurred as early as 651 is postponed through a embellishment.14 At this point Chopin taps another of the structural notions he has been pursuing: the avoidance of a functional ♭II harmony. The embellishment of ♭II never achieves its expected resolution. Recall that the seismic shifts during measures 33 through 35 resulted in the juxtaposition of three chords with the same resolutional tendency in an ascending trajectory. Only the third of those chords resolves. Now three chords with the same resolutional tendency are juxtaposed in a descending trajectory, at the downbeats of measures 65, 67, and 69.15 Only the third of these chords resolves to the expected : E♭ descends to D at 701, whereas G descends to F at the end of measure 70. At this point yet another factor comes into play: having descended a third from the potential ♭II resolution to subtonic VII, Chopin now engages (as a collision, before the
has fallen into place) a subtonic-to-dominant shift. (Compare with the third model in FC, fig. 111a.) The remainder of the progression proceeds from this dominant in a conventional trajectory, one that includes (finally!) an uncontested ♭II.16 The cadential tonic at 771 is of major quality. It is followed by a coda that twice traverses the melodic third C
place. Chopin instead interprets the D♭-E♮-G♮-B♭ chord as an evolved form of G♭➔ (appropriately spelled as B♭-D♭-F♭-A ), a transposition of the C-E♭-G♭-B chord from measure 64, thereby beginning a downward trajectory that lands on subtonic B♭ in measure 69. Phipps proposes that the chord spelled by Chopin as D♭-E♮-G♮-B♭ in measure 66 might lead to a root-position F minor chord (pp. 561–562 and ex. 13). To me that seems unlikely, given that D♭ resides in the bass.18 (A continuation to F would be probable if bass D♭ were to descend to C against the E♮, G♮, and B♭. But it does not.) Consequently for me the tension is not between competing potential resolutions to F and to C♭, but instead between remaining on D♭ (via commontone resolution) and descending to C♭.
5
Nocturne in C♯ Minor (op. 27, no. 1) ◈ in response to Felix Salzer Felix Salzer, a student of Schenker who migrated from Vienna to America at the outbreak of the Second World War, is remembered both as a central figure in the florescence of Schenkerian studies in New York City and as the author of Structural Hearing (1952), which served for several decades (until Free Composition appeared in 1979) as the principal means through which Schenker-oriented analysis could be pursued in English.1 With Carl Schachter, Salzer wrote a textbook on counterpoint; and with William J. Mitchell, he edited an influential series of volumes called The Music Forum, devoted in part to analytical essays based on Schenker’s method. Salzer’s analysis of Chopin’s Nocturne in C♯ Minor (op. 27, no. 1) appeared in the second Music Forum volume, published in 1970.2 Though Salzer does not acknowledge an involvement by Schenker himself in the Nocturne analysis, similarities between sketches in Schenker’s Nachlass3 and Salzer’s published analysis leave little doubt of a direct influence – either through Salzer’s study of the piece with Schenker during the early 1930s in Vienna or through Salzer’s access to the Schenker Nachlass, which also made its way from Vienna to New York as a consequence of Hitler’s aggression.
The A1 section (measures 1–28)
The A1 section (measures 1–28) In the manner of an Indian raga the nocturne’s C♯ Minor tonic is evoked initially through an unwavering left-hand arpeggiation. Though subdued, a harmonic progression emerges gradually out of the tonic expanse: I ➔ IV5–6♮ V⇨ I (measures 3 through 6). The foundational C♯ pedal is maintained even against B♯ and D♮ (measure 5). Enhancing the languorous mood, voice-leading activity is minimized between IV6♮ and V⇨, where Chopin takes advantage of the fact that the former’s pitch collection (F♯, A, D♮) is a subset of an evolved form of the latter’s (F♯, A, D♮, with added B♯). (See 5.1.) Chopin’s maintenance of D♮ during the dominant harmony (resulting in a ⇨ rather than a ➔ surge) flouts the near-universal practice of resolving the “Neapolitan” wobbly note (or at least allowing a place for its imaginative resolution), as Chopin does in measure 21, where the parenthetical D♯ within the local third-progression in 5.1 is justified by the sounding of D♯ within the left-hand arpeggiation. Whereas a tonic-establishing linear progression descending from the Kopfton usually follows a diatonic course, descents at several levels within 5.1 proceed as E>D♮>C♯. (The incomplete neighbor F♯ coming between E and D♮ at 43 is unremarkable, given that I➔ IV occurs in the context of Kopfton .) Another convention is flouted as well: whereas in a minor key the mediant often plays a prominent role during the bass’s traversal of the span from the tonic (at 31) to the dominant (at 94), its introduction at 71 is immediately rescinded.4 That episode nevertheless serves Chopin’s compositional agenda in three ways: (1) the diatonic E>D♯>C♯ descent to the tonic root in the bass normalizes the melody’s eccentric E>D♮>C♯; (2) the melody’s G♯>F♯>E third echoes the E>D♮>C♯ third and establishes a precedent for the prominent G♯>F♯>E span between 112 and 131; and (3) the mediant’s later emergence in measure 48 is adumbrated. The tonic pillar’s evocative calmness is enhanced by the cessation of melodic and harmonic activity in measure 10 (the final measure of the A1 section’s a1 half). Having just heard a V⇨ I succession in measures 5 and 6, listeners will understand that a tonic resolution has been deferred. The contorted dominant that lingers through measure 10 creates a singular antecedent effect. Closure is attained only with a2’s PAC in measure 18, concluding the initial presentation of A1.
Example 5.1 Analysis of Nocturne in C♯ Minor (op. 27/1), mm. 1–28. The a2 half of A1 (measures 11 through 18) is built from two phrases that relate to one another as a local antecedent–consequent pair, as graphed in 5.1. (That is, a local interruption occurs in measure 14, within the second half of the period delineated by the more basic interruption in measure 10. The dominant of 143–4 is interpreted as possessing an imagined diatonic D♯.) Note especially Chopin’s persistence in employing the F♯>D♮ third first stated in measures 4 and 5. The cadence in measure 18 completes the tonic pillar’s agenda. A written-out repeat of A1 (with variants) commences in measure 19. The listener’s sense of the nocturne’s formal shape will shift during the repeat. Whereas initially it appears that the nocturne opens with a regular tonic pillar of binary construction (in which Kopfton is introduced and then extended via a descending thirdprogression to the tonic root), the non-completion of its repetition – with the onset of the contrasting B section beginning at measure 29 – leads to the revised designation of the tonic pillar as irregular – that is, without closure on the tonic (likewise the case in many of the mazurkas that we explored in chapter 3). The agenda of measures 19 through 28 (including a two-measure extension at the end), which repeat a1, is not further pursued until measures 84 through 94 (including a two-measure preface and a one-measure internal expansion), which constitute the A2 section. In the meantime, the initial tonic and Kopfton are restored near the onset of the B section, whose exuberance starkly contrasts the languid repose of the outer A sections.
For me the A1 section’s mesmerizing effect stems in large part from the persistent traversal of descending third-progressions from Kopfton E. Comparison with Chopin’s Mazurka in A Minor (op. 7/2), measures 33 through 40, is instructive. Observe how an upward detour from the tonicized A Major tonic’s third C♯ to incomplete neighbor D precedes a descending motion through B to A four times within eight measures (graphed once in 2.15).5 The arpeggiation B>G♯>E transpires during the succession from
to
, during which the preceding
D neighbor is transferred to the tenor register for downward resolution in conjunction with the arrival of I. In the Nocturne in C♯ Minor, a similar upward detour from Kopfton E to incomplete neighbor F♯ (via chromatic passing note E♯ during the tonic’s surge, since the mode is minor) is followed by a D♮>B♯ arpeggiation during the succession from IV6♮ to a dominant configured as V⇨ rather than as V➔. Though the neighbor F♯ does not sound before the resolution during measures 5–6 or at the dominant of measures 9–10, it follows the mazurka’s precedent through transfer to the tenor register for the resolutions of measures 13–14 and 17–18. Salzer does not display a descent from the Kopfton during the first two of these four statements. Instead he focuses on an ascending third from E through F♯ to G♯. In his analysis of the third statement (see his fig. 5), an E>D♮>C♯ descent (against which F♯ resolves to E in the tenor register) coordinates with an E
to
.6
Consequently, in my view Salzer has lost sight of one of the A1 section’s principal unifying threads. Salzer’s reading of the harmony likewise differs in significant ways from mine. Three layers of harmonic analysis annotate 5.1. The highest level shows the basic progression within A1 and its incomplete repetition, interpreting chords that contain the uncommon pitch D♮ as dominants. The middle layer focuses on the midpoint interruption within the initial A1’s a2 component, where again a dominant (now normatively spelled) is a critical structural element. The bottom layer shows several foreground progressions, again incorporating dominant chords containing the pitch D♮. In all, I read dominant functions (at one structural level or
another) at seven locations. Salzer’s application of Roman numerals in his fig. 5 is inconsistent. They are as well deserved in measures 1 through 6 (where none are displayed) as in measures 19 through 22 (where they occur). More crucial to my reading of the large-scale shape of the section, the dominants of measures 9–10 and 26–28 do not enter into his harmonic thinking, whereas for me they serve (despite their uncommon constitution) as the structurally most significant dominants within A1 and its incomplete repetition (the only dominants in my upper row of Roman numeral analysis). Likewise the dominant at 143–4 (which emerges in my middle layer of analysis) is unlabeled in Salzer’s graph.
The B section, part 1 (measures 29–64)
The B section, part 1 (measures 29–64) The tempo change and new thematic content at measure 29 coincide with the onset of the nocturne’s B section, which opens with a much expanded reiteration of the tonic-tosubdominant succession of measures 3 and 4 [5.2]. The surge propelled there by a augmented fourth now derives its energy from an
diminished fifth (measures 33 and
41). Yet whereas the A1 section’s motion to IV resides within a harmonic trajectory, the subdominant target of the B section’s initial surge instead resides within a descending circle of fifths connecting the C♯ Minor tonic and its upper-third chord (measures 30 through 48). Though the spelling of the chord at 483 might suggest a continuation of the circular progression, with E➔ targeting A, Chopin’s continuation does not support that reading. At that point Chopin shifts to a key signature in flats, in a mildly deficient means of conveying the key of D♭ Major (anticipating C♯ Minor’s parallel major, C♯ Major, which prevails beginning in measure 65).7 Alas, the chord of 483 falls in the cracks, with a spelling that mingles elements from C♯ Minor (E-G♯-B-C ) and its enharmonic equivalent D♭ Minor, preceding the transformation to D♭ Major (F♭-A♭-C♭-D♮). Retaining the C♯ Minor signature, 5.2 reveals that Chopin here redeploys another feature from the A1 section, though in a contrasting context: whereas D♮-F♯-A in measure 5 absorbs B♯ to become V⇨ (leading to I), E-G♯-B in measure 48 absorbs C to become ♯VI⇨ (leading to II♯).8 In fact, a broad chromaticized voice exchange
transpires between
measures 30 and 48, dynamically targeting the supertonic, which in turn targets (as II➔) the dominant. (Consequently the E major chord of measure 48 – the goal of the circle of fifths – serves as an interior element within a broad I8–7–6♯ initiative, wherein the concluding I6♯ is presented in an evolved state: C -E-G♯-B, derived from absent root A♯, instead of diatonic C♯-E-G♯-A.) Though a high G♯ [A♭], reminiscent of that in measure 6, emerges during this progression (as shown in 5.2), it returns to the texture’s interior at measure 52. The plainness of the dominant arrival contrasts its A1 predecessor (measures 25–26). In both contexts a dominant extension precedes the next compositional initiative. That of measures 52 through 64 features ascending motions connecting the dominant’s root and third (G♯
There are three main reasons why I regard the E of measure 30 as a reinstatement of the Kopfton (covered by G♯), rather than following Salzer’s lead by delaying that reinstatement until measure 48. First,
resolves the local dissonance of
measure 29 (carried over from measure 26). Second, E is reinforced through the voice exchange in measures 30 through 32. Third, the EF♯>E in measures 46 through 48) curious. I instead regard the G♯ as a neighbor to F♯ (thus F♯F♯) prior to a G♯ arrival at measure 48, since F♯ – not G♯ – is a stable member of the circle of fifths’ F♯ and B chords. (The excursion to G♯ is not displayed in 5.2.) Salzer offers no interpretation of the chord at 483, which I regard as a potent chromatic variant of the tonic’s 6-phase chord, surging toward the supertonic. We likewise have divergent views of the mediant that precedes it: for Salzer it is the principal connector between the tonic and the dominant, whereas for me it is an upper-third extension of the tonic, an intermediary between the tonic’s 5- and 6phase chords. I regard II➔, rather than III, as the principal harmonic event between the perimeter tonic and dominant chords. That chord is not labeled in Salzer’s Roman numeral analysis. Though I commend Salzer’s display of the dominant prolongation in measures 52 through 63, I suggest that the slur labeled “6th (5+1)” in his fig. 5b (p. 293) should be omitted. The penultimate note of this sixth, D♯ [E♭], reinstates the interrupted D♯ of measures 49 through 52. (See my D♯-to-D♯ slur in 5.2.) By definition an interruption involves a descending motion whose completion is delayed. Whereas a foreground D [E♮] leads from this D♯ to the reinstated and now wobbly Kopfton E♯ [F] of measure 65 (to be explored below), the D♯ of measure 63, reinstated at 792, ultimately finds its successor in C♯ at 941.
Example 5.2 Analysis of Nocturne in C♯ Minor (op. 27/1), mm. 29–64.
The B section, part 2 (measures 65–83)
The B section, part 2 (measures 65–83) Though the interruption at
, supported by V♯, is achieved in measure 52, in this case
Chopin builds some redundancy into his structure, electively reiterating the B section’s principal events in the context of the parallel major key, C♯ Major. Consequently all three viable “three–two” descents are utilized within this nocturne: and ♯
,
. Concurrently the subdominant chord is again featured, becoming a
unifying feature despite contextual differences. Whereas the F♯-A-C♯ chord first stated in measure 4 and repeated several times during A1 fulfills a normative harmonic function (as IV) between the tonic and dominant, and the F♯-A-C♯ chord of measures 34–36 and 42– 44 is an internal element within a descending circle of fifths that connects the tonic and the mediant, the F♯-A♯-C♯ [G♭-B♭-D♭] chord in measures 66 and 70 serves as an unfurled embellishment of the major tonic. A portion of the circle of fifths recurs as well. Whereas in measures 30 through 48 the minor mode’s diatonic C♯ F♯ B E trajectory is pursued (with each chord eventually surging toward the next), in the context of C♯ Major (measures 71 and 72) a less common path transpires: C♯ F ⇨ B♯ [D♭ G⇨ C], as shown in 5.3. Though B♯ Major, whose tonicization is accomplished through repetition of the same foreground progression that earlier established the C♯ Major tonic, generally would be regarded as a remote key, it nevertheless holds a special place within C♯, as a chromaticized variant of the dominant’s upper-third chord (major B♯-D -F as variant of diminished B♯-D♯-F♯).9 When the pitch A [B ], which I regard as a substitute for the dominant root G♯, arrives at 791, D and F reveal themselves to be wobbly notes, for tonal order is restored through their lowering to D♯ and F♯, respectively. (See 5.3.) The A serves as the G♯ dominant’s minor ninth (as in measures 25 and 26).10 Its resolution (as an incidental dissonance) to G♯ first in the upper register (at 833) and then in the lower register (during the cadenza that follows) provides a normative dominant context for the B section’s close.
I expressed concerns above regarding how Salzer treats the soprano D♯ [E♭] of measures 63 and 64. That concern likewise pertains to the similar construction in measure 68. Despite Chopin’s slurring, the tonic pedal point, and the nonalignment of chord members, I propose that measure 68 should be read as representing A♭-C-E♭-G♭. My application of the V numeral (at various structural levels) has been much freer than Salzer’s (beginning, as noted, with the chord of 53–4). Likewise here we are at odds: my structural dominant, emanating from its upper-third chord, takes hold in measure 79, four measures before Salzer applies the Roman numeral V in his Example 5.
Example 5.3 Analysis of Nocturne in C♯ Minor (op. 27/1), mm. 65–83.
The A2 section and coda (measures 84–101)
The A2 section and coda (measures 84–101) Each of the three graphs presented thus far conveys the basic contour of tonic to dominant (at one structural level or another), supporting some manifestation of
to some
manifestation of . The model in 5.4 shows how they interact and how the Urlinie then continues to its inevitable close on at 941. The coda that follows develops the distinctive E♯>C♯>G♯ [F>D♭>A♭] arpeggiation of measure 65, now presented (twice) more slowly and filled in during measures 94 through 98. The subdominant of measure 66 finds its counterpart in measure 99. Whereas both Salzer and I place the principal interruption after the dominant arrival in measure 52, he proposes that the major tonic’s ♯ in measure 65 inaugurates the post-interruption descent to . I instead regard that ♯ as the onset of a parenthetical insertion that reiterates the descent to
, thereby delaying the
A2 tonic restoration until measure 84. In addition, Salzer proposes that ’s successor (C♯) holds sway beginning at measure 84. I instead interpret that moment as the initiation of a postinterruption third-progression descending from . I accept the contorted E>D♮>C♯ line that follows as fulfillment of the descent to background . (Salzer does not connect those three pitches as a line.) The C♯ in the lower register at 941 is the moment of cadence. (It is displayed up an octave in 5.4.)
Example 5.4 Analysis of Nocturne in C♯ Minor (op. 27/1).
6
Preludes in E Major and E Minor (op. 28, nos. 9 and 4) ◈ in response to Fred Lerdahl Building upon the foundation that he established with Ray Jackendoff in A Generative Theory of Tonal Music (1983), Fred Lerdahl’s sophisticated and multi-faceted Tonal Pitch Space (2001) develops and demonstrates innovative ways of charting key shifts and chord-to-chord progressions in chromatic music. The essay below, which compares my interpretation of Chopin’s E Major and E Minor Preludes with his, is a study in contrasts: his abundant Roman numerals in a range of keys (presented in a grid formation annotated by squares, circles, and arrows) versus my sparse rows of numerals with, in these two cases, no diversion from the tonic key whatsoever.1 This juxtaposition will encourage readers to ponder some of the major questions confronting any analyst of nineteenthcentury music: Which combinations of notes congeal into chords? Which chords should be interpreted as harmonic, and which as prolongational or connective voice leading? At what point do pitches that are chromatic within the home key begin to take on diatonic roles in tonicized keys? If indeed some of a musical structure’s pitches do not sound explicitly in a composition, how can one guard against being either too unimaginative (and thus overlooking relationships likely intended by the composer) or too fantastically imaginative (and thus making unjustified claims)? For the most part I simply place my perspective beside Lerdahl’s in the essay that follows. There is a huge gulf between our outcomes. Readers consequently have a good opportunity to ponder our contrasting analytical practices and to decide which approach (if either) they might wish to pursue further. In one respect, though, I have elected to mount a
rebuttal. In that I am uneasy about how Lerdahl has organized these scores’ pitches into various hierarchical levels (a task that must precede the application of his innovative techniques for generating keys and Roman numerals), I reveal for the reader as much of how my analytical thought process regarding hierarchy operates – and why I consequently am led to reject many of Lerdahl’s interpretations – as I can convey in words. These works have been much studied and commented on already, of course. Lerdahl draws inspiration especially from Edward Aldwell and Carl Schachter’s analysis of the E Major Prelude’s second and third phrases.2 With regard to the E Minor Prelude, two essays by Schachter3 and an article co-authored by Justin London and Ronald Rodman were consulted.4 The authors of the latter provide, as their fig. 6, a transcription of Schenker’s unpublished analytical jottings on the E Minor Prelude.5 Unfortunately their transcription is rife with errors and omissions.6
Structural overview of the Prelude in E Major The Prelude in E Major’s three phrases, each four measures in length, present the two halves of an A1 A2 binary form with some redundancy: despite its contrasting internal content, the second phrase repeats – and more fully conveys in both soprano and bass – the structural framework of A1. The content of measures 5 through 8 is displayed within square brackets in 6.1 to indicate that it reiterates the
background structure
presented already in measures 1 through 4. On the one hand the analysis conveys details concerning a concrete harmonic progression (dependent upon a potent dose of hierarchical thinking, to be explored presently), almost all of whose bass pitches can be located in the score, though sometimes in enharmonically equivalent spellings. On the other hand much of the open-notehead structural melody is imaginatively constructed in this analysis: though each pitch relates to an actual note in the score, only the G♯ of measure 8 and the concluding E actually sound in the upper register during the composition. One of the melody’s main characteristics throughout is an upward striving from the interior to the top, a process that succeeds during A1 only on the second try, with the attainment of Kopfton G♯ [A♭] at 81. Yet that accomplishment is short-lived: in both A1 phrases, whatever progress in rising above the initial B has been achieved is wiped out before the cadence.
Example 6.1 Analysis of Prelude in E Major (op. 28/9).
The Prelude in E Major’s first phrase (measures 1–4) The first interval of a structurally deep ascending arpeggiation guides the melody of measures 1 through 3: the tonic’s BC♯ third (likewise filled in) leading back to the neighbor of the initial inner-strand B, which is restored at the phrase’s cadence. (Whereas conceptually the pitch C♯ “belongs” at the downbeat of measure 4, passing note D♯ from measure 3 is extended as a suspension against bass C♯ and then F♯, finally resolving at the end of 42. The resolution phase of a C♯>B suspension during the remainder of measure 4 likewise occupies only one-fourth of a beat.) The non-attainment of Kopfton G♯ is a motivating force for the repeat of A1 (measures 5 through 8), where the elusive G♯ goal in fact is attained via an alternative route.
Example 6.2 Analysis of Prelude in E Major (op. 28/9), mm. 1–4. Whereas many analysts grant harmonic status to almost all chords within a composition (for example, I IV II V III VI for the first six chords in 6.2), the imposition of a greater distinction between the workings of harmony (in the sense of Schenker’s Stufen) and of connective voice leading results in a clarity that rewards the increased difficulty of execution. (It seems to me that, in that numeral-intensive methodology, chord labels are
applied rather indiscriminately. My practice adds the step – a challenging one – of carefully pondering a work’s hierarchical associations to develop a sense of which chords stand out in relief as goals of linear initiatives or as prolonged entities before Roman numerals are applied.) Within this phrase an ascending 5–6 sequence is deployed to connect the tonic’s 5- and unfurled 6-phase chords, with a G♯D♯>(C♯) and a reiteration of (G♯)
A major component of my disagreement with Lerdahl in all three phrases is his treatment of the dominant. (A different dominant issue arises in each phrase.) In that the first phrase ends in a half cadence, the dominant serves as the goal of its harmonic trajectory. Even before comparing Lerdahl’s reduction with the score, one might be struck by the singularity of a conception that proposes a dominant arrival already in the second of four measures, inaugurating a ten-beat prolongation. (Lerdahl displays the low B bass noteheads of both measures 2 and 3 with downward flagged stems, connects those noteheads using a dotted slur, and connects the second B and the D♯ of measure 4 using a solid slur.) In my experience harmonic goals generally are attained somewhere near the end of a phrase, especially one as metrically regular as is this one.9 Thus my placing of the dominant’s structural arrival point at 43 is a more normative reading, at least from a statistical perspective. That arrival point is preceded by a surging supertonic (II➔). Chopin deploys such a goal-directed supertonic only at 42 – not before the B chord of either measure 2 or measure 3.10 Given Chopin’s famously idiosyncratic use of slurs, I am wary of making analytical decisions concerning a work’s structural framework based upon how he has marked up his score.11 Yet the three bass slurs deployed by Chopin in measures 1 through 3 (A>F♯>B, B>C♯, and A>B) seem to me to be consistently applied, in that they all span the interval of a descending seventh (each displayed as an ascending second in 6.2 to enhance clarity).12 Whereas A>F♯>B might have been followed by B>G♯>C♯, the acceleration of the sequence’s pacing during measure 2 results in the omission of a low G♯ during 24: yet note that G♯ is in fact a chord member at that point. Consequently I hear the sequential initiative leading through – not to – the B major chord that Lerdahl interprets as the phrase’s dominant arrival. Only after the attainment of the tonic 6-phase chord at 31 does the persistent upward thrust of the three individual strands displayed in 6.2 abate, with a corresponding shift from the process of 6-phase attainment to that of 6phase prolongation, which nevertheless reprises the G♯
The Prelude in E Major’s second phrase (measures 5–8) Whereas II➔ is the principal intermediary between the tonic and the dominant during the first phrase, Chopin explores an alternative means of filling in the bass E
Example 6.3 Analysis of Prelude in E Major (op. 28/9), mm. 5–8. The circle’s initial fifth (E>A) is traversed with its own internal division into two thirds (displayed as E>C♮>A on three successive downbeats in 6.3).16 So far, so good. Now the treacherous link between A and D♯ must be negotiated. Chopin here pulls off an ingenious feint. As mentioned above, one of music’s well-worn paths is to proceed from E and A to D and then G. Through the end of measure 7, Chopin persists in fostering the impression that the A chord (which evolves into A➔) will proceed in that direction.
(Because enharmonic reinterpretation is a factor in his ruse, alternative spellings of the chord at 74 are juxtaposed in 6.3.) Though C♯-E-G-B♭ corresponds to A➔, ultimately Chopin treats that chord as F -A♯-C♯-E, an evolved form of D♯➔, the third element in the alternative trajectory of the circle of fifths. (Because the same four pitch classes represent both A➔ and D♯➔ between 72 and 74, a collision bracket appears at that point in 6.3.) Chopin negotiates what might have been an awkward link with maximal smoothness: the most parsimonious voice leading imaginable is no voice leading at all! The A➔ chord, which might have resolved to D♮, instead transmutes into D♯➔, which in due course resolves to the circle’s final element, G♯. Unhelpfully, Chopin’s spelling of the D♯➔ chord as G-B♭-D♭-F♭ at 74 reflects his upcoming enharmonic presentation of the G♯ mediant as an A♭ chord. The root trajectory E
seventeen beats, respectively. I reject that interpretation, proposing in its stead that the second phrase functions as a variant of the first (maintaining the tonic opening and HC close), within the most conventional of all musical forms: the binary antecedent/consequent pair. Here Chopin twice attains V (at 43–4 and at 84) but goes no further (the antecedent phrase and its repetition). Then, shifting that V to an earlier point within the allotted four measures (at 114), he succeeds in achieving the goal tonic at the final downbeat (the consequent phrase). Either placing such a crucial dominant as that of 84 within the third phrase or eliminating it altogether – see fig. 3.2, TSR d, c, and b and PR (prolongational reduction) a–b – is, in my view, a misrepresentation of what Chopin is doing here.18 Positing a cadence on the mediant (at 83) is essential to Lerdahl’s interpretation of the broad structure: the equal subdivision of an octave into three descending major thirds (E in measure 5, C♮ in measure 6, G♯ in measure 8, and E in measure 9). This reading is fleshed out with arrows wending through grids of regional space and Roman numerals in his figs. 3.4 and 3.7a. Thus we disagree not only regarding which chord corresponds to the cadence, but also regarding the A major chord at 71, which I interpret as the goal of a descent in thirds (E>C♮>A over three measures) within the broader circle of fifths. Lerdahl instead hears a prolongation of C➔ from 61 through 74, thus harboring hopes of a resolution on an F major chord longer than I do. (Though in note 16 I acknowledged a potential for such a continuation after C➔, the emergence of the A chord at 71 decisively shifts the odds in favor of a circle-of-fifths continuation, which is confirmed by the succession from D♯➔ to G♯.) Lerdahl’s proposal of a prolonged C➔ chord was strongly influenced by an analysis published by Edward Aldwell and Carl Schachter.19 They interpret the A major triad at 71 as “an emphasized passing chord.” (They also propose a “cadence in A♭ [G♯]” in measure 8.) Lerdahl has, with proper acknowledgement, incorporated their reading into his conception. Lerdahl’s path through regional space (as displayed in his fig. 3.4) depends upon enharmonic equivalence (with the shift displayed between A♭ and G♯). In his view “the journey in the unfolded toroidal structure begins and arrives on different Es” (p. 94). My alternative reading instead maps back onto the original
E. Viewing a fresh grid (Lerdahl’s fig. 2.22a, regarding E as tonic), one might proceed from E through G to C (as does Lerdahl), but then move leftwards to A, followed by a bold upward shift to D♯ (a boldness that is mitigated by the collision of those two entities within the same diminished seventh chord), thereby putting the phrase’s concluding G♯ and B close at hand. Given that early on in my study I developed multiple concerns regarding Lerdahl’s hierarchical assessments and reading of the phrase goal, my perusal of his various charts was pursued dutifully, rather than with enthusiasm. In some cases I was unable to comprehend the logic behind the display of certain paths: for example, why does an arrow connect V and A♭ in fig. 3.7a but instead vii° and A♭ in fig. 3.7b? (I am not expert enough in his methodology to distinguish between a minute typographical error and a conceptually meaningful distinction.) And I was surprised that a circled
was included in fig. 3.13b. Indeed, I strongly endorse
interpreting the A major chord of 71 as an important structural element. But Lerdahl does not: he describes it as “an incidental consequence of the voice crossings in bars 6–7” (p. 101). It seems to me that his representation would more accurately represent his conception if
were omitted, though I suspect that his
comment about how “the diatonic substratum” “shines through” (p. 101) might offer a clue regarding why he included it.20
The Prelude in E Major’s third phrase (measures 9–12) The rich harmonic agendas of measures 4 and 8 have implications for the construction of the third phrase (which serves as a consequent A2 within the prelude’s binary form), in that now the harmonic activity must extend beyond the dominant to the tonic for a PAC. A chord of such importance as a final tonic generally will be introduced on a strong beat, ideally the concluding measure’s downbeat. Chief among Chopin’s concerns appears to be deciding whether or not to proceed sequentially to a tonic 6-phase chord, as occurred during the first statement of A1. To better understand his options, consider the three sequence segments displayed in 6.4. The first, a diatonic sequence, corresponds to the opening of the first phrase. Though such a trajectory could be employed again, a literal repeat of the first phrase through the prolongation of I6 would not be viable for A2, because the remaining harmonic content (likely some form of II V I during the final three beats) could not reasonably be situated in such a way as to facilitate placement of the cadential tonic in a metrically strong position. Chopin’s alternative trajectory begins in measures 9 through 103 as an obstinate sequence, ascending in half steps. As shown in the second sequence segment displayed in 6.4, the rigorous pursuit of that trajectory for the same number of chords as occurs during the first phrase’s diatonic sequence would lead to V rather than to an unfurled I6. That alternative goal has a significant advantage: it would allow for a downbeat arrival of the cadential tonic at 121 (assuming a willingness to jettison the more involved approach to V projected by one or the other version of A1). Yet the trajectory that Chopin elected to pursue during the third phrase turns out not to be obstinate, but instead idiosyncratic (also shown in 6.4): it begins as if it were going to ascend by half steps, but then proceeds more broadly so that one would expect (if one had never heard the phrase before) that a chromatic variant of I6 (C♮-E-G♮) will emerge at 114. Observe how this model harbors several modest surges: E➔ to A, F➔ to B♭, G➔ to … Chopin indeed could have allowed the G➔ chord to follow its natural inclination and resolve to C♮, which might then lead to ♮II5♮ supporting soprano F♮ and V supporting D♯ during the first two beats of measure 12, followed by I at 123. Contrary to such expectations the G➔ chord instead leads to B at 114, thereby reverting unexpectedly – in a musical non sequitur – to the goal of the hypothetical obstinate sequence that at first had seemed to be the trajectory that Chopin was pursuing. (See the arrows in 6.4.) Since the
sequence reaches V (a PAC’s conventional penultimate chord) at the end of the phrase’s third measure, the prime position for a tonic close on the final measure’s downbeat is available. Consequently Chopin avoids the down-to-the-wire cadence attainments of both A1 phrases by presenting a robust four-beat tonic in measure 12.
Example 6.4 Sequences related to Prelude in E Major (op. 28/9), mm. 1–3 and 9–11.
Again in the third phrase, Lerdahl’s and my hierarchical perspectives conflict. For me, the ascending sequence’s alternation of local 5- and 6-phase chords places emphasis on the former, even if the latter are unfurled into position and occur on downbeats. Consequently the initiating tonic (which via the shortcut described in note 7 incorporates both the 5-phase bass E and 6-phase bass G♯) inaugurates a stepwise upward motion E(G♯)
In my view, the sequence’s final VL chord (B♮-D♮-G♮) “should” lead to ♮VI5♮ (C♮E-G♮). The substitution of V results in a retroactive enharmonic transformation of B♭: roots A
Structural overview of the Prelude in E Minor Whereas the Prelude in E Major engages two alternative versions of its binary form’s A1 section, in the Prelude in E Minor a single A1 suffices. Kopfton sounds even before the first chord is struck – with no struggle for attainment, as in the other prelude. The structural line descends through at the end of measure 9 to in measure 10, followed by repetitions that lead to the eventual incorporation of the truant . The phrase ends in an interruption. The normative standards of formal construction that Chopin upheld would ordain that after an interruption on
during A1, should be restored so that a descent to may
ensue during A2. Though that in fact does occur, Chopin has reconstructed the phrase’s interior to a greater extent than would have been necessary to fulfill his formal obligations. As will be explained in greater detail below, a slithering downwards through tonal space, mostly in half steps, occupies the prelude’s first eight measures. Tonal coherence is maintained because both the beginning and ending points of the passage project the tonic (a diatonic minor I followed by I➔). In the process a number of vibrant chords are passed through, any of which potentially could be asserted to take on a harmonic role. During A2 Chopin undertakes such a conversion of function for one of these chords: instead of slithering as far as I➔, which targets IV, he converts what in measure 6 was no more than a diminished seventh passing chord into an asserted V➔ harmony, which resolves to a minor I. (The exact G-B-E-B sonority that began the phrase is restored at the end of measure 17.) The progression continues without surge from that I to IV (which now undergoes a conventional 5–6 shift), then onwards (incorporating some extraordinary local embellishment) through V♯ to I to complete the phrase.
The Prelude in E Minor’s first phrase (measures 0|1–12) Just as a 5–6 sequence may be pursued as an obstinate ascent in half steps (as shown in 6.4), a parallel progression of chords may descend obstinately in half steps.23 The proposed model for Chopin’s extraordinary progression in the prelude’s first eight measures, shown in 6.5, displays an expansion from a progression of such chords to the fuller sonority of diminished seventh chords.24 Slurs are employed to connect each line’s perimeter pitches: B>G♯, E>B, B>F♮, and G>D. The relationship between the initiating and concluding chords is of critical importance for the viability of such a progression. As the harmonic analysis below the system in 6.5 reveals, these pitches here realize a frequently encountered chordal evolution: from diatonic E-G-B to surging G♯-B-D-F♮, an ideal means of propelling the succession from I to IV.25 Chopin of course understood that the innards of such a progression might hit upon some pitch combinations quite foreign to an E Minor tonic context. It is important for my analysis that these chords’ harmonic potentialities be held in check: we tiptoe through this field of chords without provoking them into harmonic assertiveness. By pursuing a style of harmonic analysis that imposes a high standard for the bestowal of a Roman numeral label, we avoid numerous unwieldy and misleading symbols that would seek to impose harmonic meaning where, I contend, none was intended.26 Each internal chord has the potential to take on a harmonic role. (We shall see how Chopin activates one such potentiality during the A2 section.) But if its context does not offer evidence that a chord is actually being asserted as a harmony, then the imposition of a Roman numeral label generally will impede understanding.27
Example 6.5 Analysis of Prelude in E Minor (op. 28/4), mm. 0|1–12. There was good reason for Chopin to be timid about during the structural descent: since
’s harmonic support, IV, is presented in first inversion, bass C descending to
dominant root B against G (hypothetically inserted by revising the melody in the second half of measure 9 to D>C>A>G) to F♯ would result in parallel fifths. Chopin averts that unpleasantness twice by leaping from A to F♯. In the final iteration of the cadential succession he slips a G in (justifying the absence of parentheses around the open G notehead in 6.5), deftly delayed until the phrase’s final downbeat (121) to become an accented passing note, thereby staggering the arrival points of B and F♯.28 Had IV not been inverted, the conventional model
I
IV—————
V♯
I
(as in FC, fig. 16, ex. 5, model 2) could have been pursued without impediment.
Again with the Prelude in E Minor, my concerns regarding Lerdahl’s reading mounted as I studied his TSR and PR analyses (presented in his fig. 3.19), even before I proceeded to the more innovative aspects of his practice – the display of the path through regional space and the tree diagram (figs. 3.20 and 3.21). Though there is much variability in how Chopin wends his way downwards during measures 1 through 8, there is nevertheless a subtle consistency: each of the voices engaged in the descent of parallel chords makes a move before any of the voices takes another turn. Incorporating both my spellings from 6.5 and Chopin’s sometimes wayward spellings from the score, the following chart (which should be read line by line from top to bottom) – noting in particular the horizontal lines (which in all cases coincide with bar lines within the score) that indicate the congealing points of the parallel progression’s successive individuated passing chords – conveys the inner workings of the passage. m. 1
G
B
E
m. 2
F♯
A
↓
↓
↓
E♭[D♯]
F♮
↓
↓
↓
↓
D
↓
G♯[A♭]
↓
E
↓
↓
↓
G♮
↓
↓
↓
C♯
↓
↓
C♮[B♯]
↓
F♯
↓
D♯
↓
↓
D♮
↓
↓
m. 3
m. 4
mm. 5–6
mm. 7–8
↓
F♮
↓
↓
↓
B
If this segmentation holds, as I suggest it does, then it renders much of Lerdahl’s foreground reduction (TSR f and PR e–f) untenable, since two of the four chords between the perimeter chords are missing from his reading, while four chords that represent “uncongealed” states (points along my chart that are not directly above a horizontal line) are present. Among the other levels, Lerdahl’s TSR d holds some promise in that the two perimeter chords (representing the initial minor I and I➔) are present (at least if one fixes the typographical error in the latter by hoisting the misplaced natural up a third). The next level (TSR c), where is the sole entity positioned between the initial tonic and the cadential dominant, is less successful, in my view. My reading could be summarized as follows: An initial tonic (I) Some connective chords A restoration of the tonic, now surging (I➔) The goal of the surge attained (IV) The continuation to the dominant (V♯) This is an oft-told story. Lerdahl’s narrative in TSR c is not a viable abridgement of that story: An initial tonic (I) A connective chord The dominant (V♯) Three separate problems emerge here: (1) the connective chord that Lerdahl displays is among those that I have referred to above as “uncongealed,” and thus hierarchically of very low ranking, lower than several other chords in its vicinity that are excluded; (2) the connectivity that Chopin achieves results from a close association among multiple passing chords (the four-chord interior to the long
slurs in my 6.5) all functioning at the same hierarchical level, from which no individual one should be singled out for inclusion at a deeper level; and (3) the connectivity that Chopin pursues between measures 1 and 8 is that between two forms of I, which Lerdahl commutes into a connectivity between I and V♯. Paralleling his dependency upon Aldwell and Schachter in the E Major Prelude analysis, Lerdahl acknowledges a dependency upon an analysis of the E Minor Prelude published by Justin London and Ronald Rodman.29 The emphasis upon the chord that I have found problematic is in fact a prominent feature of their presentation. It would be illuminating for readers to detect and come to terms with the many ways in which my 6.5 contrasts both the left half of Lerdahl’s fig. 3.19 and the first page of London and Rodman’s ex. 1. Observe especially how my slur connecting Kopfton B in measure 1 and the G♯ of measure 8 cannot be made to jive with their prolongation of A from measure 5 through measure 9.30 Both Lerdahl and the London/Rodman team consider two essays by Schachter that shed light on the E Minor Prelude.31 Whereas I propose that Chopin has entered into a fully chromatic tonal space during measures 1 through 8, with a uniform bass descent in half steps – G>F♯>F♮>E>D♯>D – Schachter instead proposes some internal hierarchical differentiation, resulting in a foundational line that descends as G>F♮>E>D. (Note the stems marking those four noteheads in the graph published with the 1994 essay.) Given the extraordinary lack of agreement between Lerdahl’s and my readings regarding which simultaneities between measures 1 and 8 constitute the essential chord progression, I cannot endorse his display of the phrase’s pitchspace journey in fig. 3.20 or the tree diagram conveying a regional prolongational analysis in fig. 3.21. As Lerdahl himself states (and as I have already quoted in note 8), “It is sometimes troublesome to determine the grouping structure of a piece, but once that is in place the rest mostly follows like clockwork” (p. 7). Indeed, the “clockwork” part of his effort processes the TSR and PR structures of fig. 3.19 in an exemplary fashion. (His discussion relates Chopin’s harmonic practice within this prelude to Wagner’s penchant for being in a key without touching upon its tonic chord.) Even from a statistical perspective, the
dissimilarity of our conceptions is astonishing: whereas my analysis retains one key throughout the phrase, Lerdahl proposes a succession of six: jumping from e to a back to e and then over to G followed by a return of a and finally back to e; and whereas I convey the phrase’s harmonic progression using just three Roman numerals, Lerdahl’s grids contain a total of forty Roman numerals, of which ten are actively engaged via circles and arrows.
The Prelude in E Minor’s second phrase (measures 12|13–25) Though the downward contour from the opening of A1 is maintained during the corresponding measures of A2, the latter realization is somewhat more aggressive. For example, whereas diminished F♯-A-D♯[E♭] sounds against soprano B in measure 2, the bass rambunctiously continues onward to F♮ as – rather than after – D♯ falls into place in measure 14. Then, from 162 through 171 Chopin introduces a significant jolt (achieved by injecting several leaps, inaugurating a stretto, pumping up the volume level, and introducing a downbeat dominant root B) that converts the penultimate chord of the earlier parallel progression (D♯-F♯-A-B♯[C] in measure 6) into a potent, asserted dominant ninth (B-D♯-F♯-A-C in measure 17). Consequently the parallel progression serves now as a connection between two different harmonies, as is indicated by the open parentheses between I and V♯ in 6.6. That example also shows how, within the projection of I-space that transpires during measures 13 through 17, the internal dominant harmony supports the A of a B>A>G third-progression. (This A undergoes a downward migration so that the third-progression’s G ends up sounding at the bottom of the texture, while the tonic root E, expected in the bass, sounds at the top of the texture. See the arrows in 6.6.)
Example 6.6 Analysis of Prelude in E Minor (op. 28/4), mm. 12|13–25.
Even without the fanfare of a surge comparable to that which transpired during 82, IV emerges as the principal connector between I and V♯ during A2. (Note how closely the melody that IV supports during 181 relates to that of 92.) The IV chord’s 6-phase F♯ (at the fourth eighth note of measure 18) serves as the starting point for a descending third to the leading tone (F♯>E>D♯) whose E gets “stuck” for two measures, making the arrival of D♯ at 202 all the more gratifying. (Compare with the repeated sounding of resolution pitch D♯ in the corresponding passage of A1 – measures 10 through 12.) Coordinating with that interior strand, the structural A (= ) thrice descends to F♯ (= ), again as in the earlier passage. In this case the truant never sounds (in contrast to A1, where a belated G is heard at 121), and thus the structural G (= ) is displayed within parentheses in 6.6. In both phrases the extension of the initial I-space coordinates with the filling-in of the tonic triad’s upper third (B>G♯ during measures 1 through 8 and B>G during measures 13 through 17). Consequently the filling-in of the dominant triad’s upper third (F♯>D♯ during measures 18–20 through 24) is especially appealing.32 Yet Chopin goes further. The initial phase of the dominant prolongation in measures 18 through 20 (like that in measures 10 through 12) engages, in the bass, the same BB neighboring motion that embellishes the melody in the phrases’ opening measures. Thus C’s recurrence in the bass at 211, supporting the passing note E within the dominant’s F♯>D♯ third, invokes several layers of association. One of tonal music’s more poignant embellishing chords, built from four pitches each a half step distant from one of the major dominant triad’s members, emerges over the course of measure 21: C-E-G-A♯[B♭]. Though the
augmented sixth
typically would resolve outwards to a octave, Chopin luxuriates in the chord, pursuing in two voices the same sort of descending chromatic motion as was utilized in three or four voices during both phrases’ opening measures: C>B>A♯ coordinating with A♯>A♮>G♯>G. (Brackets in 6.6 mark the locations of the two intervals that are filled in.) Consequently the augmented-sixth interval sounds as a diminished third ( Chopin as
, spelled by
, at the bottom of the texture at 231), resolving to a unison B in coordination
with the dominant root’s restoration at 241. E’s descent to D♯ completes the dominant’s prolongation, which is followed by the cadential tonic at the final downbeat. At the outset I suggested that “Chopin has reconstructed the [second] phrase’s interior to a greater extent than would have been necessary.” In assessing how Lerdahl interprets the second phrase in his fig. 3.19, it appears to me that he has reconstructed the second phrase’s interior to an even greater extent than has Chopin. Comparing my 6.5 and 6.6, note that the two phrases are of approximately the same length – twelve and thirteen measures. The dominant arrives in the tenth measure of the first phrase, whereas in the second it arrives somewhat abruptly in the sixth measure, after a curtailed subdominant. Chopin has emphasized the revving up – the presentation of the initial I-space – in the first phrase, while focusing more on the leave-taking – the expansion of the cadential dominant – in the second. Yet in both cases the harmonic progression proceeds from I through IV to V♯. Even with Chopin’s alterations in pacing, one can perceive a strong correlation between IV in measure 9 and in the first half of measure 18, and between V♯ in measures 10 through 12 and in the second half of measure 18 through measure 20. Granted, the bass B at 171 is a conspicuous note: low, loud, and metrically strong. Yet I propose that Chopin has applied those markers to convert a chord that earlier (measure 6) played no harmonic role into a functional dominant within a middleground progression that expands the phrase’s initial Ispace, before the continuation to IV and then V♯. Lerdahl instead hears the onset of the dominant function at 171 as extending for eight full measures, though indeed he proposes that not all of the dominant’s pitches are in place until the second half of measure 20. (Note the B–F♯ diagonal line spanning those measures in his PR c– d.) Consequently the seeming correlation between his regional prolongational analysis in fig. 3.21b, which displays the noteheads E, A, B, and E, and my I IV V♯ I harmonic analysis in 6.6 is incidental: his A and B correspond to measures 14 and 16, respectively, whereas my IV and V♯ both reside in measure 18. In addition, though I concur with his placement of the first phrase’s soprano pitch G at the downbeat of measure 12 in PR c–d, placing the second phrase’s G in measure 17, thereby neglecting the A of the thrice-stated A>F♯ third (corresponding to an A that was significant to the analysis in the first phrase),
seems inconsistent. In my imaginative approach to analysis, A>F♯ may stand for A>G>F♯ whether (measure 12) or not (measure 20) a G actually sounds within the composition at that point. In his reading a sounding G in the “wrong” location trumps the parallelism between the two phrases (based on the similarity of context). Finally, two small points: (1) both phrases begin with an upbeat B
third), there is no cadence at that
point, as is proposed in TSR d. Though I do not endorse the London and Rodman graph of the second phrase (which they in any event have constructed in part only to knock down, as if their fabrication of a Schenkerian graph for the work would match the best of what a more committed Schenkerian analyst might be able to achieve), we concur on one important point: V♯ resolves to I during measure 17.33 (As do I, they display tonic root E within parentheses, attached to a beam, at that point.) At a broader level, our graphs both convey the same structural bass arpeggiation E–B–E over the course of the phrase. I am not so enthusiastic about their reading of the descent from , especially their placement of background within the prolongation of V♯ (at 211). In his Chopin Studies graph, Schachter proposes a later dominant arrival – at 191 – with the bass B at 182 serving as a passing note between A and C.34 Whereas I am drawn by the similarity of content between all of measure 10 and the second half of measure 18 and by the BBB bass motion over two-and-a-half or three measures, I suspect that Chopin’s soprano slur, which extends to the downbeat of measure 19, and the attainment of a downbeat arrival point for V♯ (matching measure 10) were factors in Schachter’s hearing a prolongation of IV throughout measure 18.35
It is uncommon to have an E–B–E bass arpeggiation in which both of the E noteheads appear within parentheses, as displayed in my 6.6 (measures 13 through 17). Yet I would argue that the inverted opening tonic is the principal reason why Chopin neglects the E in the bass again at 172. (It resides in the soprano.) The perimeter sonorities of this five-measure tonic expansion match exactly: G-B-E-B. Whereas in the first phrase IV is approached via a descending bass (from the imagined E through D to C, resulting in an inverted IV), in the second phrase the tonic’s third G leads upwards to IV’s root A (181). Whereas Lerdahl, London and Rodman, and I all agree that soprano F♯ (=
) arrives before bass C emerges at
211, Schachter instead proceeds in his structural descent from A to G at that point, in the tenor register. (To his credit, that reading is consistent with his interpretation of the first phrase, which has proceeded only so far as a middleground
by the
point of the cadence in measure 12.) He labels the C chord as VI (within parentheses). If I were to acknowledge a harmonic function for this embellishing chord, it would instead be II➔. London and Rodman use words such as “problematic” and even “unruly” to describe the E Minor Prelude. I demur. To be sure, Chopin’s subtle, inventive writing calls for an approach toward analysis that is both imaginative and flexible. In this prelude, at least, his innovations transpire within a conventional framework.
7
Prelude in G Minor (op. 28, no. 22) ◈ in response to Alison Hood Just as my Harmony in Schubert appeared around the same time as Suzannah Clark’s monograph on that composer,1 so also Alison Hood’s book-length study of Chopin’s music and the present work appear within a year or so of each other.2 Though I had not seen her volume before mine went to press, I was able to study an article she published on Chopin’s Prelude in G Minor (op. 28, no. 22) and later revised for her monograph.3 Since those who keep abreast of developments in the field of tonal analysis likely will compare our two books, the juxtaposition of my reading of this prelude with hers here offers readers an opportunity to explore the considerable contrast in our methods, our presentations, and our outcomes.
The A1 section (measures 0|1–8)
The A1 section (measures 0|1–8) More so when performing the Prelude in G Minor on a nineteenth-century fortepiano than on most modern instruments, the left-hand octaves shine through boldly, projecting the A1 section’s principal melody. The tonic’s root consequently emerges among the right-hand pitches, rather than at the bottom of the texture, during 42. (In 7.1, root G is placed within parentheses in the bass register.) The phrase proceeds from that tonic to the major dominant, as is typical of an A1 section within an A1 A2 binary period. (As of measure 8 the listener has no reason to suspect that the prelude will extend beyond sixteen measures in length.) The goal dominant’s root likewise does not sound in the bass. In fact, root D is postponed until the start of the A2 section: E♭ descends to D in the right hand during measure 9, completing a chromatic G>D fourth that transpires at the top of the texture. That chromatic line causes the subdominant that comes between I and V♯ to be presented as a major chord (with E♮ rather than diatonic E♭ at 62 and 72). A concurrent interior line also takes on a maximally chromatic aspect: D♭ occurs during 61, resulting in a potent I⇨ surge towards IV♮. Though IV8–7 might have directed the Urlinie downwards from C to B♭, so that A (the antecedent phrase’s goal ) could arrive in conjunction with the onset of V♯, in this case C extends into the dominant’s domain, with the descent through B♭ to A occurring during 82. In the context of a small-scale A1 A2 binary form, the antecedent phrase’s descent from to
is interpreted as a background line, interrupted before the
final . Consequently 7.1 displays four open noteheads with upward stems connected to a beam. (Note the upward transfer of Kopfton D just after it is established. The lower register will be reinstated later.)
Example 7.1 Analysis of Prelude in G Minor (op. 28/22), mm. 0|1–8. The instability of the pitch B♭ at 82 (in a dominant context) is an important factor in deciding how to interpret the pitches that precede measure 1. Rather than displaying A as a passing note between tonic pitches B♭ and G, 7.1 proposes (through what it includes and what it omits) that the listener (aided by the discerning performer’s shaping of the line) instead should interpret the initial B♭ as an appoggiatura embellishment of A, followed by G>F♯ (below E♭>D).4 The resulting F♯-A-C-D chord, which targets the initial tonic, is prolonged until 42, in the process evolving into the more dissonant state F♯-A-C-E♭. I applaud a perception displayed within Hood’s Graph 2G: a stepwise descent at the top of the lower staff during measures 5 through 8 (D>C>B♭>A). Though I would advise beginning the slur that binds these notes with the prior D of measure 4 (thereby capturing the not-yet-evolved tonic support that inaugurates the I-to-V♯ progression), this line – in the register that both Hood and I acknowledge to be the melody’s principal domain – should be a primary focus of the listener’s attention. Its halting on A (one step shy of the key’s tonic pitch) is a prime motivating factor for the impending onset of what one initially should expect will be a normative eight-measure consequent phrase, the second half of a parallel period. What Hood makes of her perception cannot be discerned from her graphs 2G and 2H, for two reasons: (1) though 2H contains abundant Roman numerals over most of its substantial length, this passage curiously appears without a harmonic analysis; and (2) though slurs within 2G bind elements within the passage together,
there is no visual indication of how these measures connect to what precedes and follows them. Both quandaries are clarified by looking elsewhere – at graph 1E or 1F for a sense of the local harmonic progression, and at graph 1D for Hood’s interpretation of A as neighbor to the tonic third. Hood and I are at opposite poles regarding both the extent and structural depth of the phrase’s goal dominant chord. For me, it arrives at 81 and functions as the prelude’s background V♯, supporting the Urlinie’s pre-interruption
(as
shown in 7.1); for her, its emergence occurs instead at 52, and its foreground role apparently allows a Roman numeral (V in her style of analysis) to be omitted, even in a graph (1G or 2H) in which dozens of other numerals are included. To clarify my reading of Chopin’s harmonic conception, for a moment assume that measure 5 does not exist. The preceding chord (B♭-D-G) and the following chord (B♮-D♭-F-A♭) are, in my view, the same harmony, first in its diatonic state and then in a highly evolved state. Such an evolution of the tonic generally comes about as the succession to IV (here represented by IV♮ during 62) draws near. Though in this case that evolution is extreme – I⇨ rather than I➔ – the transfer of root from G to C at 62 nevertheless shines through. Now reinstating measure 5, we come to understand that the tonic is prolonged via a conventional local progression (not fully displayed in 7.1) whose concluding tonic happens to be highly evolved: I II⇨ V♯ I⇨. The fifth-relationship between II and V♯ transpires with exactly the same ⇨ evolution as that between the terminal I and the IV♮ that follows.5 Taking into account this more developed harmonic conception, the fact that the phrase fills eight measures within an opus that includes several preludes of around sixteen measures in length, and a realization that the next phrase (to be discussed in detail below) begins exactly as would a consequent phrase within a parallel period, I propose that the dominant arrival in measure 8 and the to which the melody descends conform to the normative closure of A1 within an A1 A2 binary form. If the music that one is analyzing seems ambiguous, it is important to compare the passage in question with other passage(s) within the same movement that the composer may have fleshed out more fully.6 In this case the logical
comparison is between measures 0 (for which supportive harmony is absent) and 8. Hood’s and my graphs both convey that the G and B♭ in the middle of measure 8 do not correspond to a tonic resolution of the preceding dominant. (Though Hood displays the G as a passing note between F♯ and A in her graph 2G and I display it as a neighboring note between two F♯s in 7.1, neither conception projects G as an asserted tonic root.) Hood reverses that hierarchy in her reading of measure 0, where A appears as a passing note within a slurred B♭>G third. (“The first appearance of this figure unmistakably outlines tonic harmony” (paragraph 17, emphasis added).) She indeed replicates this tonic in measures 8|9, starting with upbeat bass G.7 Though I am strongly supportive of imaginative thinking as a component of analysis, my internal ear prolongs the right-hand notes E♭, A, C, and E♭ through the rests of measures 8 and 9, with (importantly) the conclusion of a chromatic descending fourth that began with the high G of measures (4)|5 achieved with the arrival of D at 92. Bass G at 91 connects the A and F♯ of that prolonged chord. For me, an imagined tonic chord (unmistakably!) does not emerge above that G. Transferring this reading of measures 8–9 to measures 0–1, B♭, G, and E♭ would be interpreted as appoggiaturas to members of the opening F♯-A-C-D sonority. I likewise suggest that no tonic chord occurs in measure 2, where E♭ sounds throughout and where I imagine C continuing after its eighth-note sounding as well. The chord is G-B♭-C-E♭, rather than the tonic Hood proposes. As 7.1 shows, the chord of measure 2 may be interpreted as a connector between two different inversions of the embellishing chord that precedes the initial tonic. (In the context of the consequent phrase that begins in measures 8|9, this embellishing chord takes on the role of extending the dominant harmony of measure 8.) Chopin later provides strong support for this reading. Near the end of the prelude the G-B♭-CE♭ chord is repeated during each measure from 36 through 38. Then, magnificently, in measure 39 it evolves further, with a chromatic shift from C to C♯ coinciding with the concurrent sounding of all four pitch classes in one of the prelude’s boldest chords. This embellishment of the dominant possesses a ⇨ quality. Recall my assertion that the chord at 61 serves as I⇨. Comparing those two chords, one notes their obvious dissimilarity. Consequently, I cannot endorse the notion that a tonic chord occurs in measure 2. The tonic’s first sounding occurs
in measure 4, supporting Kopfton in the melody. A conventional descent from to ensues, in coordination with a harmonic progression from I through IV♮ to V♯.
The A2 section that Chopin might have composed
The A2 section that Chopin might have composed (measures 8|9–(16)) Not all of a work’s notes are of equal importance. I propose that the doubled A♭ at the end of measure 15 is an extraordinary note with far-reaching consequences. That measure’s slur connecting the bass melody’s E♭, C, and A♮ (also incorporating passing note B♭) and the right-hand chord that sounds immediately thereafter – which listeners as yet have no reason to regard as anything other than F♯-C-E♭ – bring to mind the content of 81: a dominant harmony (successor of the subdominant), which in the consequent phrase is positioned a tad earlier to make room for the tonic during the phrase’s final measure (which we suspect will be measure 16, thereby complementing the eight-measure antecedent). This is a conventional compositional strategy that Chopin ultimately does not realize. A hypothetical conclusion to A2 that fulfills the promise of what precedes the fateful A♭ (resulting in a prelude of sixteen measures) is displayed in 7.2. Postponing a consideration of that A♭’s consequences until the next section of this chapter, let’s explore (with the help of 7.3) the normative eight-measure version of A2 that Chopin might have composed.
Example 7.2 Alternative version of Prelude in G Minor (op. 28/22), measures 15 and 16.
Example 7.3 Analysis of Prelude in G Minor (op. 28/22), mm. 8|9–16 (incorporating 7.2). The chief difference between the two phrases (prior to the cadence) concerns how the tonic, once attained, is prolonged. (Compare measures 4–6 and 12–14.) Both versions are highly chromatic, yet they pursue different strategies, resulting in contrasting evolutions of the tonic (both of which target IV): first I⇨ (B♮-D♭-F-A♭ at 61), then I➔ (B♮-D-F-G at 142). The cadence supplied in 7.2 borrows material from Chopin’s cadence in measures 40 and 41, while completing the descending background line left dangling after
in
measures 8 and 9. The at the downbeat of hypothetical measure 16 (reminiscent of 82) “belongs” at the end of measure 15, where it appears in 7.3. Any notion of a parallel relationship between the phrases of measures 1–8 and 9– (16) would be difficult to develop in the context of Hood’s erratic application of Roman numerals: whereas no IV numeral appears below the subdominant of measures 6 and 7 in any of her graphs, a iv appears below the minor subdominant of 151 in her graph 2H (though not in graph 1F or 1G, which also incorporate Roman numerals). Explanations for how Chopin proceeds from I to IV might indeed take several courses. Yet before proceeding to that investigation, I suggest that some revision in the hierarchical relationships among pitches that Hood displays is in order. Graph 1F shows a bass descent from E♭ through D♭ to C in
measures 13 through 15. To my ears the line possesses a more uniformly chromatic character, with the final note of each beat within measures 13 and 14 serving as the principal note, in coordination with the likewise chromatic soprano, as follows: B♭
A
A♭
G
E♭ > D
D > C♯
D♭ > C
C > B♮
Two intervals of the tonic triad (whose third shifts from B♭ to B♮ over the course of the passage) are traversed: B♭ to G, and D to B♮. An interpretation of the chordal progression would need to accommodate the following:
g
A➔
f
G➔
One might regard these chords as the first two cycles of an obstinate sequence whose next chord, e♭, fails to emerge owing to the interaction between the g and G➔ chords, resulting in a succession instead to c, as follows:
G Minor:
I (
)
I➔
IV
Or, one might regard f as a chromatic upper-third substitution for D in a tonicprolonging
I
II➔
I➔
tonic expansion. The f enhances the “dominant-emulating” quality of the G➔ chord by being “pre-dominant emulating,” so that measures 14 and 15 take on the aspect of
IV
V7
I
in what some would interpret as a brief tonicization of the C Minor subdominant. None of these notions coordinate with Hood’s hierarchical interpretation of the bass, from which the Roman numeral analysis in her graph 2H is derived. After twelve measures of music during which only one Roman numeral has been applied, suddenly two measures are annotated by eight numerals (some surrounded by parentheses or single quotation marks) in the context of three keys. Though these numerals are correct insofar as they indicate root and quality for a range of stacked-third chords, they do not succeed in conveying what I regard to be the measures’ essential feature: the evolution of the meek diatonic minor tonic (which Hood displays as i within parentheses and as
of V within single quotes,
thereby diminishing its hierarchical importance) into a surging, iv-targeting I➔ (which she labels as
of iv without discernible connection to the preceding
minor tonic). Finally, whereas my perception of how what has occurred thus far conforms to the conventions of a parallel period guides my ears to expect that after the IV of 151, V♯ will follow (in accord with the prior succession from IV♮ to V♯ during measures 7 and 8), Hood’s analysis is silent concerning measure 15’s F♯[G♭]-A-C-E♭ chord (exactly the same evolved state as in measure 8, though in a different inversion). That brings us to the fateful moment of bass A♭’s arrival (triggering F♯’s enharmonic shift to a G♭ role, in accord with Chopin’s spelling), which both prevents closure in measure 16 and directs the progression on a more expansive course, to be explored below.
Chopin’s expanded A2 section (measures 8|9–41)
Chopin’s expanded A2 section (measures 8|9–41) Two common continuations from IV are available within Chopin’s tonal syntax. Perhaps the dominant will follow directly; or perhaps the path to the dominant will be expanded through a 5–6 shift applied to the subdominant. In G Minor, subdominant C-E♭-G’s 6phase chord might emerge as diatonic C-E♭-A; or, a more colorful “Neapolitan” variant (C-E♭-A♭) might sound instead. Chopin chose this latter alternative (as displayed in 7.4), going so far as to briefly tonicize A♭ Major. (The initial statement of the A♭ chord in measures 15 and 16 is already surging as I➔ towards IV within the tonicizing progression in A♭ Major, as is conveyed by the parentheses around 8 to the right of “A♭ Major: I” in 7.4.)
Example 7.4 Analysis of Prelude in G Minor (op. 28/22), mm. 8|9–41 The two continuations from G Minor’s IV under consideration – dominant D-F♯-A and lowered supertonic A♭-C-E♭ – are antipodally related (that is, their roots are separated by a diminished fifth or augmented fourth). This is an ideal context for the mehrdeutig deployment of a diminished seventh chord.8 The four pitch classes on the fourth and fifth eighth notes of measure 15 might have been spelled either as F♯-A-C-E♭ (an evolved state of G Minor’s V♯ chord, which Chopin could have confirmed by resolving ninth E♭ to D, as occurs in 7.2) or as C-E♭-G♭-B (an evolved stated of a ♭II chord surging within its
own tonicization, which Chopin does confirm by resolving ninth B [A] to A♭ at the end of measure 15 and by undertaking a chromatically filled-in voice exchange – – over the bar line between measures 15 and 16). As 7.2 and 7.3 demonstrate, the first interpretation would lead to a PAC in G Minor at the normative point, the phrase’s eighth measure. In contrast, 7.4, which corresponds to what Chopin actually composed, shows how the ♭II alternative results in a longer route to the PAC. Once a cadence during the phrase’s eighth measure is decisively rejected, Chopin seems in no hurry to reach his goal: the phrase expands from the normative eight to an astonishing thirty-three measures by means of the already mentioned tonicization as well as several internal repetitions and expansions, acknowledged by 7.4’s grid of measure numbers and by a hairpin symbol. The more developed harmonization stems in part from Chopin’s decision to replace the single-arpeggiation bass (G–D) of A1 with a double-arpeggiation bass (G–D–G–D–G) during A2. Whereas the “Neapolitan” version of IV6 proceeds to V7 and then I to support the span from through
to during the opening segment of A2, the path from to
proceeds by way of incomplete upper neighbor C, which is presented in the soprano register during measure 24, supported by the supertonic harmony. After a repetition of this portion of the structure, the A (= ) is transferred downwards, not to the register in which the descent to
transpired during A1, but instead (in the middle of measure 34) to the
register of the initial sounding of Kopfton D a seventh below Middle C (in measure 4). From that low A, prolonged through measure 40 via embellishing chords (including the potent C♯-E♭-G-B♭ of measure 39, mentioned above), the background line’s concluding G emerges by stepwise descent, supported by the PAC tonic. Doublings of G an octave and two octaves higher bring closure concurrently in all of the registers in which portions of the fundamental line have sounded during the prelude. Hood’s graph 1F contains a remarkable analysis that highlights our widely divergent views of the work’s harmonic dimension. She deploys only three analytical symbols to provide the basic harmonic sense of measures 9 through 22: i N i. (In her work, N stands for Neapolitan; the latter i is followed by an Arabic 6 to
convey that the tonic chord appears in its first inversion.) Though my 7.4 incorporates equivalent symbols – I ♭II I – my contextualization of the Neapolitan chord contrasts Hood’s in important ways. Note first that our difference of opinion regarding the arrival point of the phrase’s initial tonic chord emerges once more: Hood places the tonic in measure 9, whereas I place it in measure 12. Yet we agree that, one way or another, the phrase establishes the G Minor tonic before the Neapolitan arrives. Though I acknowledge that ♭II is tonicized, I nevertheless regard it as the asserted 6 phase of a hierarchically deeper chord – namely, IV, whose attainment is emphasized through the transformation of the minor tonic into a surging I➔. In Hood’s Graph 1F this IV chord lacks a label (as is also the case in the more detailed Graph 1G, though in Graph 2H a iv appears among the twenty symbols – numerals, N, and +6 – that annotate this fourteen-measure passage). Likewise, in my view a harmony that is hierarchically deeper than ♭II precedes the tonic resolution – namely,
. (The three bass noteheads for this passage
connected to a beam in 7.4 are G, D, and G.) Hood displays evidence of some sympathy for that view in her graph 1B (though, again, no V label appears). I am not in a position to decide whether the competing hierarchies displayed in 1B and 1F amount to an assertion that the Neapolitan imposes a shift in the relationship among these various chords (in accord with the “ambiguity” theme of Hood’s article); or whether, instead, the annotation of the latter graph with harmonic symbols is in need of repair. I also note a significant discrepancy between the presence of Roman numeral i at measures 34–35 in graphs 1A through G and its absence in graph 2H.9 Again, is this an inadvertent omission; or is Hood intending to juxtapose two quite different readings of the closing measures, fostering the notion of ambiguity? (Though neither version matches what I display in 7.4, graph 2H is far closer to my view. However, I suspect that Hood would quickly add V and i numerals, to conform with the other graphs, if the discrepancy were brought to her attention.)10 Though other issues could be addressed (for example, Hood’s +6 label, in the context of C Minor, for what I interpret as the initial statement of the ♭II chord at the end of measure 15), by now it is clear that there is little common ground between our interpretations, despite our use of similar analytical strategies.
Readers may wish to extend the comparison of our perspectives beyond this single brief prelude, placing Hood’s recent monograph alongside mine for a double dose of invigorating Chopin study.
8
Prelude in C♯ Minor (op. 45) ◈ in response to Jean-Jacques Eigeldinger and to Charles J. Smith Jean-Jacques Eigeldinger’s lifelong dedication to Chopin has enriched the musician’s library with important books, articles, and scores. He edited all of the preludes (both op. 28 and op. 45) for the recent Peters Urtext edition and has displayed his musicological acumen in a wide-ranging article on the Prelude in C♯ Minor, op. 45.1 Though devoted in large part to contemplations regarding Chopin’s interactions with Delacroix’s views on painting and his indebtedness to Beethoven, that essay offers a sophisticated analytical study of the prelude as well. (Eigeldinger acknowledges the contribution of Georges Starobinski in its formulation.) Another noteworthy analysis of that work, by Charles J. Smith, has appeared in a volume of essays, intended for students, by a range of luminaries in the field of analysis, edited by Deborah Stein.2 In that Smith has held a special interest in both Chopin and in harmonic analysis throughout his career, the opportunity to explore his reading of the prelude here is especially welcome.
The Prelude in C♯ Minor’s introduction (measures 1–5) The opening measures of the Prelude in C♯ Minor only gradually come into focus as an establishment of the C♯ tonic, confirmed by the potent G♯>C♯ bass succession over the bar line between measures 4 and 5, supporting a PAC in that key. Parallel progressions of chords were featured often in Baroque thoroughbass treatises.3 Yet once harmonic thinking began to emerge as a central component of musical speculation, their analytical treatment turned out to be especially problematic.4 Though certainly one could concoct a Roman numeral label for each chord within Chopin’s progression, in my view that exercise would be pointless, since many of the internal chords do not fulfill the roles that they would in harmonically asserted contexts. (Though the labels I VII VI V IV III II, for example, may succeed in indicating where within tonal space the various chords of a parallel progression reside, they do so at the expense of syntactic sense. Any harmonic system that can blithely accommodate VII proceeding to VI, or IV to III, is so watered down as to be of no value.) I propose instead that Chopin pursues a focused and nuanced downward linear initiative for three measures, broken off (at 41) just before the phrase’s concluding V➔ I cadence, where the logical next chord within the pattern – E♯-G♯-C♯ (displayed conjecturally in 8.1a) – is replaced by E♮-G♯-C♯ (which here functions as a cadential whose bass G♯ is tardy), embellished by a suspension (quarter note A) and retained for half a measure to help break the momentum of the descending progression. Chopin’s writing divides the preceding descending seventh (which in retrospect will be interpreted as a broad connection between I and ♮II) into three thirds. Note how the A and f♯ chords become nodal points through the insertion of downbeat neighboring chords, thereby expanding the domain of each within the stepwise descent from one to three quarter notes. Consequently the model in 8.1a displays three levels of activity: the foundational c♯ to D♮ (traversing a descending seventh that projects I to ♮II), the segmentation of that seventh into three thirds (with internal nodal points at A and f♯), and local passing chords that connect nodal points and neighboring chords that prolong the two internal nodal points.
Example 8.1 Prelude in C♯ Minor (op. 45) (a) Analysis of mm. 1–3; (b) Analysis of mm. 1–5. In that music analysts for good reason have come to regard the ♮II (“Neapolitan”) chord as a normal occurrence within minor-key contexts, some care in assessing how it comes about here is in order. (This assessment will prove to be crucial for our understanding of a later passage from the prelude.) I propose that Chopin is proceeding in this descending path not according to diatonic precepts (even if A and f♯ coincide with diatonic chords within C♯ Minor), but instead in an obstinate manner. As such, he is not bound by the dictates imposed by the C♯ Minor key signature, which favors seven specific pitch classes. When thinking outside the diatonic realm, the numbers from 0 to 11 (with C = 0) offer a neutral means of displaying pitch interactions, in a modulo 12 framework free from the hierarchical differentiations imposed by key-based (modulo 7) thinking. Chopin’s descending triads thus may be represented as follows:
8 4 —————
4
1 —————
1 —————
1
9 —————
9 —————
9
6 —————
6 2
m
M
m
M
Note especially that each chord’s third and fifth hold over from the preceding chord, and that the chordal qualities alternate between minor (m) and major (M). Once the descending trajectory has run its course (as determined by the composer), the endpoint is thrust back into the context of diatonic tonal space, which must somehow make sense of it according to the conventional relationships within the key. Though in this case the chord that is thrust back is not diatonic, it happens to coincide with the common “Neapolitan” variant of the supertonic. The graph displayed in 8.1b thus interprets chromatic D♮ as a frequently encountered and therefore unremarkable wobbly note resulting in ♮II, with diatonic pitch D♯ restored (as it almost always is) during the dominant harmony that follows. Minor-key tonality ultimately prevails: D♮ is subservient to D♯, and the major dominant is the principal structural event between the perimeter tonic harmonies, as indicated by the beamed bass notes, C♯–G♯–C♯ (Schenker’s “sacred triangle”). The graph displays one unusual feature: because the soprano melody’s descending seventh during the parallel progression places the endpoint chords in contrasting registers, a foundational linear connection emerges between the first chord’s lowest sounding pitch, E (which I propose serves as the Kopfton), and the ♮II chord’s highest pitch, D♮, which proceeds via the D♯ wobble correction to tonic C♯, completing a third-progression. After the cadence, the Kopfton is reinforced (indeed, in this unusual context it needs some reinforcement) through the bass melody’s projection of an apex E in three successive registers – at the middle and end of measure 5 and the end of measure 6, and then repeated. Eigeldinger interprets Chopin’s opening melody not as a descending seventh followed by cadential gestures, as I do, but instead extends a bit further, to a
descending octave, split into two tetrachords: C♯–G♯ and F♯–C♯ (p. 246). To support his tetrachord interpretation, he directs readers to measures 80 and 81, where those tetrachords (plural) allegedly recur (note 29).5 Exploring the latter assertion first will provide some useful perspective for an assessment of the former. The G♯-C♯-E-G♯ chord that boldly brings the cadenza to an end at 801 would lead listeners to expect a specific continuation: the dominant’s root G♯ will be retained while the three remaining pitches of
will sooner or later fall into
place (or will be imagined to fall into place if not literally stated). Nothing through measure 82 hints at any progress in achieving that result. Instead, the dominant’s third (B♯), imagined fifth (D♯), and seventh (F♯) emerge concurrently at 831. Between measures 80 and 83 Chopin presents a descending arpeggiation touching upon all of the cadential chord’s members: G♯>E>C♯>G♯. During this arpeggiation he incorporates at each nodal point exactly the same sort of embellishment as was deployed at the two internal nodal points during the introduction: half-step lower neighbors. The following stages convey my conception of how Chopin constructed this intriguing melody: G♯
E
C♯
G♯
G♯>F
E>D♯
C♯>B♯
G♯
G♯>F
E>D♯
B♯
F
G♯ C♯ B A >F
E>D♯
C♯
F
B♯< Observe how, as the melody takes on its distinctive shape, two pitches (C♯ and G♯) are elided, one pitch (B♯) is displaced, and one pitch (the initial G♯) is embellished by an upper-fourth flourish. That flourish indeed corresponds to Eigeldinger’s upper tetrachord – the only meaningful fourth available within this
context. I reject his assertion that an F♯–C♯ tetrachord occurs as well: no F♯ sounds during the passage, and the D♯ does not descend to C♯. The accentuated metrical placement of F and D♯ (both half-step lower neighbors) in measure 81 corresponds to my reading of the introduction’s accentuated G♯ at 21 and E♯ at 31 as neighboring embellishments (as shown in 8.1a). Whereas Eigeldinger proposes two descending fourths – C♯–G♯ and F♯–C♯ (with some unexplained notes coming between them) – as the foundational organizing principle of the introduction’s melody, I propose instead a succession of three interlocking descending thirds, set off by lower neighbors and presented uniformly as the second through fourth quarter notes of three consecutive measures: C♯>B>A
A>G♮>F♯ G♯
F♯>E>D♮ E♯
The persistence of third-relationships during the main section of the prelude further supports this reading.6 Eigeldinger has put his finger on an important point by suggesting that the introduction wavers between C♯ Minor and A Major (p. 246). He directs our attention especially to the pitch D♮, which differentiates A Major’s diatonic pitch collection from that of C♯ Minor. As an experiment, perform the introduction as written until 42, substituting D♮ for D♯ at that point. You will discover that the following B♯ will want to shift to diatonic B♮ and that the low bass note E (instead of G♯) will sound right. Letting those notes proceed according to their inclinations, one ends up cadencing on A at 51. Indeed, the introduction’s nodal c♯, A, f♯, and D♮ chords are all diatonic in A Major, and if Chopin had in fact proceeded as in our experiment, one likely would regard the initiating c♯ chord as tonic A’s upperthird chord. The descent would in that case be interpreted as a filling in of the A>D♮ fifth, corresponding to I ( ) IV. It is only through the strength of Chopin’s cadence that an analyst may, instead, retrospectively assign the initiating c♯ chord – despite its brevity and weak metrical placement – the structural role of initiating
tonic. As stated at the outset, “the opening measures of the Prelude in C♯ Minor only gradually come into focus as an establishment of the C♯ tonic.” Smith’s analysis takes the unusual tack of comparing Chopin’s composition to the narrative trajectory of a thriller movie, proposing that just as the film audience tries to resolve the various plot entanglements and figure out who the culprit is, so also auditors of Chopin’s prelude will ponder it as a puzzle that needs to be resolved. I don’t buy it. As Smith suggests, sometimes the key to resolution is “hidden in plain sight” (p. 240). In this case the introduction is that key.7 If one does not suitably come to terms with its nuances before proceeding to the main body of the work, the complications that arise likely will be perplexing. I do not think that Chopin intended to obfuscate what he was doing: the introduction pursues a straightforward course in a direct and uncluttered presentation. Nevertheless, Smith (following Eigeldinger’s lead) proceeds to segment the melody into tetrachords rather than trichords, and consequently his reading of the passage does not sufficiently correlate with the contour of the work’s main section (to be explored below) for him to recognize the latter as a gargantuan variant of the former. Smith’s annotated score 20.1 (p. 243) contains a curious – and telling – use of curved arrows. During the first four chords, the initial c♯ is the target of an arrow that curves leftwards from the fourth chord; whereas during the fifth through eighth chords the initial A is the target of no arrow, while the eighth chord’s arrow curves to the right, targeting the ninth chord. Compare that inconsistent reading with 8.1a, where the fourth and eighth chords perform equivalent roles as expanders of the nodal points that immediately precede them. Though Smith yearns for a D♮ chord in measure 4 (a chord that is crucial to his plot denouement later in the work), I contend that such a D♮ chord is a conspicuous part of the prelude’s fabric at the end of measure 3.8 The plot thus may be summarized as follows: after the initial tonic, a descent in thirds through A and f♯ proceeds as far as D♮, which (following the conventions of the “Neapolitan” chord’s usage) leads to a V➔ I cadence. As we shall see, the main section of the work at first pursues the same trajectory, reiterating the introduction’s c♯, A, f♯, and D♮ nodal points (measures 6|7 through 18) and thus giving auditors a second chance at
comprehending this essential component of the plot, after which multiple wobbly notes transform the second through fourth chords, so that ultimately D♯ (II➔) rather than D♮ (♮II) precedes the main section’s V➔ I cadence in measures 66 and 67 (which, as we shall see, Smith relegates to the status of a retransition). Smith gives considerable weight to chords that he regards as tonicized. In his fig. 20.5 (p. 248) he shows a triangular relationship among the introduction’s c♯, A, and tonicized f♯ (to which D is appended off to the side). An arrow points directly from f♯ back to c♯. My 8.1b accounts for all of those chords (with a contrasting reading of their hierarchical relationships) and notably includes one that is absent from Smith’s account: the G♯ dominant, a member of the introduction’s foundational sacred triangle, C♯–G♯–C♯.9
The Prelude in C♯ Minor’s main section
The Prelude in C♯ Minor’s main section (measures 5–67) During the prelude’s introduction a brief though dense linear passage connects I (measure 1) and ♮II (measure 3) prior to the V➔ I cadence. Chopin’s construction of the prelude’s main section pursues a similarly modest agenda, now astonishingly expanded: between the I of measures 5 through 8 and the II➔ of measure 65, Chopin passes back and forth among the nodal points established during the introduction, even as they undergo chromatic mutation. (See 8.2.) The extraordinary size of this connective passage stems not only from the fact that Chopin now pursues a roundabout course, with multiple ups and downs along the descending-seventh trajectory, but also from the substitution of multiplechord progressions for the individual chords that connect or expand nodal points during the introduction. For example, a connective b chord comes between the c♯ and A nodal points during measure 1. In descending from c♯ to A during measure 7 through measure 13 that b chord indeed recurs (measure 11), though now it resides within a segment of the descending circle of fifths: c♯ F♯➔ B/b E➔ A. The G♮ connective chord that passes between A and f♯ during the introduction is replaced by a more dynamic C♯➔ during 141. (Note that its context retains the sense of stepwise descent between soprano pitches A and F♯, now incorporating diatonic G♯, along with a lower sixth in the alto register.) Though the D♮ chord emerges directly after f♯, its prolongation during measures 15 through 18 incorporates vestiges of the G♯-B-E connective chord of measure 3: the E at the end of measure 15 passes between the melody’s F♯ and D♮, whereas the embellishes
of measure 17
. Likely a shorter composition would have resulted if this D♮ chord
(asserted as ♮II) had proceeded to dominant G♯, as was the case during the introduction. Chopin instead backtracks to f♯ in measure 19 – creating some distance from the chord that during the introduction resided at the juncture of the linear initiative and the concluding harmonic initiative. The prolongation of this chord, including a modal shift to F♯ at measure 31 and a mutation to F♮ at measure 55, is one of the principal features of the main section, followed by the definitive descent to D♯➔ at measure 65. (One may trace the progress of the f♯ chord’s evolution in 8.2, noting especially how f♯, F♯, or F♮ resides at the internal phrase boundaries, indicated by the bar lines.) One might even regard all the
material between the f♯ of measure 19 and the F♯ of measure 64 as a parenthetical passage.
Example 8.2 Analysis of Prelude in C♯ Minor (op. 45), mm. 5–67. At first it seems that the prolongation might be of brief duration, since the new phrase that begins at measures 20|21 inaugurates, starting on f♯, the same circular progression that earlier led from c♯ to A. Listeners are poised for a D♮ arrival at 271. Chopin indeed is prepared to confirm that D♮ with a five-measure tonicizing expansion deploying a local I– IV–V–I harmonic progression (compensating for the absence of even an embellishingchord expansion at the D♮ nodal point during the introduction). This progression does in fact transpire, though down a third, since B♭ unexpectedly displaces the D♮ goal at 271. Its cadence measure (31) offers yet another surprise: a further drop – now from B♭ to G♭ – occurs. This G♭ is confirmed via a similar five-measure expansion (transposed), which cadences successfully in measure 35. It may appear that Chopin has managed to move from a sharp key (F♯ Minor) to a very flat key (G♭ Major). Yet ultimately G♭ will be accepted as F♯, even if the notation in flats persists for some time in the score. This is a thorny and controversial issue. In my view, the passage’s obstinate chord progression should be interpreted outside the realm of diatonic tonality. In a modulo 12 context (already called into service during our discussion of the introduction’s obstinate progression), the following grid aptly represents the “descending in thirds” progression: 1
9 —————
9
6 —————
6
5
2 —————
2
1
10 —————
10 6
m
M
M
M
In a modulo 12 context an octave may be traversed (here as 6>2>10>6) with no enharmonic seam. Whereas the introduction’s obstinate progression alternates between minor and major chords each of which shares two pitches with its predecessor, here a midcourse shift in the relationship between adjacent chords results in the juxtaposition of three major triads (starting with the elided 2-6-9 of measure 27), connected by only one common tone. Once that modulo 12 progression concludes, the goal chord is thrust back into the diatonic context. In this case accommodation is easy: the progression has come full circle, from a minor to a major chord rooted on F♯. The emergence of the enharmonic G♭ spelling comes about through the use of modulo 7 notation (wherein three “major thirds” span an augmented seventh) to convey a modulo 12 conception. The trajectory proceeds upwards from F♯ at the onset of the next phrase, which begins at measures 36|37. (This discussion will be presented in terms of sharps, corresponding to my 8.2, not the flats of Chopin’s score.) Whereas each of the section’s first two phrases was inaugurated with the traversal of a descending major third, navigated via a segment of the circle of fifths (c♯ to A in the first, and f♯ to (D♮) in the second), now an obstinate ascending 5–6 sequence is set in motion to chug upwards a major third (F♯ to A♯), with D♯➔ (F♯’s chromaticized 6-phase chord) in measure 39 targeting the passing chord G♯ (measure 42) and E♯➔ (G♯’s chromaticized 6-phase chord) in measure 47 targeting goal A♯. Yet A♯ is not one of the nodal points introduced during the introduction, and so Chopin revises course mid-sequence by shifting E♯➔ down a half step to E➔ (measure 53), thereby targeting nodal A. Yet, just as the goal chord of measure 27 is elided and displaced by a chord a major third lower, so also is this A goal (measure 55) elided and displaced by F♮. Thus we have ended up “in the cracks” (outside the
confines of the initially established nodal points) after all. This wayward F♮ nevertheless is treated to the same sort of chordal expansion as was the F♯ arrival of measure 31. We now seem even further from tonal resolution than was the case at that point. The section’s final phrase sets things aright and achieves the long-awaited goal with surprising alacrity. First the usurping F♮ chord is simply hoisted up a half step to the legitimate nodal F♯ (measure 64), the oddity of the voice leading (three simultaneous wobbly-note resolutions!) mitigated by the concurrent sounding of a descending passing note (E) in the bass. F♯’s major quality (acquired in measure 31) is not relinquished. The presence of pitch A♯ as third of the F♯ chord leads to the substitution of II➔ for the introduction’s ♮II as the progression continues downwards its final third. Of course, either incarnation of the supertonic may serve as the predecessor of V♯. That dominant (measure 66) in turn targets the tonic goal (measure 67), bringing to a close the extraordinary twelvefold expansion of an idea that during the introduction transpired in just five measures. It is understandable that Chopin elected to present a large chunk of this sharp-key composition using flats. He has thereby spared performers (including many amateurs) from having to read numerous frightfully spelled chords, such as the E♯➔ chord (with suspended ninth) at 491, whose appropriate spelling would be E♯-B♯-F -G -B♯. Granted, an enharmonic shift is required at some point in order for the section to end where it started – in C♯ Minor, rather than D♭ Minor. The logical spot for that shift within one’s analysis would be during the modulo 12 equal subdivision of the octave (measures 21 through 31): from f♯ to F♯, rather than f♯ to G♭. In his ex. 2 (p. 247) Eigeldinger instead copies Chopin’s flat notation at that point. Sharps are restored at measure 51’s E-A-C♯ chord. Undertaking a cosmetic (and therefore distracting and potentially misleading) enharmonic shift while concurrently charting chordal associations in an analysis is exceedingly dangerous. Consequently my analytical diagrams generally do not follow composers when they employ spellings of convenience. (Theory-savvy readers of technical analyses should be able to handle a few double-sharps!) Given that chords related by a third have been a pervasive feature of the entire composition, it is reasonable that Chopin pursues an ascending-third trajectory from the stable F♯ chord of measure 37. Yet what should that initiative’s goal be?
Earlier the relationship between A and f♯ was established. Does the conversion of f♯ into F♯ warrant targeting upper-third a♯ (or A♯) instead? Or should A be maintained nevertheless? The ascending 5–6 sequence that Chopin employs could lead to either goal, depending upon how the 6-phase chords are constructed. F♯ D♯➔ G♯ (an elaboration of F♯5–6 G♯5) is a good start in either case. But should G♯’s 6-phase chord be E➔ (G♯-B-E, surging towards A) or instead E♯➔ (G -B♯E♯, surging towards either a♯ or A♯)? The score bears witness that Chopin wove indecisiveness on this point into the fabric of the work: he initially selects the latter trajectory (measure 49) but soon shifts to the former (measure 54). Thus two potential fifth-relationships are juxtaposed: E♯➔ A♯ and E➔ A. When goal A is displaced by F♮, a descending third-relationship is implied: A (imagined) to F♮. Eigeldinger’s spelling of E♯ as F (his annotation for measures 47 through 63 – during which the cosmetic enharmonic shift from sharps to flats occurs – reads “F A F”) equates the initiating and closing elements of this complex and fascinating passage, a reading that not only betrays an insensitivity to the difference between descending fifth (ascending fourth: E♯F♮) relationships but that then proceeds by claiming that the home key of C♯ Minor is “symmetrically divided into three enharmonic thirds”: c♯, F, and A (p. 246). Whereas I accept A as one of the work’s main players (what I have referred to as a nodal point along the c♯>D♮ trajectory, whose D♮ will be replaced by D♯ in measure 65), I reject Eigeldinger’s F: as E♯ it is an internal element of a sequential progression, and as F at the cadence it is a temporary usurper of F♯, whose restoration in measure 64 is accomplished before further progress in the tonal trajectory occurs. Indeed, the equal subdivision of an octave is featured occasionally in music of this era: Chopin in fact pursues it in the 6–(2)–10–6 passage of measures 21 through 31, as I have noted above. But to pick a C♯ here, an A there, and an F somewhere else and claim that these are the “poles around which the piece’s harmony is constructed” (p. 246) distorts their compositional roles within Chopin’s prelude. As the juxtaposition of 8.1b and 8.2 makes clear, the bass C♯–G♯–C♯ sacred triangle plays a foundational harmonic role both in the introduction and in the main section, and in both contexts some sort of supertonic (♮II or II➔),
achieved via a descent in thirds, serves as the principal connector between the tonic and the dominant. As is typical of tonal music in general, the bulk of Chopin’s creative energy here is devoted to what comes between the initial I and the cadential V♯. In claiming that the D♮ chord of measures 15 through 18 “is established without any functional raison d’être” (p. 246), Eigeldinger neglects its potential to continue immediately to V➔, a scenario that Chopin passes over in favor of a longer and far more captivating build-up to the supertonic (II➔) in measure 65. If the prelude’s main section is in fact a “gargantuan variant” of the introduction, as I have proposed above, then there is a significant structural connection between the cadences on tonic c♯ in measures 4–5 and 66–67. (Play them one after the other to hear how they rhyme.) My reading of the form gives them comparable status: as close of the introduction and of the main section. The latter is divided into four parts (indicated by bar lines in 8.2), set off by a rather amorphous halt on F♯ in measure 19 and dynamic (and equivalently formulated) cadences on F♯ in measure 35 and on its usurper, F♮, in measure 59. (Eigeldinger’s ex. 2 likewise presents the expanse from c♯ in measure 5 to c♯ in measure 67 as a single multi-sectional entity, though his internal bar lines do not in all cases coincide with mine. He annotates the goal c♯ chord with the word “Reprise,” which I take to imply a dovetailing of the end of the main section with the onset of its modified repetition.) Smith proposes a contrasting view of the form, which he classifies as rounded binary (p. 242).10 Though he divides what I call the main section into the same four parts as I do, my first two parts correspond to his first section, my third part to his middle section, and my fourth part to his retransition (p. 241).11 Consequently what follows the cadence of measure 67 is for him a more vital part of the formal design than it is for me. (In my view a one-part form has fully run its course by the cadence of measure 67 and will be reprised in an abbreviated version that retains all essential deep structural features; whereas Smith’s middle section, which cadences in F Major, requires the material after measure 67 to re-assert the tonic and to balance the open-ended first section.) As the remainder of this essay will help clarify, I propose that the prelude is organized as a set of four distinct passes through the same structural “theme”: the introduction, the main section, its modified repetition, and the coda. That view is
incompatible with Smith’s interpretation of the passage leading to the cadence in measures 66–67 (for me the site of the work’s background Urlinie descent) as a retransition. Despite our disagreement regarding the prelude’s form, Smith’s fig. 20.3 (which he calls the “Schematic form”) and my 8.2 have much in common over the course of what I call the main section until the final part, between F♮ and c♯ (measures 59 through 67), where his representation goes blank while mine robustly includes three of the section’s seven open noteheads and two of its four Roman numerals. This is an intensified replication of our disagreement regarding measure 4, discussed above. Whereas Smith’s focus emphasizes tonicized keys (going so far as to omit the structural dominant, which is labeled as V7/c♯ in his score 20.6), my perspective intermixes chords derived from modulo 12 progressions, chords modified by multiple wobbly notes, and structural harmonies regardless of whether or not they are reinforced by local progressions that incorporate their leading tones. I regard tonicization and structural depth as distinct notions that often do not correlate.12 Given the roster of chords left after his selective purging, it is not surprising that Smith has appended a listing of two chordal cycles to his fig. 20.3: B♭–D–F♯ and F–A–C♯. (They are presented in triangular diagrams in his fig. 20.4 as well.) His commentary explains: “This C♯–A–F cycle … accounts for the overall shape of the prelude’s beginning (C♯ minor to A) and end (F back to C♯ minor); in contrast, the D–B♭–G♭ cycle is the source for the harmonic motion through the middle” (p. 247). Whereas the latter corresponds to my 6–2–10–6 cycle (modulo 12) for measures 21 through 31, the former, which Eigeldinger endorses as well (as we have seen), falls apart for me because all of the various A(♯) and F(♯) chords above the open parentheses in 8.2 serve as nodal points (with or without wobbly-note mutation) along the path between the hierarchically deeper I and II➔.13
The modified repetition of the Prelude in C♯
The modified repetition of the Prelude in C♯ Minor’s main section (measures 67–84) After the PAC that is achieved in measure 67, the prelude could proceed directly to the coda (jumping from 671 to 842) with no injury to the form. Instead, Chopin electively repeats the structure that has just been presented, now in a much tidier (though, due to the cadenza, still very impressive) manner. A repeat of the initial c♯-to-A motion transpires during measures 67 through 75. (See 8.3.) Then Chopin takes advantage of a nifty trick of the trade: adding F to A-C♯-E results in II⇨. Thus the progression avoids entirely the intricate and extended navigation among mutating nodal points that characterizes the main section’s initial statement. The written-out cadenza briefly postpones the denouement, in the process accomplishing a shift from II⇨ to II➔ (thus bringing this progression into a closer alliance with that of the earlier main section, where II➔ occurs in measure 65).14 From the cadenza’s initiating D♯⇨ chord (which Chopin spells enharmonically using easier-to-read G♮ in place of F ), the second through ninth four-note groupings work downwards by half steps. The ninth chord in the series (eight half-steps below the starting point) incorporates a mutation: presented by Chopin as F♮-B-D♮-G♯ rather than as F♮-BC♯-G♯. From that point he works his way back up again, achieving C♯-G♮-E-B♭ (which represents D♯➔: F -A♯-C♯-E) in the middle of the thirteenth four-note grouping. That chord returns and is prolonged at the end of the cadenza, where the correct spelling is employed. Bass F at the start of the final four-note grouping resolves to the dominant’s G♯ (three octaves lower) at 801. A three-measure expansion of the cadential chord (measures 80 through 82) precedes a staid V➔ I close. Though the rhyme with measures 4–5 and 66–67 is inexact, the effect is one of increased stability due to the downbeat arrival of soprano . Yet eighth notes rise again from the depths, initiating a brief coda.
Eigeldinger tacitly confirms the formal redundancy of this section by giving it hardly any attention in his analysis. The word “Reprise” in his ex. 2 suffices.15 The annotations in Smith’s score 20.8 demonstrate one of my principal concerns with conventional harmonic analysis: the use of widely divergent symbols for essentially the same harmonic function. The cadenza connects two very similar chords: A-C♯-E-F and F -A♯-C♯-E, both of which target V♯. My notational practice, either with Arabic numerals (as displayed in 8.3) or with arrows (II⇨➔), emphasizes that a mere wobbly note differentiates those two sonorities. Smith’s conventional analysis instead makes them seem disparate: Ger versus vii°7/V. (If one agrees with me that their shared root is D♯, then the “= A7” in Smith’s annotation will seem curious as well.) Equally problematic, in my view, is the label i for the chord of measures 80 through 82 (Smith’s 81 through 83), though so much ink has been spilt on that issue over the years that I will hold my peace.
Example 8.3 Analysis of Prelude in C♯ Minor (op. 45), mm. 67–84.
The Prelude in C♯ Minor’s coda (measures 84–91) Whereas the penultimate left-hand pitch in the cadential measure 67 is G♯, an accented A emerges at that location in the counterpart measure 84. This A of course brings to mind the various A major chords that have initiated progressions away from tonic c♯ in the preceding regions of the prelude (measures 1, 13, and 75). In those earlier contexts A led either to f♯ (on the way to D♮ or D♯➔) or directly to D♯⇨. Now, with the help of the G♮ that emerges in measure 85, A➔ targets D♮ directly. (See 8.4.) Listeners thus may admire the range of similar though distinct trajectories that Chopin juxtaposes in this work. Yet there is something even more delicious to savor: the chord of measure 85 (spelled A-C♯E-G♮) is the enharmonic equivalent of the chord of measure 76 (spelled A-C♯-E-F ). Consequently alert listeners might develop a special interest in finding out how Chopin will proceed after measure 85: will A➔ lead to ♮II; or will D♯⇨ lead to V♯? Chopin chooses the ♮II route, thereby restoring the introduction’s version of the dominant preparation. The PAC that follows brings the progression to a close, with lingering echoes of Kopfton E in the post-cadential measures.
Example 8.4 Analysis of Prelude in C♯ Minor (op. 45), mm. 84–91.
9
Ballade in F Minor (op. 52) ◈ in response to Laufer Edward Edward Laufer’s detailed analysis of Chopin’s Ballade in F Minor appears in a book devoted to sonata forms.1 Given the venue, Laufer focuses especially on the work’s form and motivic associations. I am not persuaded by his formal assessment, which has appeared with some frequency in the literature devoted to this ballade. I propose that Chopin instead pursues a creative variant of an A1 A2 binary form, with multiple repetitions of A1, incorporating variation and internal expansion, accounting for the bulk of the work, followed by a single A2 statement near the end. (Laufer refers to the latter as a coda.) Since my focus is on harmony, I will not dwell on our disagreement regarding the form, but instead will glean as much as I can about harmonic matters from Laufer’s generous graphs. Though his examples are dense – to the point of sometimes exceeding what might reasonably be squeezed onto a page2 – Laufer’s use of Roman numerals is uncommonly sparse. Consequently I sometimes reconstruct the implied harmonic progressions through an assessment of the graphs’ pitch content and of the associations indicated by slurs and beams.
The introduction and the initial statement of A1 (measures 1–22) The Ballade in F Minor’s A1 section presents a conventional trajectory from a minor tonic (introduced at 82) to its major dominant (attained at 222).3 This trajectory is presented four times over the course of the ballade (incorporating progressively more extraordinary elaborations and expansions), after which a tonic-cadencing A2 finally commences at measure 211. Consequently a cadential dominant and the onset of a fresh tonic are juxtaposed multiple times: at measures 22–23, 57–58, 151–152, and 202–211. That same juxtaposition is deployed at the juncture of the introduction and the initial A1: a C major dominant is tonicized from the opening measure through the fermata chord of 72, thereby coordinating with what precedes each of the later A-section onsets. Gradually emerging out of a misty repeated octave G, the introduction’s tonicized C chord soon surges towards IV, whose 6 phase leads the progression onwards to V♮ and then I.4 (See 9.1.) The entire progression is repeated during measures 4 and 5, followed by fragments that extend the introduction for an additional two measures. The establishment of G (F Minor’s ) at the top of the texture as the introduction begins is critical. Whereas G is emphasized from the outset during the dominant-focused introduction, during each statement of A1 or A2 it serves as the successor of Kopfton A♭, which first emerges (in the same register as the introduction’s G) during 131. As 9.1 shows, Chopin’s melody juxtaposes a pair of unfolded thirds over the course of the ballade’s first thirteen measures: G down to leading tone E♮ during the dominant introduction, followed by tonic resolution F up to Kopfton A♭ during the opening measures of the A1 section. (As often is the case in minor-key compositions, an upper-third chord – A♭-C-E♭ – plays a role in the prolongation of the initial F-A♭-C tonic.)
Example 9.1 Analysis of Ballade in F Minor (op. 52), mm. 1–13. During the initial statement of A1 (measures 7|8 through 22), IV comes between Ispace (which eventually surges, targeting IV) and the cadential
. (See 9.2.) Tonic F’s
minor seventh, E♭, sounds in a consonant context during an excursion to the tonic’s upperthird chord (A♭-C-E♭ in measures 12 through 15). E♭’s ultimately dissonant character is unleashed through the restoration of tonic root F and the shift from A♭ to A♮ during 161. (An E♭-G(♭)-B♭-(D♭) embellishing chord separates the A♭ chord from the F tonic both upon arrival and upon departure.) The upward melodic unfolding from F reaches Kopfton A♭ during the prolongation of the upper-third chord.
Example 9.2 Analysis of Ballade in F Minor (op. 52), mm. 7|8–22. Once attained, the subdominant is prolonged via a tonicization of B♭ Minor, supporting a local third-progression from D♭ down to B♭, as is displayed in 9.2. This tonicization likewise proceeds to an upper-third chord (again aided by an intervening embellishing chord). The progression continues with II7 and then
within B♭ Minor.
Though prolonged for several measures, the F dominant does eventually resolve to B♭, at which point B♭’s role as IV within the broader F Minor progression is fulfilled by the continuation to dominant C. The sketch proposes that what conventionally might occur as a stepwise connection between Kopfton A♭ (during 131 and 141) and its incomplete upper neighbor B♭ (at 162 and 221) here coordinates with a registral shift, so that the seventh A♭>B♭ (broken up into three thirds) is traversed instead of the second A♭
second, that fourth remains an interior interval, preceding the arrival of the summit pitch A♭ (measure 13). The graph presented in Laufer’s ex. 7.3a does not make these correlations. The tall stem marking the C of measure 8 as the Kopfton imposes a visual barrier between related pitches. At the phrase ending, what I interpret as a structural divide between measures 22 and 23 does not register as such in Laufer’s graph. Our differing views stem in part from our contrasting determinations of the Kopfton: from Laufer’s (= C), the B♭>G third of measure 22 is interpreted as an unfolding from an outer to an inner strand, encouraging a continuation from dissonant B♭ to an A♭ resolution (as is conveyed by his soprano beam); whereas from my , a succession to
(the
conventional point of interruption within an A1 A2 binary form) is attainable, since B♭ may be interpreted as ’s incomplete upper neighbor.6 Laufer complicates matters further by suggesting that the subdominant is the goal – that the “quick V” that follows serves “only to reintroduce the I” (p. 162). Despite the duration of its tonicizing prolongation, IV is displayed in my 9.2 as an interior element of a conventional tonic-to-dominant progression, with HC at 222 rather than IAC at 231. If the dominant here seems a bit slight, keep in mind that Chopin will fortify an equivalent dominant arrival point later (in measures 195 through 210). One small point: within the B♭ Minor tonicization, dominant F major arrives without seventh E♭ at 182. An embellishing chord (over F pedal) at 202 presents as its third an E♭ that is retained when the F chord is restored. Laufer shows elements of the embellishing chord in his ex. 7.3a but does not acknowledge the restoration of the
. Here as elsewhere, a more generous display of Roman numerals
would have been useful. (Note that a I numeral appears neither at measure 8 nor at measure 23 in Laufer’s graph. Nor is the hierarchical relationship between the mediant and what I call a surging tonic clarified in measures 12 through 16. I suspect that Laufer intends III5–6 IV, which I regard as viable.)
The second statement of A1 (measures 23–57) Though the section that begins in measure 23 might have served as a consequent to the A1 antecedent, it turns out to extend no further than did that initial A1. Since it likewise cadences on the dominant (measure 57), it should be regarded as a varied repetition of A1, incorporating a bold internal expansion. Note in the score how what occurred during the upbeat half of measure 8 now is positioned during the downbeat half of measure 23. This metrical shift persists up to the point where the cadence would be expected. Instead of extending just one beat beyond measure 36 to attain that cadence (incorporating the C chord of 222), Chopin pauses on the B♭ subdominant, concluding the trajectory to the dominant only after the insertion of over twenty measures of new material. The subdominant chords of 362 and 571 represent the same moment within the harmonic trajectory introduced during the initial statement of A1. Especially since a G♭ chord leads away from the B♭ minor chord in both measures 31 (as in measure 17) and 38, this region will come across as a juxtaposition of two contrasting means of extending the subdominant before it eventually yields to F Minor’s dominant in measure 57. In all, the subdominant controls all but nine of the section’s thirty-five measures. An analysis of these added measures is offered in 9.3. The material falls into two parts. During the relatively static first part the minor subdominant is fortified through the transfer of its structural soprano pitch, B♭, upwards by an octave – to the register of the initial A♭ Kopfton (measures 13 and 27), to which it relates as an incomplete upper neighbor – and through its evolution into a surging B♭➔ chord – by means of D♭’s shift to D♮ and the addition of minor seventh A♭. During the dynamic second part that surge’s energy ignites a spirited circular progression that traverses all the diatonic roots in the tonicized key of B♭ Minor, as noted in 9.3.
Example 9.3 Analysis of Ballade in F Minor (op. 52), mm. 36–57. During the B♭ Minor tonicization within the initial A1, a B♭>A♭>G♭>F fourth was traversed (bound by a slur in 9.2, measures 16 through 18). That fourth plays a role in both parts of the expansion displayed in 9.3. The shift from F to G♭ (tentatively touched upon at 371, then decisively embraced in measure 38) begins an ascending trajectory that reaches B♭ in measure 46. (Note the slur, incorporating an internal downward registral shift, below the staff in 9.3.) Whereas the G♭ chord might have served as ♭II (a chromatic variant of IV’s 6-phase chord), offering an alternative route to the goal C major dominant, instead an A♭-C♭-E♭-(G♭) passing chord leads back to the B♭ subdominant, which is subsequently embellished by F-A♮-C-E♭ in measure 49. Then during the circle of fifths the same filled-in fourth, highlighted by the beam above the staff in measures 50 through 57 of 9.3, reverts to the descending direction. Mapping 571 of 9.3 onto 221 of 9.2, we should not be surprised that the C dominant (supporting
) that follows in measure 22 also
emerges in measure 57. Will a fresh start, beginning in measure 58, lead to success in achieving the longedfor PAC goal in the context of A2? Or will Chopin instead undertake an even more daring expansion of the A1 structure?
Two issues regarding hierarchical relations surface during a comparison of my 9.3 and Laufer’s ex. 7–4. First, I hear the soprano G♭ introduced in measure 38 extending through measure 45, noting that a descending G♭>E♭ third is answered by an ascending D♮E♭ slur and parenthetical reinstatement of G♭ below E♭.) Instead, I suggest that G♭ here resolves as a 9♭–8 suspension, confirmed by Chopin’s alto-register F during 562. (Laufer’s reading of a G♭ prolongation until the downbeat of measure 57 is presented most clearly in his ex. 7–4 c.)
The third statement of A1 (measures 58–151) At a basic level the tonal tale that the A1 section tells is unremarkable: after its initial stabilization the tonic surges, targeting the subdominant, which, after a tonicizing expansion, proceeds to the dominant for a half cadence. In an idiosyncratic organizational plan, Chopin repeats A1 several times, maintaining approximately the same structural framework for the tonic, for its surge, and for the dominant arrival, while developing the internal subdominant prolongation in ever more wondrous ways. During the first three statements of A1 this burgeoning content is anchored by straightforward and repeated presentations of the subdominant chord in a characteristic register (as first stated during 162 and 221). The following account of how those subdominant expansions transpire during the first three A1 sections will guide our discussion. First statement: 162–221 The foundational state of the subdominant tonicization, featuring a third-progression (D♭>C>B♭) supported by a harmonic progression within the tonicized key of B♭ Minor [9.2]. Second statement: 311–362 A reprise of the foundational state of the subdominant tonicization. 362–571 A fresh expansion of the subdominant, featuring a fourth-progression (B♭>A♭>G♭>F) supported by a descending circle of fifths within the tonicized key of B♭ Minor [9.3]. Third statement: 661–992 What begins as a straightforward reprise of the foundational state of the subdominant tonicization is transformed into an extended traversal of the D♭>C>B♭ third-
progression, incorporating an interruption and a shift to B♭ Major [9.4]. 992–1452 A fresh expansion during which B♭ Minor is restored, again traversing a thirdprogression (D♮>C>B♭), this time with C supported by a dominant whose prolongation incorporates a segment of an obstinate ascending circle of thirds (F
Example 9.4 Analysis of Ballade in F Minor (op. 52), mm. 66–99.
Example 9.5 Analysis of Ballade in F Minor (op. 52), mm. 99–145.
In coordination with greater underlying energy, generated by a steady stream of sixteenth notes, the foundational harmonic trajectory from the minor tonic through a surge to the subdominant is reprised during measures 58 through 66. A bass motion from B♭ through D♭ and E♭ to F again initiates that subdominant’s tonicization during measures 66 through 68. (The chord above bass E♭ during 672 evolves into II ⇨ in tonicized B♭ Minor.) Yet whereas in the previous presentations of A1 an expansion of B♭’s dominant for seven beats is followed by its resolution to B♭, now the F dominant extends from 681 through 801. The phrase in fact ends on a half cadence (with an interruption after C, B♭ Minor’s
, as shown in 9.4). A consequent phrase that achieves the desired PAC
(supporting ) commences as the tempo is restored in measure 80. A wondrous parallel progression extends the F major dominant chord of measure 68. Though its most characteristic surge would be in the form of V➔ (as appears to be emerging during measure 70), C soon wobbles to C♭, so that V⇨ (A♮-C♭-E♭-G♭) sounds during measure 71. This chord, rooted on an unsounded F, is enharmonically equivalent to its antipode, C♭➔, as Chopin acknowledges through the spelling C♭-E♭-G♭-B♭♭ during 712. Without losing its V⇨ function, this chord spelled as C♭➔ is the starting point for a parallel progression that ascends obstinately in major seconds: C♭➔ D♭➔ E♭➔ F➔. Thus through the ascent of three whole steps V⇨ maps onto V➔! To close the phrase a cascade of sixteenth notes transports the melody’s C (=
) to the upper region of the keyboard,
after which it eventually descends three octaves to Middle C, above which the initiating D♮ of the post-interruption phase of this subdominant prolongation will be introduced in measure 80. Though the progression of measures 80 through 99 resides squarely in B♭ Major, and though the thematic content comes across as fresh, nevertheless there are associations with the pre-interruption phase of the subdominant prolongation. (Both phases of the prolongation are displayed in 9.4.) Note especially how the melody’s upper thirds in measures 66–67 (D♭C) find their way into a major-key context in measures 84 through 90. The descent from C to B♭ is suppressed at the cadence of measures 91 and 92, though it may be imagined. An expanded repetition of the passage (acknowledged by the two tiers of measure numbers in 9.4) leads definitively to the PAC (supporting C to B♭) in measure 99, in coordination with a ritardando. Chopin’s local harmonic progressions
juxtapose the two principal means by which the tonic is departed: via a 5–6 shift that leads to II, and via a surge (I➔) that targets IV. The tonic’s 5- and 6-phase chords are connected via a segment of the descending circle of fifths (B♭ E♮ A♮ D G) in measures 80 through 83. The simple addition of the tonic’s minor seventh, generating a surge effect in measures 86 and 87, serves as the foundation for an impressive expansion during the repetition in measures 92 through 95, where the endpoints of a long crescendo symbol coordinate with the tonic’s 8 and 7♭. (The bass ascends by step from root B♭ to seventh A♭.) Though the B♭ goal of 992 resembles its predecessors in 221 and 571, both its major quality and its sounding during the measure’s second beat contrast those earlier contexts. These “flaws” are sufficient reason for Chopin to forgo an immediate succession to F Minor’s C dominant to conclude this A1 presentation. The ensuing further expansion of the subdominant (which eventually reverts to its initial minor quality) offers some of the ballade’s most inventive writing. Third-relationships come to the fore during the phase of the subdominant prolongation that extends from 992 through 1452. At the outset a major-mode variant of the passage from measures 36ff. is pursued. (Compare these passages in 9.3 and 9.5.) Whereas the B♭ minor chord is followed by G♭ major, now B♭ major is followed by G minor (preceded by its D♮➔ embellishing chord); and just as A♭ in measure 45 connects ➔
G♭ and the restoration of B♭, so also E A♮ in measures 104 through 107 might have ➔
proceeded to F B♭. Instead, Chopin abandons this trajectory. (Note the instructions to ♮➔
slow down and diminuendo during measure 107.) A second D G ensues, this time inaugurating a progression that quickly proceeds via II➔ to V, whose minor quality begins the process of restoring the minor modal character of the tonicized B♭, in accordance with its diatonic role as IV in F Minor. Of course, this F minor dominant in the tonicized subdominant key is the same chord that elsewhere functions as the ballade’s tonic. Chopin goes so far as to prolong it employing the same strategy as in the tonic prolongation – namely, through an excursion to its upper-third chord and back. (Compare the A♭ major chords of 121 and the end of 1132.) Whereas during measures 8 through 16 only the A♭-CE♭ upper-third chord sounds between the initial F minor tonic and its surging F major evolution, the projection of the shift from B♭ Minor’s diatonic dominant (F-A♭-C) to its leading-tone enhanced version (F-A♮-C) during measures 111 through 138 is mirrored by the juxtaposition of two variants of the upper-third chord: A♭-C-E♭ and A♮-C♯-E♮. (The
ascent of a half step between A♭ and A♮ is accomplished by means of a 5–6 shift during measure 128. By resorting to enharmonic spellings, Chopin facilitates the ascent to A♮ rather than to B♭♭.) In a context that is rife with third-related chords, the A♮-to-F relationship that restores the F dominant attains a prominence that in more traditional writing likely would be fulfilled by fifth-related chords. For example, at the outset Chopin supports the arrival of the tonic in measure 8 by means of a C-to-F fifth-relationship. (See 9.1.) As if to signal the newfound importance of F’s upper-third chord (even though F here functions as the subdominant’s dominant rather than as the movement’s tonic), the A Major passage during measures 129 through 136 draws upon thematic and harmonic content from that opening C Major region. Chopin even reprises the fermata usage of measure 7 in measure 134.7 Such third-play is further developed in fascinating ways. For example, the relationship between the A and F chords, discussed above, is replicated in the excursion to A’s upper-third chord, C♯ major, in measure 132. Is Chopin pursuing an equal subdivision of the octave (4 + 4 + 4 = 12)? In this case no, since C♯ reverts to A, and A eventually yields to F. A similar scenario emerges during the remainder of the section, where the relationship between A and F is replicated twice: as C to A♭ and then as E♭ to C♭. (See 9.5.) One wonders once again whether an equal subdivision of the octave is under way (3 + 3 + 3 + 3 = 12). Again no, since the C♭ chord resolves directly to the F chord. (The C♭ chord offers a consonant context for the introduction of the F dominant’s minor seventh, E♭.) Though this might seem a curious juxtaposition, it corresponds to the Neapolitan-todominant succession, here deployed as embellishment of a dominant that has already been established. The invigorating succession from C➔ to f from measures 110 and 111 is here contorted to become C♭ to F. Whereas the B♭ chord that emerges during measure 145 is now of the appropriate quality, its metrical positioning matches that of 162 rather than that of 221. Consequently Chopin reprises the foundational subdominant prolongation here, thereby attaining the ideal subdominant chord at 1511. Without further ado, the dominant goal arrives immediately thereafter, followed by the onset of the fourth (final) statement of A1. Though many details in Laufer’s exx. 7.5a and 7.5c are commendable, the display of how two crucial dominant harmonies relate to their broader contexts seems
problematic to me. First, consider the dominant that I propose extends from 681 through 801. Laufer’s graphs make it appear that the melodic trajectory from D♭ through C completes its path with an imagined B♭ during measure 80. (Note that this B♭ is placed within parentheses in his ex. 7.5c, though not in ex. 7.5a.) I propose instead that an interruption delays that melodic goal: in my 9.4, C in measure 68 connects to a B♭ imagined in measure 92 and stated in measure 99. Laufer’s reading in his ex. 7.5 seems to contradict his own graphs in ex. 7.6, where, instead of descending to B♭, the beamed C of measure 68 either connects with upper-third E♭ or is juxtaposed with the D♮ of measure 81. Second, whereas I propose that the dominant harmony in measure 91 resolves to the tonic of measure 92 (more definitively stated at the end of the varied phrase repetition, in measures 98 and 99), Laufer here does not imagine a B♭ resolution pitch for the melodic line. (Though his reading of F in measure 87 as the starting point for a linear descent subtly contrasts my reading of that F as D’s upper third, we both acknowledge the arrival of C in measure 90.) Consequently what here appears from Laufer’s notation to be an interruption actually is not one, whereas what in the vicinity of measure 77 appears not to be an interruption actually is one. My assertion of an interruption before the onset of the B♭ Major material that emerges in measure 80 is of special importance given Laufer’s proposal that a sonata-form “second subject” begins at that point. (On p. 162 he acknowledges that the key scheme differs from what one would find in a classical sonata.) That notion would be hard to reconcile with my interpretation of the B♭ tonicization as residing within an F
the following downbeat. Laufer graphs a structurally deep tonic restoration in the first two (see his exx. 7.3a and 7.4a), but one does not find in ex. 7.7 any trace of the corresponding dominant harmony in the third. (In his commentary on p. 166, he describes the chord of 1512 as a “rather insignificant V.”) His point is that the subdominant, already extensively prolonged, continues through this region to measure 160. Not only is the dominant so “insignificant” that it is not included in Laufer’s richly detailed graph, but the tonic chord of measure 152 (for me the starting point for the fourth statement of A1) is annotated as “not real I” (ex. 7.7a): “This return must be read … as parenthetical” (p. 166). Concerning measures 99 through 145, the details of Laufer’s ex. 7.7 and my 9.5 diverge on two points. First, I regard the ritenuto marking of measure 107 as indicative that the harmonic trajectory being pursued will not be continued. For me, the surging D chord of measure 108 is a restoration of that introduced in measure 100, offering an opportunity to pursue an alternative course. Laufer instead integrates the latter D chord within the context of what directly precedes and follows it. Second, I regard the F chord that emerges in measure 111 as an important harmonic arrival point, prolonged until its resolution at 1452. Laufer both refrains from projecting such a prolongation and visually emphasizes bass A♭ at 1132, further diluting F’s impact.
The fourth statement of A1 (measures 152–210) As a generator of interesting content, Chopin’s strategy thus far has been highly effective: by clearly delineating four basic structural elements for A1 at the outset – a minor tonic, its evolution into a surge targeting the subdominant, a modest tonicization of the subdominant, and finally a cadence on the major dominant – listeners are introduced to a paradigm whose repetitions are laden not only with creative variants in the local figuration but also with progressively more daring broadenings of the subdominant tonicization that nevertheless do eventually proceed to the C major dominant. As a result the ballade will come across (assuming that an A2 complement to A1 eventually emerges) as an amalgam of a theme and variations, a simple binary form, and a fantasie. Elements of the last have given rise to Laufer’s claim of a relationship to sonata form. The fourth (final) statement of A1 is radical. Amidst animated figuration in both the right- and left-hand parts, the chord progression from the minor tonic through its surge to the subdominant proceeds as expected, while the subdominant’s tonicization leads yet again from I (B♭) to V♮ (F). Yet this time that V♮ (which arrives in measure 162) does not return to B♭. (It did so directly during the first two A1 statements and after a local interruption during the third statement.) Chopin instead abandons this trajectory in midprogression! Perhaps Chopin wishes to convey some frustration with a process that has generated ever more robust content without achieving the PAC that would confirm a remolding of A1 into an A2 shape. In any event, he has elected to shift from one to another of the principal routes through which the tonic and the dominant are connected in tonal music: seeing that I ➔ IV resists accommodating his plan (but instead generates longer and longer subdominant expansions), he switches to I5–6 II. Whereas IV was tonicized in the earlier passes through A1, now I6 (asserted as VI) is. Chopin nevertheless achieves some continuity between these passages by deploying, now in D♭ Major, thematic material that was introduced when B♭ Minor temporarily shifted to B♭ Major earlier. (Compare measures 84ff. and 169ff.) This quest for continuity between contrasting paths through A1’s tonic-to-dominant tonal trajectory does not seem to me to be generated according to the precepts of sonata form, as Laufer and others have proposed. Instead, what was at first a modest tonal utterance during the initial A1 is imbued with ever more wondrous outpourings from Chopin’s fantasy in the succeeding reiterations of that formal unit.
Though in its local context the F major chord of measures 162 through 168 will come across as V♮ in the tonicized key of IV (B♭ Minor), it nevertheless is reminiscent of the initial F Minor tonic, with a modal shift from minor to major. As such, Chopin uses it as a springboard in shifting to the F Minor tonic’s 6-phase chord, D♭ major, which emerges in measure 169 and extends through measure 191. Because Kopfton A♭ is supported by 6phase D♭ as well as by the initial F Minor tonic, it may serve as the starting point for descending linear progressions in tonicized D♭ Major. The first transpires between measures 169 and 177 (as shown in 9.6). The passage is a model of elegant writing, incorporating both a surge from I➔ to IV and the traversal of the IV–V succession via a 5– 6 shift. Yet the linear progression’s goal D♭ does not sound (and thus it is imaginatively inserted – within parentheses – in the graph), thereby providing the impetus for a repetition, one that further develops both the tonic surge and the 5–6 shift (as is documented in 9.6). During this repetition the prolongation of the A♭ dominant culminates in the arrival of its seventh G♭, which triggers the resolution to D♭ major. This time, the melody’s linear progression traverses a third (A♭ to F). As the broad progression in F Minor draws to a close, that third is followed by second (supported by II⇨) in measure 194 and then third
(supported by V♮) in measure 202. As with the earlier extended
prolongations of IV, here the F Minor tonic’s 6-phase chord (tonicized as D♭ Major) dwarfs both the evolved supertonic and the dominant that follow to form the cadence. Chopin provides more heft for the phrase’s ending by inserting parenthetical passages offering somewhat frantic chordal progressions, the first of which re-targets the cadential (measures 195–196) and the second of which comes between that and the onset of its resolution (measures 198–200).
Example 9.6 Analysis of Ballade in F Minor (op. 52), mm. 152–210. Alas, with the arrival of the cadence in measure 202 we find that, even with a dramatically instigated alternative harmonic path, the dominant persists as the goal: we have traversed yet another A1 structure, not its A2 complement. If the latter is ever to emerge, it appears that an even more radical transformation of content will be required. Consequently what transpires beginning in measure 211 bears distinctive evidence of novelty from the outset. In that Laufer and I hold contrasting views regarding the hierarchical relationship between the B♭ chord of measure 151 and the F chord of measure 152 (discussed above), it is not surprising that the D♭ Major tonicization that commences in measure 169 is displayed in different ways in our respective graphs. For Laufer, it is the subdominant’s upper-third chord (his ex. 7.7a); for me it is the tonic’s 6phase chord (9.6).8 Either way, it is prolonged until II⇨ emerges in measure 194. I place greater weight on that potent supertonic surge than does Laufer: in my view, it supports the melody’s descent from A♭ to G, after which the A♭ of the cadential serves as a neighboring note. (Observe that both F and G are members of the II⇨ chord. G arrives from above, not from below.) Laufer instead interprets that G as a passing note between F and A♭. Consequently he prolongs (A♭) into the domain of the dominant. Within the D♭ Major tonicization, Laufer again displays a tonic-cadencing progression as if there were an interruption: I propose that the A♭>G♭>F>E♭ line beamed in measures 172 through 176 of his exx. 7.8a and 7.8d should continue with an imagined D♭ in measure 177, corresponding to a cadence on the D♭ tonic.
(See 9.6.) That tonic then surges, leading to the arrival of IV at 1822 (not 1812, as Laufer proposes). A similar surge of IV’s 6-phase chord (as II➔) heralds the arrival of V at 1842. (Observe how in both cases the surge coordinates with a long crescendo marking, so that the resolutions occur at moments of peak intensity, just as a decrescendo begins.) Laufer instead extends the IV5–6 trajectory through measure 189. A key factor in my reading is the assumption that the embellishing chord B♭-D♭-F-G♮ at 1871 “should” resolve to C-E♭-A♭ (an inverted dominant). That chord’s E♭ is elided during 1872. Instead, F is retained as an anticipation of the following downbeat chord’s F.9 Whereas I regard measure 211 as a new beginning (finally, the onset of A2!), Laufer places that measure at the end of his fig. 7.8 graphs. He proposes both that the Urlinie reaches goal there and that a coda commences there. (Note that in his fig. 7.9a – but not 7.9b through 7.9d – the goal F appears within parentheses. In his fig. 7.10 the parentheses recur, and the chord is annotated as follows: “evades strong close on .”) Given my reading of the ballade’s deep structure thus far as consisting of four distinct melodic descents from to
, each supported by the
harmonic trajectory from I to V♮, I propose that the A♭ of 2111 serves as the initiation point for a descent that attains the Urlinie’s goal at 2231 (to be explored below).
The A2 section (measures 211–239)
The A2 section (measures 211–239) The triplet sixteenth notes that pervade the A2 section complete the gradual enlivenment of rhythmic content that has characterized the ballade. The A2 section, whose structure unfolds beginning in measure 211 (as shown in 9.7), is loosely related to its A1 predecessors: the Kopfton (now stated at the outset) is supported by the tonic harmony, with a pervasive deployment of II at diverse structural levels (contrasting the tonicized IV favored in the initial statements) proceeding to V♮ (with C-F-G to C-E♮-G in measure 218 echoing the earlier occurrence of that distinctive construction in measures 201 and 202). Yet certainly a sense of novelty prevails. Finally we achieve a breakthrough, extending beyond the confines of the dominant-cadencing A1 to A2’s long-anticipated PAC tonic, presented fortissimo at 2231, with reiterations at 2251 and 2271 (where the minor tonic’s third finally is correctly spelled as A♭). Though an impressive hierarchical nesting of chordal activity is documented in 9.7, that visualization actually is somewhat simplified from Chopin’s version, since a chord-dense parenthetical passage, reminiscent of those in the vicinity of measures 196 through 200, emerges between
(at 2184) and
(at
2224). I regard it as a written-out manifestation of something that otherwise might have been improvised, serving to heighten the already considerable intensity in the final approach to the cadence.
Example 9.7 Analysis of Ballade in F Minor (op. 52), mm. 211–239.
The chordal progression in measures 215 and 216 may seem baffling. The middleground C major dominant harmony attained at the end of measure 214 is here embellished by a chord spelled as F-B♮-D♮-A♭. To get back to C, Chopin traverses a segment of the modulo 12 division of the octave into six equal parts, each spanning two half steps. The forzando markings highlight two successive -2 shifts, shown in 9.7. By this means we arrive at the diminished seventh chord corresponding to dominant C, which is fully restored with the resolution of D♭ to C in the bass (a conversion to a less evolved state of V) during 2161.10 In this construction, the E♮-D♭-G-B♭ chord at the end of 2151 serves as a local connective chord (filling in the first whole step) rather than as a resolution. The prominence of II during the harmonic progressions (at various levels) that are integrated to form A2’s structure contrasts the tonicized IV within the various manifestations of A1. As soon as the PAC is achieved (at 2231) Chopin boldly substitutes IV for II during two quick reiterations of a tonic-affirming progression. Whereas the minor tonic of 82 eventually surges (as F-A♮-C-E♭ during 161), the surge in measure 223 (spelled as A♮-C-E♭-G♭) gets under way breathtakingly soon after the moment of cadence. Chopin has spelled that juxtaposition not with A♭ to A♮ (as was the case during the A1 surge), but instead as G♯ to A♮. Whereas some analysts (including Laufer) would argue that Chopin here elides the minor tonic entirely (until 2271), intending G♯ as an accented passing note between the dominant’s G and a major tonic’s A♮, I support the alternative view that, since Chopin frequently employs quirky spellings, one should not give too much weight to the curious G♯ here. As a listener (not watching the score), I acknowledge the expected cadence on the minor tonic and then am jolted by the surprising and vigorous surge towards IV. In either reading, the IV (with soprano B♭) that emerges in measure 224 corresponds to that of measure 22. As such, the melodic third from B♭ down to G should be expected in coordination with the dominant’s arrival. (Contrasting the earlier presentations, here IV’s 6-phase chord emerges between IV and V♮.) Yet in this case E♮F at the cadence. (Thus the structural G is placed within parentheses in 9.7.) Chopin responds to that lacuna by emphasizing a G>F second following the cadence (measure 227). After several reiterations, a long tonic-affirming cascade descends to the downbeat of measure 237, followed by a final cadential gesture that reinstates the I5–6 II approach to the dominant, Chopin’s final word on the matter.
Though Laufer’s paucity of Roman numerals makes an assessment of his reading of the work’s harmonic dimension especially challenging, I question his interpretation of measure 212, based upon the notes included in his graph (ex. 7.10a). I suggest that I6 (or VI), rather than I, sounds at the downbeat of that measure. Perhaps Chopin delayed sounding D♭ in the bass to avoid forming parallel fifths against the melody’s G
10
Barcarolle in F♯ Major (op. 60) ◈ in response to Rink John John Rink’s extraordinary devotion to Chopin has resulted in an impressive series of books and articles, as well as a critical edition of the piano concertos and contributions to several online Chopin resources. An essay on the Barcarolle was his first Chopin publication, in 1988.1 Carefully crafted and richly illustrated with graphs, it both offers a detailed analysis of the work and assesses the several manuscripts that have survived. Though my analysis differs from Rink’s in numerous ways (in part because I propose that the Barcarolle’s Kopfton is , rather than ), his reading is brimming with intriguing ideas.
The introduction and the A1 section (measures 1–
The introduction and the A1 section (measures 1– 16) The introduction’s initiating C♯-E♯-G♯-B chord, which targets the A1 section’s opening tonic (measure 4), possesses two distinct layers of dissonance. The audacious D♯ of 12–3 is an incidental dissonance: it embellishes the leading tone (E♯), which falls into place just before the onset of the downward chordal cascade that lowers the C♯➔ chord by an octave via a stepwise parallel progression. In contrast, the chordal seventh (B) is an essential dissonance: it is still a force to be reckoned with during 32, after the registral shift has been accomplished. It resolves – in register – to the tonic’s A♯ during 42.2 Concurrently the initial chord’s highest pitch (G♯), having been transferred down an octave by 32, descends to the tonic’s F♯, also in the register below Middle C. (These resolutions are displayed via a slur and an arrow in 10.1.) After the surging C♯➔ chord, the tonic’s filled-in F♯
Example 10.1 Analysis of Barcarolle in F♯ Major (op. 60), mm. 1–16. The perky C♯ that concludes measure 4 is the first hint of an initiative that will have a major impact upon the broad sweep of the A1, B, and A2 sections. Whereas the introduction begins boldly in the upper register and gradually descends, Kopfton A♯ (first stated during 42) is transferred up an octave in measure 7 and finally resounds in the upper register during A2 (near the end of measure 30, supported by the tonic’s surging 6-phase chord). Thus A♯G♯ octave of measures 1 through 3. Observe in 10.1 how the second of those arpeggiations is stretched (via an internal C♯
registral shift) into a thirteenth over the course of measures 4 through 6, followed by a descending sixth that brings the Kopfton to the register of the introduction’s lower G♯. Immediately thereafter a chromatic filling-in of the A♯E♮>D♯>C♯.3 Despite continuing activity above these strands, Kopfton A♯ is not attained in the upper register during A1, and so a line from the middle-register A♯ of 94 and of 112–3 (the latter supported by the tonic’s 6-phase chord) leads downwards by step to G♯ (emphasized by a trill) when I6 proceeds – as it often does – to II. Though II’s evolved state (II➔) targets V, the confluence of the pitches C♯, E♯, and G♯ at 121 does not represent an asserted dominant, but instead serves as an unfurled passing chord within a prolongation of II➔. (The essence of this prolongation is displayed in 10.1.) Note how yearnings for the upper register continue to affect the musical fabric, here splitting the “descending” fifth-progression extending from G♯ into G♯>F♯>E♯ (presented in the chordal interior, with F♯ colliding with, rather than following, the G♯ above) followed by D♯>C♯ in the upper register. Even the G♯ from which this fifth-progression descends has a moment in the upper-register limelight, at 141. Chopin extends beyond that G♯, with a high C♯ (two octaves above the middle-register C♯ where the pitch was introduced at 121) sounding at 142. Its successor (B♯, which also sounds briefly in that high register) is restored to the middle register in 10.1, preceding the cadence on V. Because the tonic is not attained at its close, the Barcarolle’s initial tonic pillar may be described (using terminology introduced in our study of the mazurkas, above) as irregular. Though Rink’s and my conceptions of the introduction are similar, my ear does not isolate the initial right-hand B-D♯-G♯ as a sonority independent of root C♯ and consequently worthy of a
label, as Rink proposes (p. 198). The D♯ indeed is
wondrously extended for nearly two beats. Yet its role is identical to that of the eighth-note C♯ of 14 and all the upward-resolving appoggiaturas that follow during the downward cascade. The contrast in our assessments of measures 4 through 6 is of far greater consequence. For me the low register projected during measures 4 and 5 serves as a sort of subterranean germination area from which the principal melodic notes of
the upper registers sprout. (This area is entered again in measures 35 and 113, corresponding to the onsets of the C section and of the concluding region of the coda.) The voice leading from the introduction is precisely etched: the C♯➔ chord’s dissonant seventh, B, resolves by descending step (as sevenths generally do) to the tonic’s A♯, while the soprano G♯ is transferred downwards before descending by step (as a suspension) to F♯. The slurs in Rink’s ex. 9 propose exactly the opposite voice leading: that B’s resolution – upwards by step to C♯ (which Rink regards as the Kopfton) – occurs an octave higher, while G♯ ascends by step to A♯. Indeed C♯ is the first pitch within A1 to sound in the principal melodic register (at 62), and it recurs at the cadence (at 151). Yet an “insistent focus” is not sufficient grounds for the granting of Kopfton status (p. 197, n. 6, where Rink awards A♯ an honorable mention for its “important role as well”). I instead regard the initial C♯ as residing within an ascending arpeggiation (A♯C♯ fifth-progression, atypically sounding above the initiating G♯ as a consequence of further efforts to attain the high register. Though some of the factors that have affected my determination that serves as the Kopfton come later (to be explored below), even the limited content of measures 1 through 15 seems to me far more supportive of than of . Rink’s ex. 4 presents his reading of the region’s harmonic progression. It may appear that we concur, given that his
I
vi
V/V
V
is an alternative means of conveying my
I5—————6
II♯
V
Yet our conceptions turn out to be quite different. For Rink, this V resides within a broad linear descent.4 Note the stemmed bass notes D♯, C♯, B, and A♯ in measures 10 through 20 of Rink’s graph. They coordinate with the Roman numerals
vi
V
IV
III♯3
According to Rink, this V may be interpreted as an interior step along that descending path. In my view the F♯ chord at 174, which Rink displays but does not label, serves as a resumption of the tonic (as will be explained below with the help of 10.2). In such contexts an internal cadence on the dominant (which may be referred to as a back-relating dominant or as a divider) is common. In my view bass G♯ (lacking a stem in Rink’s graph) is the principal intermediary between F♯ and C♯.5 I further question his placing the G♯ chord’s arrival at 144. I propose instead that II-space begins three measures earlier. In that context the pitch C♯ emerges as a neighbor to an already established II➔ chord’s third, B♯ (as indicated by the N abbreviation in 10.1). Rink displays this C♯ instead in the soprano. It is the only soprano notehead in the vicinity that is stemmed, despite the fact that C♯ is a member neither of the vi nor of the V/V triad.
The B and A2 sections (measures 17–34) Irregular tonic pillars of the I–V type, such as that which transpires during the Barcarolle’s A1 section, are found in several of the mazurkas that we explored in chapter 3. As was noted there, often the tonic will be re-established at or near the beginning of the B section that follows. (Review 3.2 through 3.8, especially 3.6a, measures 17–23.) The E♮ that emerges at 171 should not be interpreted as a shift to the dominant’s parallel minor, but instead as an anticipation of the emerging major tonic’s minor seventh: E♯<
F♯>E♮
C♯>
F♯
through elision and anticipation becomes E♯>E♮——— C♯> F♯ The restored tonic (now surging as F♯➔) launches a circular progression that proceeds through B and E♯ to A♯. The A♯ major goal chord is prolonged via a descending parallel progression similar to that of the introduction.6 Whereas a surging A♯ major chord was deployed at the end of measure 9 to connect the tonic’s 5- and 6-phase chords (in which context C ascends to D♯), here the A♯-C -E♯ sonority serves as an upper-third embellishment of the tonic chord (with wobbly note C returning to C♯ at 241). The upper row of Roman numeral analysis in 10.2 displays its voice-leading origins.
Example 10.2 Analysis of Barcarolle in F♯ Major (op. 60), mm. 1–34. It stands to reason that the A2 section should draw upon A1’s I5–6 II➔ V trajectory, though now proceeding beyond V to I for a PAC. Those expectations are fulfilled, as 10.2 reveals. The upper-register Kopfton A♯ arrives at the culmination of a magnificent sequential ascent, connecting the tonic’s 5- and surging 6-phase chords (measures 24 through 30). As often happens, here the traversal of the ascending 5–6 sequence, which in full would run as F♯5——————————————————————————————————6 F♯5–6
G♯5–6
A♯5–6
B5–6
C♯5–6
D♯5
is abbreviated to become
B5–6 (= F♯➔
G♯➔
C♯5–6
D♯5
A♯⇨ )
(Compare this abbreviated sequence with the idiosyncratic sequence displayed in 6.4.) Whereas an A♯➔ chord (during 94) connects the tonic 5- and 6-phase chords during A1, here the sequence culminates in a chord that mutates to A♯⇨. The supertonic that follows D♯5 (= I6) is presented initially in its diatonic form, only gradually developing its characteristic surge towards the dominant, which here is gloriously stated with suspended ninth and eleventh. The excursion into the upper reaches of the piano’s range extends even beyond that of measure 14, reaching a D♯ near the end of measure 32. The D♯>E♯
descending seventh that follows will seem mildly disappointing, in that D♯’s upward yearning is not fulfilled – yet. (See measures 92 and 93.) That E♯ completes, in register, the descending third left off after the trilled F♯ of 314: the ascending F♯F♯>E♯ third, sounding in the upper register during measures 31 and 32 (as shown in 10.2).7 The contrast between Rink’s and my interpretations of the B section hinges upon what we make of the F♯-A♯-(C♯)-E chord at 174.8 For me that chord represents a restoration of the F♯ tonic (now surging), as indicated by the F♯-to-F♯ bass and A♯-to-A♯ soprano slurs in 10.2. Though the chord is of only one beat’s duration, it represents the culmination of a tonic expansion that has persisted for fourteen measures. Rink instead regards the latter F♯ as a local event: just as G♯➔ targeted the C♯ of measure 15, now F♯➔ targets the next step in a broad descending scale, B. To help us come to terms with this thorny issue, please turn to measures 103 and 104, which inaugurate the Barcarolle’s coda. Those measures contain four two-beat chords, as follows:
F♯
C♯➔
F♯➔
B
I propose that the first three chords constitute a tonic expansion, whose surging conclusion targets B.9 Despite the proximity of their roots, there is no direct relationship between the C♯ and B chords. The question is, how much more emphasis can the C♯ chord be given before the relationship between C♯ and B begins to overpower that between F♯ and F♯? Looking at the first four chords of 10.2, I maintain that root F♯’s impact extends through three chords, whereas Rink maintains that the stepwise relationship between C♯ and B overpowers the potentiality for an F♯ restoration at measure 17. Upon the arrival of B in measure 18 listeners might reasonably speculate regarding which of several viable tonal trajectories is being pursued. Chopin allows a measure for the chord’s impact to sink in before proceeding to what might
be taken as B’s 6-phase chord (B-D♯-G♯ at 193). Consequently one might suspect that I➔ IV5–6 is inaugurating a progression that will continue with V and then I. Yet F♯ is reintroduced under the trilled G♯, behaving as a suspension that resolves downwards to E♯, so that ultimately F♯➔ B E♯ A♯ charts a circular route between the tonic and the mediant, as shown in 10.2. (Rink’s commentary on the foreground jumps from measure 16 to measure 20 (p. 204), as do his foreground graphs (examples 9 and 10). The E♯ chord is not acknowledged in his middleground graph (example 4), though the 6-phase pitch G♯ is present.) In that the Barcarolle’s C section will proceed from F♯ to the tonicization of a different variant of the mediant (A Major), an F♯-to-A♯ connection during the B section makes good sense. Perhaps the most common means of achieving the mediant is via a circular progression, which in the case of ascending a major third will incorporate one imperfect fifth (here B to E♯).10 Regarding A2, a comparison of Rink’s and my analyses of measures 28 through 31 (within his ex. 4 and my 10.2) reveals significantly contrasting readings of measure 30. First of all, it seems to me that surges are at work throughout, and thus whereas we both display A♯-to-B and B♯-to-C♯ resolutions, the omission of C (which resolves to D♯) in his graph curtails the momentum before the ascending trajectory has reached its goal. Measure 30 is, in fact, different from the previous measures in three ways: unlike A♯ and B♯, C arrives after – not at – the downbeat; C ’s chord is of the ⇨ rather than of the ➔ type; and, whereas the B and C♯ goal chords (whose arrivals Rink refers to as “cadences” (p. 206)) are consonant, the D♯ chord is a surging dissonant chord. Yet those differences serve to make the attainment of goal D♯ all the more potent and notable. In that IV and V numerals are provided, Rink’s omission of a label for this VI➔ chord is curious. In my view he both misrepresents the extent of the upward initiative and loses sight of the close alliance with the harmonic progression of A1 (where the only connecting chord between I5 and I6 is a variant of the C surging chord omitted from his ex. 4: A♯➔ at the end of 94 and A♯⇨ at 302).11 In that I perceive a broad I5–6 expansion over the span of measures 7 through 30, the high A♯ of 304 is presented in 10.2 as a structurally deep event, an upperoctave replication of the Kopfton, attained at literally the last possible moment –
just before the middleground descent through G♯ to F♯ that closes A2. Rink’s ex. 4 displays that A♯ as internal to a slurred B>A♯>G♯ third. Though I cannot make out exactly what hierarchical relationship Rink intends by placing Roman numerals in two rows (I think his perspective would be more consistent if he accepted the first of the two V chords as the arrival of the dominant, with the stem from bass C♯ attached to the beam at that point), certainly the absence of a label for the D♯ chord is indicative of the contrast that our two readings offer. My version highlights I5–6 II➔ V as a shared component of A1 and A2 (and, as we shall see presently, of A3 as well).
The C and A3 sections (measures 35–103) The F♯-A♯-C♯ tonic chord’s diatonic upper-third chord A♯-C♯-E♯ was passed over during the B section, which instead features A♯-C -E♯, the diatonic chord’s first chromatic variant.12 Prolonged for four measures (20 through 23), it serves as a voice-leading embellishment of the tonic, which is restored in measure 24. Unlike A♯➔ or A♯⇨ (both of which occur in one or the other of the initial tonic pillars, as noted above), this major A♯ chord does not proceed by descending fifth to the chord that follows. During the Barcarolle’s C section the upper-third chord’s second chromatic variant – A♮-C♯-E♮ – not only is attained, but also is tonicized. The F♯ Minor flavor of the section opening (measures 35 through 38) facilitates its emergence in measure 39. Its impact persists through measure 70 and beyond. What will happen after its tonicization has run its course? Will it again lead back to the initial F♯ tonic, as was the case with A♯-C -E♯? Or might it instead behave as A♮➔, targeting tonic F♯’s modified 6-phase chord, D♮-F♯-A♮, which could lead onwards to ♮II5♮ (the “Neapolitan” chord) and beyond? Let’s look at the big picture first (with the help of 10.3), filling in some details later. Earlier, the B section’s A♯ chord coordinated with a rising third in both outer voices: from
to
. The resumption of the initial tonic puts a crimp on the upward motion in the
bass, but not in the soprano: from C the line first undergoes a wobble correction (to C♯) and then continues upwards through F♯ to a high A♯, completing an octave arpeggiation. During the C section a similar upward trajectory is inaugurated by the initial rising thirds: from
to
. Though the stabilization of the latter third initially is problematic (to be
explored below), eventually the progression of thirds continues: from
through
to
. Though an upward continuation would have been viable, Chopin chose to assert the E♮ chord as V in A Major, thereby tonicizing the A♮-C♯-E♮ chord. In so doing, the high G♯ serves as a leading tone that resolves by step to A♮, and thus an A♮
A♯ (Kopfton ) through A♮ to G♯ (measure 76). Though he might have proceeded directly from the A♮ upper-third chord to the dominant, Chopin elected to reinstate the tonic in measure 76 (thus mimicking the treatment of the B section’s upper-third chord), from which he proceeds via II➔ to V, the same succession that was employed during the progressions of A1 and A2.13 That internal tonic reinstatement is accomplished by a shift of an A♮-targeting E➔ chord to an F♯-targeting C♯➔ chord in measures 72 through 76.14 The C section’s interrupted , supported by background V, proceeds to at the PAC that concludes the first statement of the A3 tonic pillar, as shown in 10.3.
Example 10.3 Analysis of Barcarolle in F♯ Major (op. 60), mm. 1–93. Now let’s explore some more local details. The sense of a new beginning proposed for the C section, with its broad A♮C♯>A♯ melodic trajectory (incorporating an internal registral shift) during measures 4 through 7 reinforces the Kopfton. The same end is achieved by a similar means in measures 35 through 39. In this case A♮
neighboring chord (with passing note C♯ at 354 and 362
connecting sixth D♮ and fourth B).15 The F♯>C♯ span transpires between 364 and 381, embellished by upper neighbor G♯ and passing notes E♮ and D♮, followed by the C♯>A♮ span between 381 and 391, embellished by upper neighbor D♮ and passing note B. The
registral shift in this case is postponed until the end – at 391, where goal A♮ below Middle C is surmounted by an A♮ an octave higher. The C♯ in measure 41 begins the C section’s upward melodic trajectory. In that the third is a member of both the F♯ minor tonic triad and its major upper-third triad, there is some wavering between the two chords. Recall that the descending circle of fifths (traversed as F♯ B E♯ A♯) was called into service during measures 17 through 20 to negotiate the span between the F♯ Major tonic and its upper-third chord. Chopin uses the same means to instead descend in seconds from upper-third A♮ back to tonic F♯ in measures 41 through 46 (A♮ D♯ G♯ C♯ F♯). That tonic (at first in its initial major formulation, but soon with the shift of its third to A♮) is confirmed by means of a I II⇨ V♯ progression, stated twice in measures 46 through 50. Consequently it may appear that, just as the A♯ upper-third chord of measures 20 through 23 soon dissipates, likewise the A♮ upper-third chord of measures 39 through 41 is not sustained. Yet this time Chopin offers A♮ a second chance. Just as in measures 72 through 76 E♮➔ and C♯➔ will be juxtaposed to lead from A back to F♯, here F♯’s C♯➔ bows to A’s E♮➔ (measure 50), leading to a repeat of the A Major material beginning in measure 51, now transferred up an octave. Alas, the same circle-of-fifths descent that earlier plagued the maintenance of A♮ occurs again, and by measure 57 the F♯ tonic has reasserted itself. The I II⇨ V♯ progression is reprised as well. Chopin then offers A♮ a third chance, with the C♯➔/E♮➔ juxtaposition of measure 61 leading to A♮-C♯-E♮ yet again. This time, however, A♮’s fifth (E♮) plays a prominent role in the melodic line, both definitively contrasting the pitch collection of the F♯-A♮-C♯ tonic triad and anticipating the E♮ of the
third within the ascending-thirds
progression. The ascending circle of fifths (now in a chain of four chords and thereby, like measures 17 through 20, ascending a third) is called into service again to complete the attainment of that ascending third: A♮ D♯ G♯ C♯ in measures 65 and 66. (The circle’s internal D♯ chord is represented by F -C♯-E♮.) A continuation to E (via C♯ F♯ B E♮) follows in measures 66 and 67. As mentioned earlier, this E♮ chord’s resolution back to A♮ (thereby terminating the ascending-thirds trajectory) confirms the tonicization of A Major that we now may retrospectively trace back to the C section’s earlier A major chord (measure 39). The dominant’s G♯>E>D augmented fourth, which unfolds from 673 to 682, is complemented by the tonic’s C♯
As explained above, the tonicized A♮ region ultimately serves as an upper-third embellishment of the F♯ Minor tonic, which consequently extends from 351 through 762. The progression to the background dominant is facilitated by a very brief (though structurally deep) II➔ during 762. Earlier the projection of the F♯ Major tonic chord was accomplished by means of an A♯G♯>F♯), as displayed in 10.2. Now this C♯ dominant’s tonicization incorporates both a G♯
to the dominant root (G♯>F♯>E♯>D♯>C♯), as displayed in both 10.3 and (in
greater detail) 10.4a. The tonicizing harmonic progression engages two interlocking C♯– G♯–C♯ sacred triangles in support of the descending fifth-progression. The minor quality of the subdominant at 774 (whose A♮ reflects the A♮ goal of both bass and soprano from measure 68) indicates that F♯ Major has not yet gained full tonal control; though certainly by the time of the C♯7 chord at 833–4 it has.
Example 10.4 Barcarolle in F♯ Major (op. 60) (a) Analysis of mm. 76–82; (b) Hypothetical measures 77 and 78. Occasionally one encounters in Chopin’s music a progression of chords that resists explication by ordinary means.16 The passage omitted at the spot marked by a hairpin symbol in 10.4a indeed may well cause perplexity among analysts. My hypothesis regarding how Chopin conceived this passage involves a sudden shift from one viable tonal trajectory to another: a potential I5–6 II V7 I unexpectedly replaced by I➔ IV♮ V7 I.
The first four chords in 10.4b, which presents the alternative progression that I propose Chopin might have pursued, actually sound in the composition, though there their roles are camouflaged by easier-to-read spellings. Note that the example’s second chord is an upper-fifth embellishing chord of the third, replicating the relationship between the last chord of measure 76 and the first chord of measure 77, now hoisted up a half step. Those precedents suggest that the fourth chord in 10.4b “ought” to resolve to an A♯ major chord, as is shown within square brackets. That chord would be ideal in such a context, because it serves as I6 (evolved into surging VI➔). As the example confirms, the harmonic progression to V7 may proceed via VI➔ II just as easily as through I➔ IV♮ (as displayed in 10.4a). In this context the C major chord serves as a chromatic variant of A♯ major’s upper-third chord. (Consequently the Roman numeral VI is introduced below bass C , with the bullet symbol indicating that root A♯ is absent.) Just when the fully constituted 6phase chord is about to be introduced, Chopin diverts the progression to a surging I➔ (E♯G♯-B-D♮), resulting in IV♮ rather than II serving as the principal intermediary between I and V7. Why did Chopin undertake this unusual tactic? Though we will never know for sure, I find it intriguing that over the broad span of the C section an upper-third A major chord plays an important role, though it is rescinded (via the F♯ restoration in measure 76) before the broad progression continues through supertonic G♯➔ to dominant C♯. During the dominant prolongation that follows, tonicized C♯’s lower-third chord is rescinded (again replaced by a restored, and in this case highly evolved, tonic) even before it has the opportunity to sound! The A3 tonic pillar, which commences in measure 84, follows the general contour of the A2 pillar, and thus it achieves a PAC whose soprano , magnificently doubled at the upper octave at 931 (compare with the restrained cadence at 331), serves as the close of the broad A♯>G♯>F♯ fundamental line that spans the composition to this point. (See 10.3.) Whereas the A1 and A2 pillars were presented only once each, A3 is repeated in a varied form, as shown in 10.5. Note especially how 1014 through 1023 correspond to 914, how 1024 (with the distinctive ninth and eleventh above the dominant root) corresponds to 921–4, and how 1031 corresponds to 931. In that the attainment of the upper-register A♯ has already been accomplished, the variant traverses the span between that upper A♯ and an even higher F♯ (previously sounded at the cadence of 931) during measures 96 through 99, as a substitute for the A♯
region of the C section, measures 62ff.) The II of measure 101 initially takes on a ⇨ coloration, though eventually it bows to the ➔ of A1, A2, and the earlier A3. A coda (to be explored below) follows the cadence of 1031.
Example 10.5 Analysis of Barcarolle in F♯ Major (op. 60), mm. 93–116. I shall divide my critique of Rink’s analysis of the C and A3 sections into six parts. Measures 35 through 39. Rink’s interpretation of how the pitches within these measures relate with one another is commendable. (See his fig. 11 and commentary on p. 206.) Though I give more weight to A♯ and its upper-sixth F♯ and he to the internal C♯, those differences relate to the broader issue of versus as Kopfton. Nevertheless, we disagree regarding the role these measures play within the Barcarolle. For me, measure 35 is closely aligned with measure 4: my analysis interprets both as structural initiation points. Rink shares my view with respect to measure 4, describing measures 4 through 16 as “Theme A” in his formal synopsis (his fig. 1). However, in that same synopsis measures 35 through 39 are described as a “transition,” and “bars 1–39” are treated as a suitable chunk of the Barcarolle to assess at one time, both in his commentary (p. 198) and in a middleground graph (ex. 4). Consequently his series of B themes is set squarely in the key of A Major, followed by another transition that attains F♯’s dominant on C♯. My contrasting segmentation projects a broad progression from F♯ (the measures in question here, which Rink analyzes as vi in A Major (p. 200)) to C♯ all within the boundaries of what I call the C section.
Measures 39 through 50 (with a varied repetition in measure 51 through 61). Two broader analytical decisions affect Rink’s and my interpretations of these measures: whereas my C section begins in F♯ Minor, Rink’s formal unit – Theme B(1) – begins in A Major; and whereas I regard A♯ as the Kopfton (by this point lowered to A♮), Rink proposes C♯ for that role. Consequently the
tenth
(seventeenth) during measures 47 through 50 resonates for me as a “back to square one” sounding of the C section’s initiating tonic chord in a way that it would not to someone committed to A Major and to Kopfton C♯. Whereas I would not make use of Roman numerals (as Rink does, on p. 201) during the circular progression descending from A to F♯, I certainly would employ them (as Rink does not) as F♯ progresses to its dominant (twice) in measures 47 through 50, wherein a II⇨ that juxtaposes B♯ and D♮ as a diminished third, rather than more conventionally as an augmented sixth, serves as the intermediary between I and V♯. For me the passage’s principal melodic line is a descent from A♮ to G♯ ( to in F♯ Minor, a typical HC trait). From this perspective, the C♯ major chord of 501–2 (and later 611) is the phrase’s goal, while the remainder of that measure plays a transitional role preparing for the backtracking to a restatement of the phrase-opening A chord (measure 51) or to a new trajectory emerging from an A chord (measure 62). Measures 62 through 70. Rink’s Theme B(2), which transpires during these measures, resides squarely within the key of A Major. In his view the theme’s principal melodic event is a repeated traversal of an E♮>D♮>C♯ third (as shown in his ex. 6). For me, instead, the principal event is a filled-in ascending arpeggiation from the A Major tonic’s third, C♯, through E♮ to the A Major dominant’s third, G♯, which resolves to A♮ (completing a full-octave ascent from the initiating A♮ of measures 35–39) in coordination with the resolution to the tonic (as shown in 10.3). It seems to me that Rink has missed the essence of the voice leading between 653 and 673, where a straightforward example of the reaching-over procedure occurs: C♯ descends to B♯, above which D♯ reaches over. D♯ descends to C♯, above which E reaches over.
E descends to D♯, above which F♯ reaches over. F♯ descends to E, above which G♯ reaches over (concurrent). Consequently leading tone G♯ sounds in an exposed position at the top of the texture during 673. The resolution to A♮ comes across as especially pronounced not only because of its registral placement, but also because a G♯>D♮ augmentedfourth unfolding (through 682) resolves to C♯
, whose interruption
(with restoration of diatonic ♯ during the A3 section) is one of music’s principal form-defining devices. In contrast, Rink regards both the initiating F♯ Minor and the attainment of the tonicized dominant, C♯ Major, to reside within “Transition” sections (his fig. 1), thereby elevating the importance of the tonicized A Major mediant. Taking a hint from how Chopin treats the B section’s A♯ major chord in relation to the F♯ Major tonic context, I regard the C section’s A Major tonicization to reside within a broader F♯ Minor expanse, noting especially the symmetrical relationship between measures 50 and 60 (which juxtapose F♯’s C♯➔ and A’s E➔) and measures 72 through 76 (which juxtapose A’s E➔ and F♯’s C♯➔). Consequently the F♯ minor chord at 762 is for me a hearkening back to the C section’s opening measures (35 through 38), conveyed by the broad bass slur connecting those two F♯s in 10.3. Rink, in contrast, does not permit the C♯➔ of 761 to resolve: he regards it as the arrival of the structurally deep dominant, to which the following F♯ minor chord is appended (example 6).17 Granted, one cannot “prove” that one interpretation should be preferred over the other. Readers are simply encouraged to compare these two starkly contrasting views – so stark, in fact, that neither the soprano pitch G♯ during 763 nor its upper-octave replicate at 782, projecting the
of the Barcarolle’s background
descent in my
reading, is even present in Rink’s detailed ex. 6 (though the lower G♯ does appear in his ex. 2 and the higher one in his fig. 12). As one might expect if G♯ indeed is
a structurally deep pitch, a fifth-progression descends (with internal upward register transfer) from G♯ to the tonicized dominant’s root, as displayed in 10.4a. Rink displays the lower third of this fifth in his fig. 12. The thorny passage explored in 10.4b is not assessed in Rink’s essay. Measures 84 through 93. Though I propose that the high F♯ of 931 belongs with the preceding measures (in opposition to Rink’s breaking off his Theme A′ with measure 92 in his fig. 1), we both interpret this passage as a potent projection of the restored F♯ Major tonic.18 I regard this cadence as supporting the descent to the that concludes the background line broken off after the C section’s goal
.
That cadence is followed by a varied repetition of A3, which solidifies that closure through a second cadence at 1031. Rink instead postpones that closure until the second cadence – in my view not a point about which all analysts will or need to agree. In that Rink and I work from contrasting Kopftons, our structures are not identical. Yet he and I both project a sense of closure during this region (or at the downbeat of measure 93, which is curiously snipped off from this region in Rink’s formal synopsis). Measures 93 through 103. Because this region borrows thematic material from the C section’s A Major region, Rink labels it as Theme B(2)′ in his formal synopsis (his fig. 1), where he again snips off the cadential tonic chord, placing it within the domain of the coda. Fortunately his ex. 7 persists through the downbeat of measure 103, and his commentary addresses “bars 93–103” (p. 203). Though that example does not provide a detailed harmonic analysis, the bass slur from imagined F♯ (at 1003) to C♯ (at 1013) projects the sense of tonic prolongation. (A more detailed graph in his fig. 15 displays that C♯ with a stem and omits the B♯ that follows.19) I instead regard the chord supported by D♮ (at the end of 1012) as the onset of the supertonic: here II⇨ (D♮-F♯-A♮-B♯) followed by an incomplete B♯-F♯-A♯ chord into which one might imaginatively insert either D♮ or D♯, and then by II➔ (G♯-B♯-D♯-F♯) during 1021–3. Consequently bass C♯ at 1013 serves as a passing note (connecting D♮ and B♯) within the domain of the supertonic, rather than as a waning moment of I-space.
The coda (measures 103–116) Upward striving that may traverse as much as a full octave, and downward linear progressions of a third or a fifth, have been characteristic of the A and C sections’ contents. The introduction, in contrast, descends an octave by step, as does the coda, where the notes of an F♯>F♯ octave (with some potent chromatic mutation) occur between measures 103 and 110. The beginning and ending portions of that line sound at the top of the texture (F♯>E♯>E♮>D♯>D♮>…>B>A♮>G♮>F♯), whereas during the middle either the listener will imagine a pitch (C♯ during measure 106) or a pitch sounds but is covered by other chord members. The harmonic analysis that annotates the presentation of this voice leading in 10.5 reveals a boldly realized double traversal of the basic I IV V I progression. The initial tonic surges towards IV, that IV’s 6-phase chord takes on a “Neapolitan” flavor, and the dominant that follows is attained by simply adding leading tone E♯ to the Neapolitan’s pitches (resulting in V⇨, and consequently not alleviating the G♮ wobble). The tonic that resolves that dominant evolves gradually into I➔ during measures 106 through 108, proceeding to a IV♮ whose D♮ extends into the domain of V➔, where eventually G♯ shifts to G♮, resulting in a second V⇨ approach to the tonic. Indeed, Chopin has reserved some of the Barcarolle’s most memorable harmonic writing for the coda! A concluding melody begins in measure 113, notably on the same A♯ that introduced the Kopfton in measure 4. The progression’s initial I-space supports the ascending arpeggiation A♯
Though Rink expresses admiration for Chopin’s “sonorities of extraordinary dissonance in relation to the pedal on F♯′” during measures 103 through 111 (p. 210), he does not offer a harmonic analysis in his ex. 8 or 16, wherein his allegiance to Kopfton C♯ is maintained despite what I hear instead as a sweeping descending octave (F♯>F♯) filled in by step and modified by chromaticism. In his reading, C♯ plays a prominent role during the remaining measures as well (p. 212). I am mesmerized instead by the A♯ of 1151. Though I have not compiled statistical data, my experience as an analyst suggests that when such a pitch emerges after the structural close it usually will serve as an echo of the Kopfton.
Notes
Chapter 1: The architecture of a tonic pillar
Chapter 1: The architecture of a tonic pillar 1. James Samson, The Music of Chopin (Oxford University Press, 1985), p. 111 . 2. This reading proposes that E in the soprano register extends from 63 through 72. One should ponder whether an E in fact could be imagined during 71 against the E
with 6–5 suspension) and the D-F♯-C-B-E chord at
192, in the tonicized dominant key. 3. The question of where and how to end the mazurka (given Chopin’s curious Dal segno senza Fine instruction) is complicated by this 5–6 shift. I propose that measure 12 should conclude the performance – regardless of how many times the A and B sections sound in alternation – but that in the final presentation of the A section the pitch A should be rescinded. (The left-hand chord of measure 12, beat 3, could be replaced by a rest.) 4. For a literalist interpretation of this mazurka, see Nicholas Meeùs’s “Questions de méthode: La Mazurka op. 7 no. 5 de Chopin,” Analyse musicale 32 (1993), pp. 58–63 . Though its ex. 5 appears to contain a printing error, it is clear that Meeùs interprets what I call the tonic pillar as a projection of
.
5. Compare also with the opening of the Grande Valse brillante, op. 18, discussed in my forthcoming Tonal Analysis: A Schenkerian Perspective, chapter 7. 6. The embellishment of C-E-G in measures 1 through 4 and of D-F-A in measures 13 and 14 are symmetrically related: in one case lower seconds of the root and third occur, while in the other upper seconds of the third and fifth occur. In both contexts the embellishing chord is unfurled for presentation in position. Similar embellishment will occur during the mazurka’s coda.
7. Schenker offers a graph of this mazurka’s tonic pillar in FC, fig. 40, ex. 7. Whereas his reading suggests that Chopin’s motivation for the phrase expansion has to do with the slow pace of the ascending arpeggiation to the high C of 102 (which he presents as the arrival of the Kopfton), I propose instead that the unsatisfactory cadence of measure 8 results in a backtracking to permit a second cadential attempt. In the context of a IV– V succession, the C of measures 6 and 10 serves as a passing note between the structurally deeper pitches D♭ and B♭ (connected by a slur in 1.5). Consequently I do not accept this C (highlighted through presentation in the upper register) as a statement of the Kopfton. (That reading is reiterated in various graphs from the Oster Collection: Papers of Heinrich Schenker, housed at the New York Public Library for the Performing Arts at Lincoln Center. See especially file 32, item 22, listed as “in the hand of Schenker’s student Angi Elias with emendations by Schenker.”) On the other hand, during the A2 section’s traversal of the tonic pillar the high C at 36b2, which superficially matches that of 102, occurs in a tonic context and thus aptly serves as an upper third to the background . (The swift C>A♭ of the first ending is expressed in a more leisurely fashion and an octave higher as C>B>A♭ during the second ending.) In his “Idiosyncrasies of Phrase Rhythm in Chopin’s Mazurkas,” in The Age of Chopin: Interdisciplinary Inquiries, ed. H. Goldberg (Bloomington: Indiana University Press, 2004), pp. 95–105 , Carl Schachter explores this tonic pillar in detail, essentially agreeing with Schenker’s reading of the high C of measure 10 while questioning (p. 98) his relative neglect of the C at 21, which conforms in register to the mazurka’s other structurally deep pitches. 8. It is so labeled in standard editions of the mazurkas, including the National Edition used in creating this chapter. 9. This mazurka’s juxtaposition of keys is not unique in Chopin’s oeuvre. Other examples that have been widely discussed include the Scherzo (op. 31), addressed by William Kinderman in his “Directional Tonality in Chopin,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), pp. 59–75 and by Harald Krebs in his “Tonal and Formal Dualism in Chopin’s Scherzo, Op. 31,” Music Theory Spectrum 13 (1991), pp. 48–60 , and the Ballade (op. 38), addressed by Jonathan Bellman in his Chopin’s Polish Ballade: Op. 38 as Narrative of National Martyrdom (Oxford
University Press, 2010) and by Kevin Korsyn in his “Directional Tonality and Intertextuality: Brahms’s Quintet Op. 88 and Chopin’s Ballade Op. 38,” in The Second Practice of Nineteenth-Century Tonality, ed. W. Kinderman and H. Krebs (Lincoln: University of Nebraska Press, 1996), pp. 45–83 . 10. The notion of “reaching-over” is a common voice-leading principle, an essential component of the Schenkerian perspective. (See my Tonal Analysis: A Schenkerian Perspective, chapter 7.) 11. For a contrasting interpretation, see David Kopp’s analysis in his Chromatic Transformations in Nineteenth-Century Music (Cambridge University Press, 2002), pp. 235–240 . I do not concur that the tonic pillar “projects tonal ambiguity for much of its duration” (p. 236): the juxtaposition of antipodal C♯ and G♮ chords (a focus of my analysis) is a strong signal of tonic B, with only its mode (major versus minor) as yet indeterminate. 12. Compare with Haydn/Mozart, 1.5. 13. The mazurka begins in the middle of a harmonic progression. Taking into account measure 22, which presents an E major chord to lead back to the opening material (in a written-out repeat), it would be appropriate to regard the initial II as an asserted IV6. Note especially the 5–6 connection between tenor-register B at 222 and C♯ during 231 (= 11). For this reason, and by noting how bass B at 21–2 is reiterated by bass B during 31, I regard the initial E-G♯ dyad as representing C♯-E-G♯ (with the C♯ arriving half a beat later) rather than as representing E-G♯-B with C♯ serving as a neighbor to IV’s fifth, B. 14. Once introduced to these notions, my students at the University of Minnesota began referring to ⇨ as a “supersurge,” while ➔ remained a “surge” or, more precisely, a “simple surge.” 15. Note Chopin’s persistence in incorporating an upper third in the vicinity of the Kopfton ’s arrival. D♯F♯>D♯ here (measures 16 and 17) corresponds to DF>D in measures 2 through 4 of opus 7/1.
16. Compare with Schubert, 1.23. 17. This division of structural content does not coincide with the pillar’s division into two halves, each repeated: measures 5 through 8 recur as 9 through 12, and measures 13 through 20 recur as 21 through 28. Chopin transcends that surface division by extending the ascending arpeggiation into the second half. 18. Chopin’s misspelling comes about as a result of his substituting easy-to-read A♮-C♯E♮ in the preceding harmony for the correct spelling, B -D♭-F♭. Further pertinent considerations will emerge in the exploration of this mazurka’s structure in chapter 2. 19. As 1.11 reveals, the fifth-progression’s E♭, C, and B♭ are all embellished by an upper fourth or third. Chopin offsets the neglect of D♭ (resulting from its delayed arrival within the beat) later, during the mazurka’s B section: D♭
20. As noted above, the embellishment of Kopfton by an upper fourth (here G♯ during 41) is a common occurrence. When D♯ does arrive, that high G♯ serves as a sort of confirmation. 21. Schenker comments on Chopin’s slur binding measures 7 through 9 (thus extending through the phrase’s potential PAC moment) in FC, p. 110. In his Phrase Rhythm in Tonal Music (New York: Schirmer, 1989; reprint edn., Ann Arbor: Musicalia, 2007), pp. 229–233 , William Rothstein offers an extended discussion of Chopin’s phrasing within this mazurka. 22. If one answers affirmatively, an elision would occur at C ’s resolution: instead of C C♯, the shortcut C >C♯ is pursued. (Compare with TAH, 6.20.) In his “Harmonic Complexity and Form in Chopin’s Mazurkas,” Ostinato rigore: Revue internationale d’études musicales 15 (2000), pp. 102–103 , Joel Lester labels this chord as vii7/D♯ and describes the passage as “a fleeting instance” of “motion by dominants around the circle of fifths.”
23. See Edward T. Cone’s “Ambiguity and Reinterpretation in Chopin,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 142–143 . 24. Though Schenker provides a detailed analysis of this mazurka in FC (his fig. 75), it is difficult to determine which route he endorses for the fifth-progression between B and E. Observe that his graph is inconsistent in its placement of the internal G and F♯ during A1 and A2. In the former (corresponding to measures 1 through 4), the placement of G before the arrival of dominant root B would seem to favor an imaginative insertion, though no parentheses are placed around his G notehead. In the latter (corresponding to measures 57 through 60), the placement of G above the dominant root B would seem to correspond to the G of 593. I propose that his version for A1 endeavors to recompose the passage in accordance with the second species of counterpoint (wherein G would serve as a passing note above bass A), subjected to a considerable shift in Chopin’s realization, where that passing note is delayed until after
the dominant root arrives. That is, the foundational state
may shift (via
the unaccented passing note of species counterpoint being transformed into the accented
passing note of free composition) to create a “cadential ” context, as
;
or even further, so that A lingers to sound against the dominant root, as
. 25. Compare G, which here neglects to descend to F♯, with D♭ (which neglects to descend to C) in 1.6, m. 5. Carl Schachter, in “The Prelude in E Minor Op. 28 No. 4: Autograph Sources and Interpretation,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 161–182 , takes a literalist approach (as does Schenker in FC, fig. 75). Schachter’s ex. 9.4 (p. 168) displays the melody pitch E at 73 as an anticipation of that in measure 8. (The intervening G – a crucial note for me – is omitted from his graph.) He adds a special annotation above the bass beam: “No V!”
Whereas my graph projects an imagined diatonic within the descending fifthprogression from , Schachter’s descent (like Schenker’s) incorporates the earlier ♮ . An intriguing analysis by Franz Eibner in part concurs with my reading. See his “Über die Akkorde im Satz Chopins,” in Chopin-Jahrbuch 1970, ed. F. Zagiba (Vienna: Notring der wissenschaftlichen Verbände Österreichs, 1970), pp. 3–24 . The initial chord is analyzed as E Minor’s tonic and is provided only with the Roman numeral I (once with to the right, in his fig. 7 on p. 23). He comments as follows: “Durch den Dominantklang am Beginn ist nur die IV. Stufe (von T. 2) ‘tonikalisiert’ worden und also muß dieser Dominantklang in der ganzen Kadenz die I. Stufe der Haupttonart repräsentieren” (p. 6). His fig. 4 (p. 20) displays both a parenthetical D♯ below G at the end of measure 7 and a parenthetical bass B for the final beat of that measure, under which he places the Roman numeral V within square brackets. (His fig. 5 on p. 21 provides additional perspective, including an indication that the melody’s G at the end of measure 7 serves as an “Antizipationston.”) He reads the Kopfton as , supplied within square brackets and annotated with the word “Ellipse” in his fig. 6 (p. 22). (The G is connected to the F♯ of the mazurka’s B section, graphed in his fig. 7 on p. 23.) Though in disagreement with Schenker’s reading of the Kopfton as , which Eibner addresses in his n. 3 on pp. 18–19, his choice has the advantage of not raising the expectation of a G between A and F♯. I remain unpersuaded, however, due to the prominence of the initial B, its clear voice-leading descent to A in measures 2 and 6, and the relationship between the A section’s fifth and the B section’s (inverted to
sixth
), to be explored in chapter 2.
26. This D♮-F♯-A embellishment of a C♯ chord corresponds to the A♭-C-E♭ embellishment of a G chord in opus 17/2, mm. 39ff. Its exotic flavor inspired Dmitri Tymoczko to interpret the mazurka’s mode initially as “phrygian.” See his A Geometry of Music, pp. 312–313.
27. Schenker alternates between two notational practices for interruption in FC. (See editor Ernst Oster’s note 7 on p. 37 of the example volume.) I have adopted the one that I prefer. For a more detailed introduction to this important topic, see my Tonal Analysis: A Schenkerian Perspective, chapter 4. 28. I have placed the D♮ in the bass, in conformity with 143. The parentheses around the C♭ above this D♮ indicate merely that it is displayed in a higher register than where it occurs in the score. 29. Whereas Schenker (FC, fig. 106, ex. 2c) proposes a local ascending C♯E>D♯ third. It conforms to the prescription that a seventh should resolve by descending step. 30. The parentheses between I and IV in 1.21b acknowledge the several passing chords that come between the harmonic progression’s I and IV. A contrasting interpretation is offered by Joel Lester in his “Harmonic Complexity and Form,” pp. 113–117, where he proposes that the keys of C, B, and B♭ (misprinted as E♭) are “hinted at,” though “their fundamental progressions evaporate.” An important component in any analysis is to assess the function of all dissonant sevenths, since that interval may serve as a chord member within a 7/5/3 context, or instead as an embellishment within a 7–6 context. Here Lester proposes the first interpretation, and I the second. 31. Consequently the first sounding of the Kopfton occurs at 81, precisely the same moment within the structure as its upper-octave occurrence in 1.10. My conception is subtly different from that proposed by David W. Beach in his “Chopin’s Mazurka, Op. 17, No. 4,” Theory and Practice 2/3 (1977), pp. 12–16 . Whereas he interprets the E of measure 8 as the Kopfton’s onset, I propose instead that it should take hold before the series of suspensions begins. Thus I regard the tonic’s 5 phase to be elided, preceding the mazurka’s first sounding chord. 32. Performers should experiment with contrasting degrees of rubato and accentuation in the projection of measures 13 through 15. If the third note of each measure is
emphasized, the melody D♭>C>B♮ (followed by B♭>A♮>A♭) will lead to an IAC. If instead (and as I recommend) the performer leads downwards to the fifth note of each measure, then the melodic path leads to the F at 162 (as displayed by the stemmed notes in 1.22) for a PAC. 33. In his A Geometry of Music, pp. 288–290, Dmitri Tymoczko presents within his fig. 8.5.9 a root progression similar to mine, though flawed in two ways: first, I propose that it should commence with the A chord of measure 4, not the G♯ chord of measure 5; and second, he omits an analysis for the G♯ chord of 83. (The latter is not a printer’s error, because his commentary explicitly notes the exceptional “descending semitone” D to C♯.) Both of these points of contention relate to my willingness to allow imperfect fifths into my circle. His G♯ … D span contains only perfect fifths, avoiding my preceding A–D♯ and following D–G♯. Compare with ex. 362 in Felix Salzer’s Structural Hearing: Tonal Coherence in Music, 2 vols. (New York: Boni, 1952; reprint edn., New York: Dover, 1962) . Though Salzer’s model suitably starts on the A chord, he omits the D♯ chord of measure 5. In addition, he makes it appear as if a harmonic progression proceeds from III in measure 4 through V (which would be displayed as V♯ in my notation) in measure 9 (III and V are connected by an arrow) to I, contrasting my view that the initial upward trajectory breaks off after III, with a fresh start in measure 9. 34. Though Chopin’s slurring in measures 13 and 14 would support a reading that maintains the tonic until 151 (with the D-A-F♮-B chords functioning as local embellishments), his slurs so often counter his mazurkas’ structures that I here am willing to discount them. One might instead view their presence (in coordination with the dynamic markings) as helping to emphasize the subdominant statement on three consecutive downbeats. The progression proceeds beyond IV only on the third try. In performance the third-beat A chords should seem like a backtracking to the position of measure 12. 35. The 5–6 shift that often transpires during IV is realized here as (8)–7–6. (The 7 sounds from the outset.) The G♯ that arrives at 152 prevents the descending parallel fifths that would have occurred had A functioned instead as IV’s chordal seventh.
36. I suspect that Chopin’s ear was bothered by the prospect of a soprano B>G♯ leap coinciding with the bass D>C♯ step (creating “hidden fifths” in the exposed outer voices). Consequently he called upon C♯ (related to the C♯s of 133 and 143) as a substitute for G♯ at 153. The unusual situation at the cadence also in part justifies my rejection of what might seem to many as a clear instance of Kopfton . (This issue will be touched upon again when the remainder of the mazurka is assessed in chapter 2.) 37. The written-out repeat of the juxtaposed I and III phrases is facilitated by some transitional chords (during 83) that do not recur during measure 16. They are not displayed in 1.24. 38. For the written-out repeat of a1, the mediant’s C from 82 corresponds to the imagined Kopfton, with a C>B>A third-progression extending from that point through 122. 39. Though I do not regard C-E-G at 73 as a harmonically asserted chord (it is instead an unfurled embellishment of the tonic), this situation corresponds to what some analysts call a plagal cadence. 40. In 1.26 I propose that a sequential progression – A♭>E♭CF♯>E followed by B>A>G♯ followed by G♯>F♯>E, all displayed in 1.27, measures 5 through 22) give more the sense of a tonic reinstatement than of a mediant expansion.
Chapter 2: Between the tonic pillars
Chapter 2: Between the tonic pillars 1. The bass E♭>B♭ fourth is a meaningful interval in the context of E♭ Minor, whereas the upper strand’s G♭>D♮ fourth is not. The latter span, which incorporates the conventional modal shift from diatonic D♭ to leading tone D♮ near the cadence, is justified because it follows – in upper tenths – the contour set by the bass. 2. Chopin is having some fun in this mazurka by juxtaposing G➔C during the A section and D➔G during the B section. Could this be interpreted as I➔ IV V➔ I in G Major? The Dal segno senza Fine instruction in fact may be intended to eradicate the memory of which chord is first established as the tonic. My term “tonic pillar” reflects the observation that a mazurka’s A section invariably establishes the tonic key. To argue that this mazurka is in G Major would require both that the tonic pillar correspond instead to the B section role and that Chopin’s C Major key signature is bogus. (The least conventional of Chopin’s mazurkas in this regard is opus 30/2. See 2.5.) 3. The analysis of this mazurka by Nicholas Meeùs in his “Questions de méthode: La Mazurka op. 7 no. 5 de Chopin,” Analyse musicale 32 (1993), pp. 58–63 , embraces such doubt. 4. The earlier components of the circle of fifths coordinate with descending filled-in melodic thirds at two distinct structural levels. For example, a surface E♭>D♭>C third occurs within measure 13, while a broader third transpires between 132 and 143. (Only the latter is displayed in 2.4.) I propose that though A♭>G>F in measure 19 will at first seem to be of the former type, it ultimately performs (speedily) the role of the latter type. 5. The sounding of D♭ (rather than D♮) at 193 creates a motivic connection with the D♭>C over the bar line between measures 1 and 2, strengthening my assertion that the unfolded A♭
7. This small point is very important: the I harmony is reinstated at 243, not 261. (Note that now each of the tonic chord’s pitches is preceded by an upper second: B♭>A♭ D♭>C F>E♭.) Consequently measure 25 ought not to be interpreted as background V within a broad I III♮ V7 I progression. 8. In fact, Edward Laufer proposed such a reading for this mazurka in his lecture “Parenthetical Passages,” delivered at the Mannes College of Music Schenker Symposium in 1985. Ex. 19 of his handout displays bass open noteheads on G♯ (at 121), B (at 261), C♯ (at 412 or 452), and D♯ (at 433 or 473) before the close on G♯. (His Roman numeral analysis is I III5−6 IV V I.) 9. Though certainly one could deploy the Roman numeral ♭VI 5 ♭ at measure 20 in 2.8 (in keeping with Schenker’s practice in FC), I here instead account for that sonority by means of symbols to the right of the I numeral: the wobble from E to E♭ and back (3♮– ♭–♮) and the chromatic neighbor A♭ embellishing G (5–6♭–5). By this means I emphasize that chord’s alliance with the initial tonic and acknowledge that it does not lead anywhere harmonically. 10. A descending circle of fifths supports this fifth-progression. Observe how the already surging tonic E➔ that opens the A1 tonic pillar (measure 1) is echoed by the already surging G♯➔ that initiates the circle of fifths (measure 33). These chords also share an upper-neighbor embellishment (BB and D♯D♯). (The relationship between these neighboring motions was more emphatically projected in the original version of measure 33, where the E occurs on beat 3 in a rhythmic context exactly matching that of measure 1. The original and revised versions are juxtaposed in Jeffrey Kallberg’s “The Problem of Repetition and Return in Chopin’s Mazurkas,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), p. 14, ex. 6 .) Though the dominant is tonicized during the B section, the cover tone D♯’s upward tendency as leading tone eventually is fulfilled: the opening of the A2 tonic pillar’s theme coincides with D♯’s resolution pitch E in measures 57–58. 11. Reinforcing the tonic’s dominant-emulating impact, the preceding dominant is supertonic-emulating in its minor quality. Compare with Haydn/Mozart, 6.4c.
12. Though of no apparent consequence initially, the tinge of C♯ Minor supplied by A♮ in measure 53 sets the stage for the surprising turn of events beginning in measure 65. 13. Compare the addition of B♯ to D♮-F♯-A here (measure 72) and the addition of E♯ to G♮-B-D♮ in 1.8 (measure 12). That example’s resulting II⇨ is a more characteristic context for this evolved chordal formation than is this mazurka’s V⇨. 14. Though it may appear that the circular motion proceeds uniformly as B➔ E A➔ D G➔ C during measures 37 through 42, in my view the prior establishment of A as the local tonic places the B➔ E A➔ segment within its domain (extending from minor A to surging A➔), so that the progression extends beyond the tonic only with the arrival of D in measure 40, coinciding with the onset of the fifth-progression descending from Kopfton E. 15. In the context of A1, the content of measures 1 through 3 embellishes the initial tonic. The harmonic progression begins with I, not V♮. At the juncture of B and A2, the prior establishment of V♮ imbues equivalent content (measures 41 through 43) with an asserted dominant function, extending the B section’s harmonic goal into the domain of A2, preceding the re-emergence of the tonic. 16. Chopin’s spelling of II⇨ as D♯-G♮-A-C♯ at 493 is incorrect, of course. Yet in this case F ’s upward resolution to G♯ is elided, resulting in the direct succession to the dominant’s seventh, F♯. Consequently the “incorrect” G♮ reflects the line’s atypical downward orientation. 17. Compare with a similar lower-third shift in Schubert’s Piano Sonata in B♭ Major (D. 960), mvmt. 4, measures 41 through 62, which I address in my “Conspicuous 6-Phase Chords in the Closing Movement of Schubert’s Piano Sonata in B-Flat Major (D. 960),” in Rethinking Schubert (Oxford University Press, in press). 18. Two examples in Joyce Yip’s “Tonal and Formal Aspects of Selected Mazurkas of Chopin” (Ph.D. dissertation, University of Michigan, 2010) – numbered 2–4 (p. 188) and 6–1 (p. 263) – are derived from an analysis of this mazurka by Edward Laufer, presented in a talk entitled “A Different Reading for the Same Music” that he delivered at Queens College in 1993. (Similar graphs appear in his handout for the lecture
“Parenthetical Passages,” delivered at the Mannes College of Music Schenker Symposium in 1985.) Whereas he proposes a connection of the A chords at 213 and 243, I instead regard the former as an internal element within a circular progression whose endpoints correspond to the shift from A to A➔. Laufer’s title refers to his intriguing proposal that whereas the chord of measure 1 embellishes that of measure 2 (thus establishing the tonic at the outset), the chord of measure 26 may be regarded as dependent upon that of measure 25 (as its upper fifth), resulting in a bold D
.
19. The relationship between local tonic A Major and a potential D Major tonicization within this mazurka’s B section is assayed in TAH, pp. 157–160. 20. My focus away from Kopfton E during the B section is one of several potential readings, each quirky in its own way. (Chopin in fact keeps the E fire alive above C♯ during measures 35 and 39 – and 51 and 55 – and above B during measures 47 and 48.) For example, one might instead propose a fifth-progression descending from A1’s wellestablished Kopfton E through D at 332 to C♯ at 351 (extended by the C♯ of measures 41 through 47), leading to B (presented an octave lower) during measure 47 and finally A at 502 (repeated at 522, 542, and 562). 21. The b region’s D♭>C♭>B♭ third is a counterpart to the a1 region’s CC>B♭ in measure 15. In FC, fig. 30a, Schenker proposes that the D♭ neighbor is prolonged: D♭>C♭>B♭ instead of D♭>C♭>B♭. 22. Though the accented C♭ at 40b3 might be understood merely as an anticipation of the following downbeat, it instead might be regarded as a last-moment shift of the A section’s key to A♭ Minor, with which the upcoming F♭ Major relates as diatonic I6. F♭ has been a prominent feature of the local harmonic fabric even in A♭ Major, from the downbeat of measure 1 onwards. See Patrick McCreless’s “The Pitch-Class Motive in
Tonal Analysis: Some Historical and Critical Observations,” Res musica 3 (2011), pp. 59–63 , for thoughtful commentary on Chopin’s deployment of F♭ in this mazurka from both Schoenbergian and Schenkerian perspectives. 23. During his analysis of this mazurka and commentary on Schenker’s reading in Phrase Rhythm in Tonal Music (New York: Schirmer, 1989; reprint edn., Ann Arbor: Musicalia, 2007), p. 220 , William Rothstein proposes: “Chopin’s … slurs are an analytical minefield. No composer so frequently slurred against the phrase structure of his music rather than in support of that structure.” Here the slur ends not in measure 48, coinciding with the close of the antecedent phrase, but instead during the following measure, after the first three notes of the consequent phrase.
24. In some compositions it is challenging to decide whether or serves as the Kopfton. Though I regard as the better reading in this case, I acknowledge that I have received prodding from an anonymous external reviewer to instead choose . My reading is worked out in 2.18, where A and G♯ play prominent roles at various stages. Anyone intrigued by this conundrum might wish to create an alternative analysis based on Kopfton and then to compare the two interpretations. Which elements of the composition are emphasized when is regarded as the Kopfton, and which are emphasized when is? How might a performance of the mazurka suitably project one or the other of these readings? 25. Compare with TAH, 6.19 through 6.21. 26. It is important not to assume a direct correlation between tonicization and structural depth. Though C Minor is tonicized during the b region’s initial measures, root C falls within the tonal path from tonic A♭ to dominant E♭ (represented by the inverted dominant harmony of measure 16). Though neither tonicized nor presented in root position, that dominant is hierarchically deeper than the preceding mediant. (Note that its imagined root E♭ is the only element of the b region that is attached to the middleground bass beam in 2.21.) Consequently I do not concur with the reading of the
basic harmonic progression for the mazurka’s A1 section (measures 1 through 24) as I … iii … I, as is proposed by John Rink in his “Tonal Architecture in the Early Music,” in The Cambridge Companion to Chopin, ed. J. Samson (Cambridge University Press, 1992), pp. 78–97, ex. 8 (p. 90) . 27. Felix Salzer offers a reading that calls upon neither of these assertions in his Structural Hearing: Tonal Coherence in Music, 2 vols. (New York: Boni, 1952; reprint edn., New York: Dover, 1962), ex. 361 . 28. Compare with a similar parallel progression in TAH, 7.14c. 29. Note that the coda’s E>D♯>D>C third was stated several times during the b section (measures 37–42). 30. Chopin misspells the chord at 283. E♮ stands for F♭, minor ninth of an E♭➔ chord that is derived from that which occurred at 203. 31. This notion is explored in my Tonal Analysis: A Schenkerian Perspective, section 1.3. 32. Though the chord of 523 is spelled as B-D♯-F♯, the melodic A>G>F♯ third of measures 48–52 serves to extend A, so that B-D♯-F♯(-A) is understood as B7. The imagined seventh, A, resolves to VI➔’s third, G♯, at 531. 33. Though the pitches at these two locations correspond, the C chord during the A1 section proceeds to the dominant, whereas that during the B section is part of a backand-forth motion that embellishes the tonic, as is conveyed by the Arabic numerals just below the bass beam in 2.26.
34. Whereas a conventional cadential in measure 35 embellishes the consequent phrase’s dominant, the corresponding chord during the antecedent (measure 31) serves as a common-tone diminished seventh. Chopin might have spelled it more appropriately as A♯-C♯-E♮-G, with the lower three pitches ascending by minor second to resolution on B♮-D-F-G in measure 32. Concurrently ninth A♭ displaces the dominant root. All this occurs above a tonic pedal point. Perhaps Chopin’s spelling in flats was motivated
by a desire to avoid a concurrent C and C♯. (My colleague David Grayson, a pupil of Nadia Boulanger, related to me her observation that Chopin often misspelled his chords, but that Schumann did not.) For an exemplary account of Chopin’s often quirky orthography, see part I, chapter 2, of Maciej Gołąb’s Chromatyka i tonalnoséc w muzyce Chopina (Cracow: Polskie Wydawnictwo Muzyczne, 1991) ; as Chopins Harmonik: Chromatik in ihrer Beziehung zur Tonalität, trans. B. Hirszenberg (Cologne: Bela Verlag, 1995) . 35. The means by which the G♯ chord is attained offers insight into why Chopin lowers B♯ to B♮ during measures 79 and 142. Since the G♯ triad is a half step “too high” for the G Major context, the B♮ of measure 142 might be perceived as an effort to attain G♮-B♮D♮ within the downward cascade of chords. The triad’s unyielding G♯ and D♯ prevent the achievement of that outcome. 36. Compare with a passage by Schubert in my “Conspicuous 6-Phase Chords,” exx. 4 and 5. 37. Compare with 2.14, mm. 16 through 24.
Chapter 3: Irregular pillars in the mazurkas
Chapter 3: Irregular pillars in the mazurkas 1. Though Schenker’s readings of this mazurka’s tonic pillars harbor several contradictions, he does not waver from displaying the Kopfton as . See FC, fig. 76, ex. 5; fig. 83, ex. 2; and fig. 119, ex. 11. Unfortunately most of these interpretations are neither detailed nor adequately annotated by measure numbers. However, it appears that for the most part he proposes a PAC close after four measures, though he offers a contrasting reading at measure 20. In “Parenthetical Passages,” a lecture delivered at the Mannes College of Music Schenker Symposium in 1985, Edward Laufer presented an analysis in which measures 3 and 4 project and 8 project
, while the equivalent measures 7
. For him, what occurs between those pairs of measures
consequently constitutes a parenthetical passage. I instead espouse the view that each of the three regions within the mazurka’s A1 and A2 sections offers four measures of content, followed by a four-measure varied repetition. Measure 24 exceptionally departs from that design, to conclude the tonic pillar with a PAC. Compare this structure (including how repeat signs are deployed) with that which prevails during the two-pillar Mazurka in E♭ Minor (opus 6/4), analyzed in 1.15 and 2.1.
2. Though an interpretation of 182 through 192 as
(reinforced by a
voice exchange) is tempting, Chopin’s slurring, which matches that of the a1 pillar, binds the and tonic chords within measure 18. Thus I propose that I-space persists through the end of measure 18, maintaining the model of measures 2 and 6. 3. Though each measure of the introduction begins with the interval of a perfect fifth, none of those fifths are structurally significant. Instead Chopin alternates between and neighbors
, with both E♮ and B♮ consistently delayed by suspensions. The tonic
harmony emerges in measure 9, not measure 2 or measure 4.
4. Compare with Chopin’s construction in 1.9. Note how the G♮-B-D♮ chord of measure 6 there eventually takes on an E♯, thereby projecting root C♯. 5. Though initially the pitch F♭ serves as a wobble within the D♭ chord, in the broader context it is transformed into the major dominant’s third, E♮. The diatonic context would be whole step F>E♭. Here the F is lowered and the E♭ is raised, resulting in the juxtaposition of the enharmonically equivalent pitches F♭ and E♮. 6. Chopin’s particular approach to the tonic 6-phase chord in this mazurka resembles that employed by Mozart in the Trio of his Symphony in G Minor (K. 550), analyzed in Haydn/Mozart, 9.2. 7. I offer a detailed exploration of the subtonic–dominant connection in my “Schenker, Schubert, and the Subtonic Chord,” in A Music-Theoretical Matrix: Essays in Honor of Allen Forte (Part II), ed. D. C. Berry, Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic 3 (2010), pp. 127–166 . 8. See also my discussion of this passage in TAH, pp. 70–75, which includes commentary on Schenker’s reading of the passage (FC, fig. 54, ex. 6). 9. Indeed this turn of events is unusual and thus susceptible to a range of analytical responses. Michael Klein calls it a “dark subdominant … (with an added sixth)” and interprets this passage as residing within a coda in his “Chopin’s Dreams: The Mazurka in C♯ Minor, Op. 30, No. 4,” 19th-Century Music 35 (2011–2012), p. 255 . This article (pp. 238–260) offers a range of intriguing ideas that readers are encouraged to explore as a complement to the harmonic focus of my work.
10. Given the pillar’s broad harmonic trajectory from I to V♯ (supporting to ), the melodic attempt to reignite the tonic (potently colliding with the dominant during measure 33) is, in my view, doomed to failure. (The restoration of the tonic – transformed into I♯ – is deferred until the fourth measure of the B section.) Consequently I regard the melody’s A at 333 as ultimately bending to the dominant’s will: instead of igniting a reinstatement of I by means of an A
this context come across as a passing note within the third from an imagined G♯ up to B. 11. Observe how in the connection between the tonic’s 5- and 6-phase chords in measures 1 through 6, an F♯ embellishing chord of the 5-phase B intervenes, whereas in measure 73 that chord metamorphoses into an embellishing chord of the 6-phase G♯. In fact, a modest collision occurs: before the soprano E that belongs with the F♯ bass arrives, that bass has ascended to F (third of an imagined D♯). The passage is displayed with those events placed in their more normative order in 3.6a. 12. Though some analysts might contend that Chopin’s E♭7♭ spelling offers the prospect of an excursion to A♭ Major, I think instead that he is being genteel. The augmented sixth is so potent an interval that Chopin at first masks it by means of a misspelling. In my view there can be little doubt that, as the B section winds down and the D-F♯-A-C chord that initiates A2 looms on the horizon, Chopin intends II⇨ as the link between I6 and
. In his Mazurka in G Minor, op. 56/2, his innate gentility bows to the brutal
reality of the tonal situation: G♮-B-D♮ absorbs E♯ (not F♮) in measure 12. (He also shifts notation from D♮ to C .) 13. Readers are encouraged to compare my reading of the mazurka with an equally detailed one by Carl Schachter, in his “Counterpoint and Chromaticism in Chopin’s Mazurka in C♯ Minor, Opus 50, Number 3,” Ostinato rigore: Revue internationale d’études musicales 15 (2000), pp. 121–134 . Though Schachter acknowledges an earlier “1st extended cadence” targeting the tonic of measure 157, his “structural cadence” (which I read instead as an event of the coda) extends to measure 181. (See especially his ex. 1 on p. 122.) 14. The restoration of diatonic D♯ as imagined root during the domain of II warrants placing the natural sign corresponding to D♮ to the right of the Roman numeral, so that the shift from D♮ to D♯ may be noted. Because D♯ does not sound, it is marked by a bullet symbol. Compare with Haydn/Mozart, 4.15, as well as n. 24 on p. 264 of that volume.
15. The situation is similar to that at the end of the a2 tonic pillar in 3.1a, where an IAC on is forestalled by the swift insertion of and during measure 24. 16. The magic of Chopin’s composition would be lost if such measures were actually performed. Thus the recommendation that the more extended ending published by editor Jan Ekier along with the score of the Cracow National Edition (2004) be used “only if the Mazurka is performed separately (and not as part of the cycle)” (Performance Commentary, p. 6) goes too far, in my view. My hypothetical ending (3.11b) is supplied for its analytical implications only. 17. The A♭ chord’s fifth, E♭, is elided at 871. 18. Though Chopin’s D♮-G-B♮ spelling during measure 99 facilitates reading ease, analytically inclined pianists might prefer the structurally appropriate spelling, E -GC♭. The point of Chopin’s dallying is to allow time to ponder whether to proceed using C♭ or C♮ as during the descending fifth-progression. Displaying the C♭ “victor” as B♮ at 992 obfuscates the intimate bond with the C♭ at 952. 19. Charles Burkhart discusses this mazurka in two essays: “Chopin’s ‘Concluding Expansions,’” in Nineteenth-Century Piano Music: Essays in Performance and Analysis, ed. D. Witten (New York: Garland, 1997), pp. 95–116 , and “The Phrase Rhythm of Chopin’s A-flat Major Mazurka, Op. 59, No. 2,” in Engaging Music: Essays in Music Analysis, ed. D. Stein (Oxford University Press, 2005), pp. 3–12 . Despite the fact that we work from similar premises, our readings are surprisingly different. Note especially that I place more hierarchical weight on the tonic of measure 52 and the dominant of measure 68 and less weight on the subdominant of measure 82. Given that the A1 section presents an irregular pillar, the second phrase of A2 (beginning in measure 77) is duty-bound to project regularity, despite its considerable expansion. Thus from my perspective it is important that the I5–6 II➔ V of the pillar’s antecedent phrase (measures 69–76) be followed by a similar harmonization during the consequent, where V will resolve to I. For me, the relationship between F-A♭-C-E♭ at 743 and F-A♮C-E♭[D♯] at 843 is crucial, and thus the supposed IV at 821 is, in my view, internal to the sequential expansion of I5–6. Whereas Burkhart proposes the label ♮IV°7 for the
chord on D♮ during 881, I suggest instead that the chord’s root is an unsounded B♭ (with ninth C♭ spelled as B♮ due to the imminent upward diversion to neighbor C). From that perspective the antecedent phrase’s II➔ is transformed into II⇨ during the consequent. 20. Whereas we might expect G♯ to arrive before the harmonic progression that expands the C♯ dominant commences, that arrival coincides with the sounding of C♯’s 6-phase chord. 21. Like most other North American music analysts, I was accustomed to labeling chords such as D-F♯-A-B♯ as a “German augmented sixth.” Though I expressed reservations about that nomenclature in TAH (pp. 185–190), it was not until I decisively turned my back on that practice in Schubert and started providing such chords with an imagined root (here G♯) that their various roles in music were clarified. In the present context, such an imagined root is essential to an understanding of how the circle of fifths transpires. 22. Because the span from C♯ to G♯ is a half step shy of four whole steps, one of the cycles within the sequence must ascend only a half step. Chopin handles this first: though C -E♯-G♯-B at the end of measure 116 may seem to function as the local tonic’s 6-phase chord, surging (as A♯➔) towards D♯, Chopin instead treats the C as an anticipation of D♮, so that the succeeding 5-phase chord has more the character of a seismic shift up a half step from the starting point. From then onwards, however, the sequence ascends in whole steps, propelled by surging 6-phase chords. The pitch B is elided at 1171, where the chromatic passing note B♯ (which along with C♯ connects that elided B and D) occurs on the downbeat. Observe that the voice-leading technique of reaching-over is employed repeatedly in the melody. 23. Though the wobble of G♯ to G♮ for the ♮II chord in most cases will revert to the diatonic state during the dominant that follows, in this case the chordal evolution within II-space results in the reinstatement of an unsounded G♯ as root for the B♯-D-F♯-A chord during 1331. See the discussion of a similar event and an assessment of its analytical representation in note 14 on pages 101–102, above. 24. In some editions of this mazurka the a2 region (which commences in measure 65) incorporates the full statement of a1 and its written-out repetition (measures 1 through
48), whereas in the recent National Edition (ed. Ekier) from which I work only the repetition presentation occurs there. Consequently readers may need to add 24 to the measure numbers indicated in my commentary from measure 65 onwards. 25. I introduced the concept of a seismic shift in Schubert, p. 173. The notion was called upon several times in Haydn/Mozart as well. 26. The careful management of chordal inversions so as to result in a circle of fifths with a chromatic bass line was demonstrated in numerous harmony treatises from the early nineteenth century. Samples are printed in TAH, 3.7b and 3.11. Chopin’s progression employs two different sorts of enharmonic reinterpretation (displayed with both spellings in 3.15c). What arrives as B-rooted B-D♯-F♯-A in measure 180 departs as F-rooted A-C♭-E♭-G♭, and what arrives as D-rooted F♯-A-C-E♭ in measure 186 departs as A♭-rooted C-E♭-G♭-B .
Chapter 4: Étude in C Minor, op. 10, no. 12
Chapter 4: Étude in C Minor, op. 10, no. 12 1. “A Response to Schenker’s Analysis of Chopin’s Étude, Opus 10, No. 12, using Schoenberg’s Grundgestalt Concept,” The Musical Quarterly 69 (1983), pp. 543–569 . 2. Though I selected this Étude in order to compare my analytical practice with that of Phipps, his selection of the Étude was motivated by Schenker’s extensive treatment of the work in various publications, most comprehensively in his Fünf Urlinie-Tafeln (Vienna: Universal Edition, 1932) , which I have consulted through the Salzer edition, Five Graphic Music Analyses (New York: Dover, 1969), pp. 53–61 . Looking at the “3. Schicht” graph of measures 1 through 18 on p. 54, I question Schenker’s dotted slur connecting the E♭s in measures 11 and 17, essential to his determination that serves as the Kopfton. In my view the latter E♭ originates as the passing seventh within IV8−7, shifted from its normative unaccented position to a metrically strong position (though in this case the arrival of the E♭ is delayed by chromatic E♮). For a more straightforward context, consult FC, fig. 16, ex. 5, whose second model shows E in its foundational passing context (derived from the second species of counterpoint). That example’s fourth model shows how this E may shift to coincide with the arrival of the dominant root. Yet it remains a passing note. Thus, returning to the Étude’s C Minor context, the cadential ’s E♭ cannot serve – as Schenker proposes – as a reinstatement of the Kopfton, since it is hierarchically dependent upon the F and D that it connects. In addition, I disagree with Schenker’s inclusion of D (rather than D♭) in the interior strand during measure 15. (These two pitches are displayed without hierarchical distinction in his foreground graph on p. 57.) From my harmonic perspective, G-B♭-D♭ plays an important role in the succession from I to IV, serving as a reinstatement of the tonic in its surging I➔ state (imagining E♮). Consequently D♮ serves as a link between E♭ and D♭. 3. Because this descending-second motive is so pervasive, I cannot endorse Schenker’s reading of the first E♭ during 84 as a neighboring note to F. (See Five Graphic Music Analyses, p. 57.) 4. Regarding Mehrdeutigkeit (multiple meaning), see TAH, 156–161.
5. I applaud Phipps’s use of the Roman numeral I during measure 15 of his ex. 6, despite the fact that he has placed it within parentheses. I disagree with his use of that numeral during measure 17. 6. Chopin here makes the most of the fact that the diminished quality of C6 (C-E♭-A♮) results in an inherent uncertainty of intent. Will that chord proceed to D5, as the sequential pattern dictates? Or will it heed its own internal urge to resolve the augmented fourth? The addition of F to the chord pushes decisively toward the latter outcome. Fortunately those two outcomes reside in adjacent positions within the sequence, so the choice of the latter comes across as an omission of one chord within the sequential ascent. On another level, measure 24 corresponds to measure 14, where C-E♭-A♮ was complemented by F♯ to project D➔. If that F♯ is reinterpreted enharmonically as G♭, the surge would shift to F➔. With F rather than G♭ (a lessening of intensification, while retaining the function), that chord sounds in measure 24. 7. The sixteenth notes within measure 28 chromatically fill in two intervals from the B♭➔ chord: (D)>D♭>C>C♭>B♭ and B♭>B [A♮]>A♭[G♯]. 8. Compare with the embellishment of II during the Mazurka in C Major (op. 24, no. 2), measure 13 [1.4]. 9. Bass C [B♯] at 331 comes after two-measure units that emphasize E♭ [D♯] (the circle’s fourth element) and D♭ [C♯] (a passing chord). Though initially the attentive listener will regard C as the third of a chord rooted on A♭ (the circle’s fifth element), the downward trajectory from E♭ through passing D♭ does ultimately lead to C as root, taking into account the transformation that transpires during measures 33 through 35. Consequently the structural melodic line, which has descended from Kopfton G through F to E♭, now detours upwards through E♮ to incomplete neighbor F in measure 37 (in a trajectory divided between the soprano and bass) before reaching goal D in conjunction with the dominant. (See 4.3.) 10. Chopin rejects the D♭-F-A♭ sonority twice during this passage: first, the circle of fifths is abandoned just as the A♭➔ chord is targeting a D♭ arrival; and second, the minor IV’s chromatic 6-phase chord, F-A♭-D♭, is auditioned during measure 38 but
rejected, with the D♮ of measure 40 successfully leading from IV onwards to V♮. (Though D♭ is chromatic if F-A♭-C is interpreted as IV in C Minor, the onset of an F Minor tonicization would instead support CC, echoing the GG sounded during A1’s opening tonic presentation.) 11. Though Schenker’s and my conceptions of the A1 section’s second part correlate to some extent, we disagree on numerous points. Again looking principally at Five Graphic Music Analyses, note how our interpretations of the path from root C to root F are similar, even if I make more of the interior E♮-G-B♭-C chord than he does and interpret the melodic line as emanating from Kopfton G rather than E♭. I regard his assertion of ’s arrival at measure 27 to be untenable. The I⇨ chord that immediately precedes root F could contain either an imagined C or an imagined D♭ (displacing C). Either way, the D♮ of measure 27 is a neighboring note that resolves to the C at that measure’s close. D is a member neither of the C chord nor of the F chord. How, then, can it be regarded as the onset of ? Looking next at measure 28, Schenker acknowledges the addition of minor seventh A♭ to the B♭ major chord in his foreground graph (p. 58), yet he does not follow through on assessing the repercussions of that surge-inducing act – namely, the succession from B♭➔ to E♭. During measures 29 through 33 he and I present opposing hierarchies for the chord pairs. From his perspective root A♭ takes hold at measure 29, whereas in my view the circle of fifths proceeds normatively to E♭ before the arrival of A♭ (realized by a chord in first inversion) in measure 33. Though he has moderated the potent seismic shifts that raise A♭➔ to C➔ in measures 33 through 35 through the extensive use of parenthetical notes in his foreground graph, we both understand that this activity is leading the progression towards IV, though I find it curious that the IV numeral is postponed until measure 40 in his foreground graph – at the point where IV shifts to its 6 phase. 12. See Schenker’s foreground graph in Five Graphic Music Analyses, p. 58. 13. Five Graphic Music Analyses, p. 58. 14. Though not identical, the structure here closely resembles that of 264 through 274.
15. Diminished seventh chords in measures 66 and 68 soften the stark voice leading displayed in 4.3. That in measure 66 targets the chord of measure 67 as that in measure 64 targets the chord of measure 65. Because the descent of the chords is not evenly spaced (a major second from D♭ to C♭, but a minor second from C♭ to B♭), the chord of measure 68 does not function like those of measures 64 and 66. Instead it anticipates the upcoming subtonic. 16. Though this ♭II offers fulfillment after the frustrations noted in the vicinity of measures 33, 38, and 65, Schenker’s graph of the entire movement in FC, fig. 12, erases it, displaying instead a diatonic II with at measure 72. Readers mystified by such seeming errors may gain insight into Schenker’s thinking by comparing the two graphs labeled “1. Schicht” and “2. Schicht” in Five Graphic Music Analyses, pp. 54–55. 17. See TAH, p. 313, n.14, for samples of creative diminished-seventh usage on display in August Swoboda’s Harmonielehre (Vienna: Haykul, 1828) , tab. V. The date and place of publication tantalizingly encourage the hypothesis of a direct encounter with its contents (or even with the author himself) during Chopin’s two visits to Vienna preceding his migration to Paris. For an account of Chopin’s documented or presumed exposure to music theory during his Warsaw years (including notions derived from Albrechtsberger and from Kirnberger), see the exemplary account in part I, chapter 1, of Maciej Gołąb’s Chromatyka i tonalnoséc w muzyce Chopina (Cracow: Polskie Wydawnictwo Muzyczne, 1991) ; as Chopins Harmonik: Chromatik in ihrer Beziehung zur Tonalität, trans. B. Hirszenberg (Cologne: Bela Verlag, 1995) . 18. Phipps cites a motion to an F minor chord in measures 36–37 to support his assertion. Note, however, that there the bass is E♮ (sounded at 351), which targets resolution pitch F (presented in multiple registers during measure 37). In contrast, the bass D♭ (measures 65 and 66) is disinclined to ascend to F, though Phipps displays exactly that hypothetical resolution (his ex. 13).
Chapter 5: Nocturne in C♯ Minor (op. 27, no. 1)
Chapter 5: Nocturne in C♯ Minor (op. 27, no. 1) 1. It was recommended to me in 1976 by my first Schenkerian analysis instructor, John Rothgeb. 2. The Music Forum was published in New York by Columbia University Press. Salzer’s article is found on pp. 283 through 297 of volume 2. His analysis is discussed in Alison Hood’s “Intraopus Connections in Chopin’s Nocturnes, Opus 27,” in The Sources of Chopin’s Style: Inspirations and Contexts, ed. A. Szklener (Warsaw: Narodowy Instytut Fryderyka Chopina, 2005), pp. 371–385 . Hood incorporates additional commentary from John Rink’s 1989 Cambridge University dissertation, “The Evolution of Chopin’s ‘Structural Style’ and Its Relation to Improvisation,” which I have not been able to access. 3. The Oster Collection: Papers of Heinrich Schenker (housed at the New York Public Library for the Performing Arts at Lincoln Center), file 32, item 51. The archive includes several intriguing graphs by Ernest Oster of a passage from the nocturne (file 32, item 46). Oster’s placement of the abbreviation “recap.” at measure 84 concurs with my reading, in contrast to Salzer’s assertion of a formal division at measure 65. 4. It would be reasonable to propose that measures 7 and 8 should be read as III5−6 IV, with the internal III6 asserted locally as I➔. My analysis in 5.1 instead juxtaposes two continuations from the same starting point: from minor tonic to the mediant between 31 and 71 as a means of expanding the initial tonic, then a tonic restoration proceeding to a contorted dominant between 73 and 94. Chopin’s excursion to the mediant extends the first phrase into a fifth measure, requiring some compensatory compression: the second phrase begins now in the middle of measure 7, rather than at its outset. 5. In the second and fourth of these statements, C♯ is embellished by an excursion up to E (as C♯
7. Since composers were cognizant of the challenges that their works imposed upon amateur performers, they often would substitute a five-flat for a seven-sharp signature. Chopin’s four-flat signature corresponds to the initial goal, the A♭ dominant of measure 52, rather than to the D♭ tonic that emerges in measure 65. (Though my principal analysis retains C♯ as the tonic, a local tonicization of the dominant, as goal of a II⇨ V I progression in G♯ [A♭] Major from 483 through 523, is feasible.) Consequently it was necessary for Chopin to manually insert a G♭ accidental numerous times during measures 63 through 80, after which a restoration of the four-sharp signature occurs. 8. Whereas C♯ Minor’s diatonic I6 chord would inherently surge (as A➔) towards ♮II, here the supertonic’s D♯ root is targeted through the chromatic shift of the 6-phase chord to A♯⇨. 9. I display its normative functioning as a connector between the tonic and the dominant in Schubert, 1.8 (Model 2), while Schenker demonstrates its use in FC, fig. 111a (second model). Regarding the latter, see my “Schenker, Schubert, and the Subtonic Chord,” in A Music-Theoretical Matrix: Essays in Honor of Allen Forte (Part II), ed. D. C. Berry, Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic 3 (2010), pp. 127–166 . 10. Whereas it is well known that a diminished seventh chord may be used to bring about the tonal shift of a minor third through enharmonic reinterpretation, in measures 77 through 79 a diminished seventh connects two chords a major third apart. Initially A -C -E♯-G♯ serves as an embellishment of the preceding B♯ major chord. Yet upon resolution it takes on the character of a common-tone diminished seventh chord. (Compare with Haydn/Mozart, p. 213.) Chopin complicates matters by allowing the common tone (G♯) to be displaced by its chromatic upper neighbor at the moment of resolution (791, where I show a retained G♯ within parentheses in 5.3). As a result, two diminished seventh chords sound in succession. (In fact, diminished sevenths persist through the melodic peak at 811.)
Chapter 6: Preludes in E Major and E Minor (op.
Chapter 6: Preludes in E Major and E Minor (op. 28, nos. 9 and 4) 1. Lerdahl’s analyses appear in Tonal Pitch Space (Oxford University Press, 2001), pp. 89–109 . They had earlier been published, in a somewhat abbreviated form, as “PitchSpace Journeys in Two Chopin Preludes,” in Cognitive Bases of Musical Communication, ed. M. R. Jones and S. Holleran (Washington DC: American Psychological Association, 1992), pp. 171–191 . 2. Though Lerdahl consulted the first edition of Aldwell and Schachter’s Harmony and Voice Leading, readers will find the same analysis in the current fourth edition (Boston: Schirmer; Cengage Learning, 2011), pp. 589–591 and 628–629 . 3. “The Prelude in E Minor Op. 28 No. 4: Autograph Sources and Interpretation,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 161–182 , and “The Triad as Place and Action,” Music Theory Spectrum 17 (1995), pp. 149–169 , reprinted in Unfoldings: Essays in Schenkerian Theory and Analysis, ed. J. N. Straus (Oxford University Press, 1999), pp. 161–183 . (The Unfoldings page numbers will be employed in references to the latter.) Readers may wish to expand their study of the Prelude in E Minor by consulting a lively critique of Schachter’s analyses by Bengt Edlund, who both conveys a vociferous anti-Schenkerian stance and offers an alternative analysis in chapter 3 of his Chopin: The Preludes and Beyond (Frankfurt am Main: Peter Lang, 2013), pp. 201–233 , which I encountered only after the present book went to press. 4. “Musical Genre and Schenkerian Analysis,” Journal of Music Theory 42 (1998), pp. 101–124 . (Schachter’s graphs from the articles listed in note 3 are reprinted in London and Rodman’s article.) 5. This sheet is a part of the Oster Collection: Papers of Heinrich Schenker (file 32, item 98), housed at the New York Public Library for the Performing Arts at Lincoln Center. 6. A partial list of errata: missing stems in line 1; a missing slur, Roman numeral, and words in line 2; a missing accidental, commas, dash, word, and abbreviation in line 3; the presentation of a line connecting E and D♯ instead as a slur in line 5; the
transcription of fis as bis (and omission of a slur connecting ♭ and fis and another slur connecting fis and h) and the positioning of the D♮ notehead a measure too soon in line 6. 7. The complete rendering of a 5–6 sequence to connect the tonic’s 5-phase (E-G♯-B) and unfurled 6-phase (C♯-E-G♯) chords would involve a total of eleven chords (E5–6 F♯5–6 G5–6 A5–6 B5–6 C♯5). Chopin here makes use of a common shortcut, facilitated by the fact that E5 and G♯6 employ the same pitch classes. Consequently his sequence employs a total of six chords. 8. Lerdahl’s omission of commentary regarding how he went about creating his fig. 3.2 is curious, given a comment he made earlier while establishing his system’s theoretical foundations: “It is sometimes troublesome to determine the grouping structure of a piece, but once that is in place the rest mostly follows like clockwork” (p. 7). One is left with the impression that the figure depends to a large extent upon the analysis of the prelude’s second and third phrases in Aldwell and Schachter’s Harmony and Voice Leading. 9. Lerdahl’s reading is very similar to an unpublished graph by Schenker, now in the Oster Collection: Papers of Heinrich Schenker (file 32, item 108), housed at the New York Public Library for the Performing Arts at Lincoln Center. I suspect that that graph was an inspiration both for Lerdahl and for Aldwell and Schachter. 10. These comments echo my similar concerns about the analysis of TR sections in twopart, major-key sonata expositions. In my view, II➔ often will serve as the goal of TR (at the medial caesura), followed by V at or soon after the onset of S. An analysis that places the arrival of the structurally deep V before the caesura II➔ puts the cart before the horse, in my view. (See Haydn/Mozart, pp. 58–67.) 11. Schenker commented on Chopin’s slurring in the Mazurka in G♯ Minor (op. 33, no. 1) as follows: “Chopin, with his penchant for the melodic, employs the slur in his own special way. Thus the song of this upper voice, as if absorbed in itself, seeks to remain an indestructible unity and therefore basically resists articulation …” (FC, p. 110).
12. The score that Lerdahl published as fig. 3.1 deploys slurring that starkly contrasts that shared by two recent Urtext editions: the National (Cracow, 2000) edited by Jan Ekier and the Peters (London, 2003) edited by Jean-Jacques Eigeldinger. Neither editor’s critical commentary mentions alternative slurring from any Chopin source. Lerdahl’s slurring exactly matches that in the “Student’s Edition” of the Preludes by Alfred Cortot (Paris: Éditions Salabert, n.d.), though its origin may be earlier. 13. Though I interpret their formal relationship in a different way due to the contrasting context, the first two phrases of the Mazurka in B Major (op. 41, no. 2, analyzed in 3.10) behave harmonically approximately as do the first two phrases of the E Major Prelude. 14. Whereas this B♯ (spelled by Chopin as C♮) raises diatonic B (spelled as C♭ when restored by Chopin at the end of 83), its enharmonic equivalent C♮ in measure 6 lowers diatonic C♯ (restored at 71). Both are wobbles. 15. Continuing the comparison with the Mazurka in B Major from note 13, Chopin in that case highlights the peculiarity of the B–E–A♯–D♯ circle of fifths by instead traversing the parallel minor key’s B–E–A–D during the varied repetition of the mazurka’s A1 section. 16. The E>A fifth is filled in by step in the bass: E>D♮>C♮>B♭>A. The passing note B♭ seems at first to attach itself structurally to the C♮ chord (at 63), forming a C➔ surge towards F♮. Chopin indeed may be playing with listeners’ expectations by projecting the first two chords of a I
♮II5♮ V progression, a chromatic variant of the first phrase’s
I5–6 II➔ V. Yet by the downbeat of measure 7 that potentiality loses its viability, and the deeper connection between E and A becomes paramount. 17. Concerning this thorny issue, see TAH, 7.6 (including the commentary regarding Progression 3 on p. 175). 18. Continuing the discussion of slurring begun in note 12, the score that Lerdahl provides as fig. 3.1 contains a bass slur beginning at the B of 84 and extending through the E of 93. Again, that does not correspond to the recent Urtext editions, where a single
long slur extends from 51 through the final chord. Though I disagree in some details with Schenker’s unpublished analysis of the prelude (see note 5 above), his jottings for measures 5 through 8 twice show a progression from I through III (sic) to V, supporting a structural descent from to . 19. Aldwell and Schachter, Harmony and Voice Leading, pp. 628–629. 20. Dmitri Tymoczko offers an alternative analysis of this phrase in his A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford University Press, 2011), pp. 218–219 . Our widely divergent views on harmonic analysis are apparent even in some basic statistics: my example (6.3) employs three Roman numerals (one chromatically modified) and four letters indicating roots (two of which coincide with Roman numerals), all in E Major; his example (6.6.2) employs sixteen Roman numerals in the keys of E, C, F, d, A♭, and then E again. (My strongest objections relate to both passing chords, labeled as ii , and to the chord with suspensions labeled as iii within parentheses.) We both read the phrase as continuing to E Major’s dominant at the end of measure 8, contrasting Lerdahl’s close on the preceding G♯ [A♭] chord. 21. Aldwell and Schachter, Harmony and Voice Leading, pp. 590–591. 22. Though Lerdahl’s commentary acknowledges the exceptional nature of this passage – “modulates to a distant place, returning home at the last moment” and “remarkable for its pitch-space journey” (pp. 89–91) – his fig. 3.8b conveys neither a veering away from an intended course (in the way that my crossing out a chord, highlighted within a box, does in 6.4) nor even that there is an intended course targeting C. In addition, the juxtaposition of G and V/E appears to grant the G a higher hierarchical status than the structural dominant. Note that the B dominant chord of 114, because it resides within the tonal sphere of goal E, is absent from the representations in his figs. 3.5 and 3.6; and though a V appears and is circled in his fig. 3.8b, it there pales in comparison with the bold presentation of circled E, a, F, g, and G. My discomfort with this visual presentation corresponds exactly to a similar sentiment expressed in my assessment of
the early nineteenth-century author Gottfried Weber’s analytical procedure in TAH (p. 147 and 6.7). 23. A whole step in one voice occurs at the prelude’s outset: B>A in measures 1 and 2. Consequently a parallel progression of diminished – rather than minor – chords ensues. Given their role in filling in a broader tonic expanse, there is no one “correct” way to spell the progression’s internal chords. In fact, Chopin shows no predilection even to spell them using a sixth and a third above the bass, as I have done in 6.5. 24. Parallel progressions of diminished seventh chords descending in half steps were sufficiently commonplace by the beginning of the nineteenth century to be featured in the harmony textbook used at the Conservatoire National de Musique in Paris: CharlesSimon Catel’s Traité d’harmonie [1802]. See TAH, 3.11b. 25. One might propose an alternative hypothesis in which the surging I➔ is asserted earlier – at the end of measure 3 (G♯-B-D-F♮, with B locally embellished by neighbor C) – and then prolonged through the end of measure 8. (This hypothesis is closely allied with Schenker’s reading, published in London and Rodman, “Musical Genre,” p. 119.) One could accommodate that view by spelling the third tenor note in 6.5 as G♯ and adjusting the slurring. However, I do not hear measure 3 as anything other than an interior element of an expansive downward glide. Thus I stand by my reading as presented in 6.5. 26. Though a minority opinion during the nineteenth century, this perspective is not without historical precedent: see TAH, 3.4b and 7.14c. Dmitri Tymoczko’s A Geometry of Music, fig. 8.5.5 (p. 287), offers the antithesis of my perspective: seventeen analytical symbols in a total of five keys over the course of the phrase. 27. Two distinct levels of hierarchy are at play here. Several bona fide passing chords (such as E-G-C♯-A♯[B♭] in measure 4) connect the perimeter tonic chords of measures 1 and 8; while at the surface level the gradual falling-into-place of those various passing chords results in a range of incidental simultaneities that perform a connective role between the individual passing chords. For example, E-G♯-D-B at the beginning of measure 4 should not be interpreted as I➔ even though the ultimate goal of the
descending parallel progression is, in fact, a form of I➔. (On this point, I disagree with Schenker’s analysis in the Oster Collection, cited above.) 28. Note the lovely motivic association between G>F♯ and C>B in measure 12. The latter occurs twice (corresponding to the BC>B triplet should be interpreted as a layering of neighboring embellishments: C embellishes B, whereas D embellishes C. It makes no sense from a Schenkerian perspective to process the triplet – as London and Rodman do – as a filledin unfolding of the third
, since D♯ – not D♮ – is a member of the dominant harmony
prolonged since measure 10.) The C>B neighbor reiterates the bass motion of measures 9 through 12 and is then taken up by the melody during measure 13, as in measure 1. 29. London and Rodman, “Musical Genre.” 30. Regarding the critical G♯-B-D-F♮ chord at the end of measure 8, Lerdahl’s vii°/a reading (in his fig. 3.20b) is similar to my surging tonic (I➔) reading. We agree that it is a chord that potently targets the A minor chord of measure 9. In my view London and Rodman’s “Schenkerian” reading misses the point: the ♭vii7 label in their ex. 1 (presented instead as “vii7” within quotation marks in their commentary on p. 102) pertains to the D-F♮-A-C chord of 81, from which they proceed directly to measure 9’s iv6, omitting consideration of the G♯-B-D-F♮ chord altogether at this level. (They propose a subdominant prolongation from 51 through 92.) In the succeeding paragraph of their commentary they do mention the I➔ chord, labeling it vii°7/iv. It appears in the foreground layer of their ex. 1 as a connective chord between ♯vii7 and iv6. Since they were attempting to construct a Schenkerian analysis of the work, it is curious that they did not take into account that Schenker employed only one Roman numeral for all of measures 7 and 8: I♯ below a D-F♮-G♯-B chord. (Though Schenker’s analysis in the Oster Collection is sketchy, on this point the perspective is clear: the measure numbers 7–8 sit squarely underneath a I♯3 numeral – not off to the side, as in the botched London and Rodman transcription.) 31. Schachter, “The Prelude in E Minor,” and Schachter, “The Triad as Place and Action.”
32. That third is traversed both in an interior strand during measures 18 through 20, as indicated by the slurred noteheads in 6.6, and in the upper register (where a beam is employed) during measures 18 through 24. 33. London and Rodman, “Musical Genre,” p. 104. 34. Schachter, “The Prelude in E Minor.” 35. Though his Roman numeral analysis does not acknowledge F♯’s presence in the chord, I think Schachter would agree with me that by this point the IV Stufe has shifted to what I refer to as its 6 phase, with F♯ serving as the sixth above root A. (The Arabic 6 at measure 16 of Schachter’s 1994 graph instead indicates that the iv chord initially sounds in an inverted state.)
Chapter 7: Prelude in G Minor (op. 28, no. 22)
Chapter 7: Prelude in G Minor (op. 28, no. 22) 1. Analyzing Schubert (Cambridge University Press, 2011). 2. Interpreting Chopin: Analysis and Performance (Farnham: Ashgate, 2014) . 3. “Ambiguity of Tonal Meaning in Chopin’s Prelude Opus 28, No. 22,” Festschrift for Steve Larson, Music Theory Online 18/3 (September 2012) . A revised version of this article appears on pages 111 through 124 of Interpreting Chopin. 4. This relationship between B♭ and A is replicated later, in measures 24 and 32 (treble clef). The gesture collides with the dominant’s embellishing chord (B♭-E♭-G) during 342. 5. In that an evolution of the ⇨ type occurs most often in the context of II⇨ proceeding to a major dominant, it is opportune that the subdominant to which I⇨ proceeds is of major quality (atypical in a minor-key context). 6. Hood employs the word “ambiguous” or one of its derivatives a total of twenty-six times within her six-page essay. Indeed, when I was younger I found many passages in Chopin’s music ambiguous, though I did not extol ambiguity as an important compositional feature. As I have aged I have found less and less of the music that I study to be ambiguous. I regard this as a sign that my analytical acumen has developed (to the point that I now willingly publish my analyses, something I refrained from doing during that earlier phase of my career). Certainly some readers (including Hood) might suggest instead that an undesirable rigidity has invaded my thinking – that I too summarily reject alternative readings that might hold potential. Though I do not celebrate ambiguity as Hood does, I appreciate the sincerity of her conviction. 7. Hood’s graphs and her commentary present somewhat different conceptions. Her paragraph 16 asserts: “The vii°7 at the beginning of measure 8 encourages us to hear the A as part of a dominant-functioning harmony. Yet, at the same time, because B♭–A–G sounds as an upbeat (as it did previously) we can also hear it as prolonging tonic harmony, so the A is heard as a passing tone that resolves to G … it can now be interpreted in two mutually-exclusive ways.” Whereas I am using the comparatively
unambiguous context of measures 8 and 9 to come to terms with measures 0 and 1, she is imposing her interpretation of measures 0 and 1 upon measures 8 and 9 even though, as she acknowledges, the chordal accompaniment does not support it. A review of the graphs from chapters 1 and 3, above, reveals that thirteen of the forty-three mazurkas explored there do not begin on a tonic chord. Whereas I suggest that this prelude conforms to that 30 percent option, Hood is endeavoring to hear the work in terms of the alternative 70 percent option, despite Chopin’s instructive presentation within measures 8 and 9. 8. Mehrdeutigkeit (multiple meaning) is explored in TAH, pp. 155–161. 9. Compounding my confusion, the score labeled A2 in Hood’s ex. 2 places a I numeral (why capital?) at the end of measure 33 (note that the bar line between measures 32 and 33 was inadvertently omitted) rather than where I think it was intended – below the G at the end of measure 34. 10. Certainly the author of an article whose title begins with the word “Ambiguity” should be extra careful in proofreading, lest unintended additional instances of ambiguity divert the reader’s attention, as it has mine. The remarks in this chapter correspond to the article’s state on October 12, 2012, not to the version later published in Interpreting Chopin (after Harmony in Chopin went into production).
Chapter 8: Prelude in C♯ Minor (op. 45)
Chapter 8: Prelude in C♯ Minor (op. 45) 1. “Chopin and ‘La note bleue’: An Interpretation of the Prelude Op. 45,” Music & Letters 78 (1997), pp. 233–253 ; as “Chopin et ‘la note bleue’: Une interprétation du Prélude opus 45,” in Eigeldinger, J.-J., L’univers musical de Chopin (Paris: Fayard, 2000), pp. 169–188 . 2. “‘Rounding Up the Usual Suspects?’: The Enigmatic Narrative of Chopin’s C-sharp Minor Prelude,” in Engaging Music: Essays in Music Analysis, ed. D. Stein (Oxford University Press, 2005), pp. 236–252 . 3. See TAH, 3.2. 4. Ibid., 3.3, 3.4, and 3.5. 5. When working on this article, Eigeldinger regarded the prelude’s cadenza as occurring in measure 80. Yet in the subsequent Peters edition (2003), which he edited, the cadenza is counted as a continuation of measure 79. (The latter view conforms to the National Edition as well.) Consequently I have tacitly lowered all of the article’s measure numbers higher than 79 by one in my commentary. 6. Eigeldinger hears echoes of his tetrachords (with some chromatic inflection, and curiously breaking off in the middle of the second one) in the forthcoming main section’s bass. In note 29 he asks readers to ponder the following series of stepwisedescending bass pitches: C♯ (51), B (91), A (131), G♮ (171), F♯ (191), and E (231). I reject the placement of G♮ within this series, in that the G♮ chord resides within the domain of a hierarchically deeper D♮ chord; and I can make sense of E only as an internal component of an F♯>E>D♮ third whose goal D♮ is elided at 271 (as will be explained in due course). I will argue that the C♯-to-D♮ contour of this region corresponds to the C♯-to-D♮ seventh introduced during the introduction. 7. Readers will find the relationship I propose between the introduction and the main section of this prelude reminiscent of the correlation I draw between the introduction and exposition of Schubert’s Symphony in B Minor (“Unfinished”), movement 1. See Schubert, chapter 7.
8. Smith acknowledges this D♮ chord without assigning it a significant role (p. 251). In his score 20.1 he places the following symbol underneath measure 4 (not measure 3): [➔D?]. 9. In that editor Deborah Stein introduces Smith’s essay by informing readers that he “has long been interested in … the theories of Heinrich Schenker” (p. 236), impressionable young readers (the book’s intended audience) might assume that there is something Schenkerian about Smith’s analysis. That assumption would be incorrect. Any Schenker-influenced reading would acknowledge the foundational role of I V♯ I within the introduction, as conveyed in 8.1b. 10. Though the bold type in which the words rounded binary form are printed prods readers to look up the term in the glossary provided at the end of the volume in which Smith’s essay appears, the definition found there (p. 331) and the formal description of the prelude in his essay do not correspond. 11. Smith’s word “retransition” corresponds to the German word “Rückleitung” in Hugo Leichtentritt’s analysis of the prelude. See his Analyse der Chopin’schen Klavierwerke, 2 vols. (Berlin: M. Hesse, 1921–1922), vol. 1, pp. 177–179 . 12. As I did also in my critique of Lerdahl (note 22 on pp. 274–275), I trace my discomfort with this visualization back to a similar sentiment expressed in my assessment of the early nineteenth-century author Gottfried Weber’s analytical procedure in TAH (p. 147 and 6.7). 13. It is important to keep in mind that the F♮ chord of measures 55 through 63 is a wobble-infiltrated mutation of F♯, and not a misspelled E♯ chord. Consequently Smith’s application of the word “mediant” in his n. 16 (p. 241) is entering dangerous territory, in my view. Likewise, Gunner Rischel’s Roman numeral III (within the progression III IV II V I) is off the mark. (See his “Tonal analyse,” Musik & Forskning 14 (1988–1989), p. 127 .) 14. The cadenza’s emphasis upon the D♯ nodal point in part compensates for the brevity of that chord (measure 65) during the initial presentation of the main section.
15. In the glossary of Engaging Music, the volume in which Smith’s essay appears, editor Deborah Stein distinguishes two different meanings for the word “Reprise”: “a repeated section” or “the repetition of opening material later in the piece” (p. 331). In the context of my one-part form, I use the word in the former sense; in the context of his idiosyncratic rounded binary form, Smith uses it in the latter sense. I suspect that Eigeldinger intends the “repeated section” meaning as well, though the terseness of his commentary leaves that open to question.
Chapter 9: Ballade in F Minor (op. 52)
Chapter 9: Ballade in F Minor (op. 52) 1. Laufer’s essay, “On Chopin’s Fourth Ballade,” is published in Keys to the Drama: Nine Perspectives on Sonata Form, ed. G. Sly (Farnham: Ashgate, 2009), pp. 157–175 . Another substantial account of the ballade (from a contrasting perspective) that readers might wish to pursue concurrently is Michael Klein’s “Chopin’s Fourth Ballade as Musical Narrative,” Music Theory Spectrum 26 (2004), pp. 23–55 . 2. Before proceeding to publication, Laufer presented his analysis at the Fourth International Schenker Symposium (Mannes College of Music, New York, March 17, 2006). The longhand examples were printed on pages that measure 11 by 17 inches. Typeset for publication with no changes in layout, the same examples were reduced so as to fit onto pages that measure approximately 6 by 9 inches. 3. My reading of the work embraces this conventional flow from the tonic to the dominant. In his “Chopin’s Modular Forms” in Variations on the Canon: Essays on Music from Bach to Boulez in Honor of Charles Rosen on His Eightieth Birthday, ed. R. Curry, D. Gable, and R. L. Marshall (University of Rochester Press, 2008), pp. 198–199 , Robert P. Morgan proposes that the theme ends instead with “a full cadence in iv” followed by a “brief, half-measure transition back to V of F minor following the end of the theme.” That perspective coincides with Laufer’s analysis, to be explored below. 4. In his “Ambiguity and Reinterpretation in Chopin,” Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge University Press, 1994), pp. 140–160 , Edward T. Cone savors Chopin’s treatment of the ballade’s initial C chord: what may at first seem to function as the dominant of an F tonic arriving in measure 2 (displayed as one of two analytical hypotheses in his ex. 8.1) is tonicized for several measures, after which it reveals its role as dominant – of the F tonic that emerges in measure 8. Cone projects the conviction that Chopin “wished us to hear” the passages as “deliberately ambiguous” (p. 141). I endorse an alternative perspective on this issue. Whereas for many analysts a chord such as C-E♮-G-B♭ automatically will be labeled as V7 (either as a dominant or as an “applied” dominant, here V7/IV), I am comfortable with such a chordal configuration emerging at any point where a descending-fifth root succession occurs. Chromatic
pitches often are incorporated so as to enhance the forward momentum generated when a chord surges, without concurrently signaling diatonic pitch content within any key. Consequently when listening I embrace the energetic initiative of a I➔ or II➔ or VI➔ without concurrently expecting that the chords they target will function as a tonic at any level. Clearly this is a matter that defies resolution. Though Cone’s strongly worded conviction – that a “convincing analysis” “must reveal” such an intention – is reasonable, certainly others may pursue alternative perspectives with equal justification. 5. Since the cadence will be a major point of contention between Laufer and me, I mention here that Lauri Suurpää’s analysis in “The Path from Tonic to Dominant in the Second Movement of Schubert’s String Quintet and in Chopin’s Fourth Ballade,” Journal of Music Theory 44 (2000), pp. 468–469 , similarly proposes an interruption at
. Suurpää does not acknowledge Chopin’s establishment of A♭ as the Kopfton prior to the cadence. Instead he proposes a novel – and in my view doubtful – structural reading, ascending from to . (The establishment of as the Kopfton in the context of a mediant chord, as I propose occurs in measure 13, is demonstrated by Schenker in FC, fig. 38a and fig. 40, ex. 10.) For a reading more in line with Laufer’s, see William Rothstein’s “Ambiguity in the Themes of Chopin’s First, Second, and Fourth Ballades,” Intégral 8 (1994), p. 25 , where he proposes that “the dominants in question are not typical half cadences. The large-scale harmonic progression of each variation – basically I-(III)-IV-V7– closes into the tonic at the beginning of the next variation, so that a chain of overlapping progressions results.” My subtly different reading proposes that a hierarchically deep C, E♮, and G during the second half of measure 22 collide with a foreground B♭ that serves as a local voice-leading connection to the following I. 6. Though what ensues in measures 23ff. turns out to be a modified repetition of A1 rather than A2, listeners might reasonably surmise that the work has embarked upon the post-interruption half of a binary structure at that point. 7. The flourish of notes following the fermata chord in measure 134 suggests that Chopin might likewise have intended the fermatas of measure 7 as an invitation to some improvised embellishment. Nowadays any deviation from the printed score during a
performance attracts inordinate attention, since many members of the audience have heard numerous live or recorded performances of the work already. Clearly that state of affairs was not in play during Chopin’s lifetime. A modern performer might at least privately (and perhaps even publicly) seek to regain that spontaneity through tasteful additions to the printed score in contexts such as measure 7. 8. Laufer’s correlation of the D♭ tonicization to the already established B♭ subdominant echoes a reading presented by Carl Schachter in his review of Jim Samson’s The Music of Chopin, Music Analysis 8 (1989), p. 190 . On the other hand, Laufer and I disagree with Schachter regarding how Chopin leads onwards from D♭: we interpret the prominent chromatic line A♭E♭>D♭, B♮>A♮>G, and D♮>C>B♭), the upper strand appears awkwardly as A♭>G♭>E♮. Using modulo 12 numbers that line would be represented without enharmonic seam as 8>6>4. One attains the downbeat embellishing chord within the prevailing F Minor key (modulo 7), enters the domain of modulo 12 for the -2-2 parallel progression, and then thrusts the goal chord back into the modulo 7 environment.
Chapter 10: Barcarolle in F♯ Major (op. 60)
Chapter 10: Barcarolle in F♯ Major (op. 60) 1. “The Barcarolle: Auskomponierung and Apotheosis,” in Chopin Studies, ed. J. Samson (Cambridge University Press, 1988), pp. 195–219 . Readers also should consult David Kopp’s “On Performing Chopin’s Barcarolle,” Music Theory Online 20/4 (2014) , which appeared after the present book went to press. 2. The parallel progression’s upper line, which traverses all the diatonic steps within a G♯>G♯ octave, is highly embellished, particularly with incomplete upper neighbors following the principal pitches, beginning with the last pitch in measure 1: F♯C♯ and G♯A♯. Consequently only the interior B during 32 – a step below Middle C – will be perceived as the chordal seventh. It is in that register that it resolves to A♯ during measure 3. 3. Though the interior line’s G♯ sounds in the upper register at 91, it may be imagined over a wider span. An uncommon juxtaposition of B♯ and B♮ occurs during 92–3. Whereas the upper strand proceeds as B♯F♯ (bound by a dotted slur spanning measures 6 through 24) is filled in by stemmed noteheads corresponding to a descending F♯ Major scale, missing only E♯. That notation makes V/V appear subordinate to the vi and V that surround it, with V serving as an internal point within the broad stepwise trajectory. (Rink relates that “each pitch in the scale … supports a tonicized harmony with the exception of the penultimate, G♯” (p. 200).) Yet at an earlier point in his commentary Rink refers to “the resolution from the tonic to the dominant in bar 15” (p. 198), a notion that I endorse and convey much more resolutely in my 10.1 than he does in his ex. 4. In particular, that reading would warrant that V/V (my II♯) be interpreted as hierarchically deeper than vi (I6). 5. Though Rink’s foreground graph of the region (his ex. 9) contains a greater abundance of bass stems, it nevertheless does not deploy Schenker’s characteristic S-
shaped slur (F♯ via G♯ to C♯), which would decisively clarify the hierarchical relationship between D♯ and G♯. 6. During the introduction each of the parallel progression’s three principal strands traverses an octave (fifth>fifth, third>third, and seventh>seventh), and so a uniform descent ensues. During the prolongation of the tonic’s upper-third chord during the B section, the three principal strands connect different elements of the prolonged chord (fifth>root, third>fifth, and root>third). Consequently the line emanating from E♯ gets off to a slow start, since it has a shorter distance to cover. The interior strand does not pursue a maximally linear course, which would be C >(B♯)>A♯>(G♯)>F♯>E♯. (Chopin omitted the notes enclosed within parentheses.) 7. The proposed broad F♯D♯ (fourth and sixth soprano noteheads of measure 28) and G♯>E♯ (fourth and sixth soprano noteheads of measure 29). The situation is complicated by the linear activity of the interior strands. Whereas internal A♯>G♯>F♯ in measure 28 reinforces the F♯>E♮>D♯ above (both connecting members of the F♯➔ and the following B chords), the D♯ of an E♮>D♯>C♯ third (seventh to fifth within the F♯➔ chord) collides with the sounding of F♯ during 283, and that third’s C♯ (the note to which D♯ passes) sounds only an octave lower. 8. Rink lists what I refer to as the B section as a ‘Development’ – single quotes included – in his formal synopsis of the Barcarolle (his fig. 1). 9. I explore this issue in detail in TAH, pp. 162–165, incorporating analyses of a passage from Chopin’s Prelude in D♭ Major by Schenker and by Schoenberg [6.21a–b]. The C♭ in the Prelude’s measure 9 is the equivalent of the E♮ in the Barcarolle’s measure 17. 10. As suggested above, a comparison with 3.6a, an analysis of the Mazurka in B Major (op. 63, no. 1) – just three opus numbers after the Barcarolle! – is encouraged. 11. Rink’s presentation of the A♯➔ chord of 94 in his foreground graph (example 9) is botched: whereas the chord’s A♯, C , and E♯ are all accounted for, the magic is missing
because F♯’s ascent to G♯ is neglected. All the pitches of A♯⇨ in 302 are accounted for in his fig. 11. 12. The chromatic variants of an upper-third chord were introduced in Schubert, pp. 59– 60. For F♯ Major’s upper-third A♯-C♯-E♯, the first chromatic variant is A♯-C -E♯, the second is A♮-C♯-E♮, and the third is A♮-C♮-E♮. 13. Likely some Schenkerian analysts would instead interpret this passage as III5−6 (with the 6-phase chord unfurled into position) proceeding to II➔. The correlation with Chopin’s treatment of the B section’s upper-third chord has influenced my willingness to posit a full-fledged return of I in measure 76. As with the tonic chord of 174, its duration is breathtakingly brief. Nevertheless, it represents the completion of broad tonic prolongation, in this case embellished by an uncommonly potent and extended upper-third chord. 14. As commonly occurs in the shift of a minor third, the diminished-seventh sonority is called into service. From E-G♯-B-D♮ in measure 72 Chopin proceeds to G♯-B-D♮-F♮ at the end of measure 75. Resolution to A♮-C♯-E♮ seems imminent. Yet in terms of what follows, this chord behaves as if its spelling had been E♯-G♯-B-D♮, representing C♯➔. That alternative interpretation is confirmed by the arrival of root C♯ at 761.
15. This
embellishment stems from
at 64.
16. See, for example, the progression explored in 6.4. 17. Though foreground Roman numerals are not provided, it appears that Rink intends a tonicization of C♯ Major via what I would label as I➔ IV♮ V7 I. 18. Rink’s positioning of a PAC under his measure number 91 in ex. 3 is not borne out by the content of that measure in Chopin’s score. The cadence is indisputably at 931, as he proposes in his ex. 7 (contradicting his exx. 1 and 3). 19. Bass D♮>C♯>B♯ during measure 101 coordinates with the tenor register’s B♯
imagined either as D♮ (for an exotic version of II➔) or as D♯ (for a version of II⇨ whose ninth A♯ will resolve, as an incidental dissonance, to G♯ during measure 102). Rink has included the passing note C♯ in his fig. 15 but not the B♯ to which it passes. The harmonic progression is complicated by a collision. The VI➔ chord at the downbeat of measure 101 is expanded by means of a chromatic filling-in of its seventhto-fifth span: C♯>B♯>B♮>A♯[B♭]. Chopin inaugurates the succession to II⇨ before that third’s traversal is complete. Consequently between the harmonic entities D♯-F -A♯-C♯ and D♮-F♯-A♮-B♯ (a normative succession from a surging I6 to an evolved II⇨) the pitches D♮, G♮, and B♮ happen to sound at the same time. That is a purely incidental consequence of these colliding voice-leading initiatives, in no sense asserting a ♮II5♮ (“Neapolitan”) function, which Rink proposes (with his label ♭II ) as the harmonic support for background (p. 210).
List of references to music examples 1.1 5, 7, 12, 73 1.2 12, 44 1.3 9, 12, 23, 31, 74 1.4 12, 41, 79, 83, 269 1.5 12, 49 1.6 12, 14, 81, 256 1.7 49 1.8 50 1.9 11, 32, 86 1.10 27, 60, 257 1.11 29, 30, 41, 74 1.12 52 1.13 54 1.14 56 1.15 32, 42 1.16 67 1.17 25, 53 1.18 69 1.19 31, 65 1.20 41, 45 1.21 77 1.22 32, 62 1.23 37, 41, 71, 84 1.24 39, 41, 58
1.25 37, 84 1.26 41, 86 1.27 63 2.1 50 2.3 50, 53, 95 2.4 53 2.6 53, 83 2.15 160 2.16 114 2.18 73, 74 2.19 74 3.2 96, 98, 99, 101, 236 3.3 99, 101, 236 3.4 11, 236 3.5 111, 236 3.6 236, 283 3.7 236 3.8 236 3.10 273 6.4 236, 283
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Index of Chopin’s works Ballades op. 38 (F Major), 254 op. 52 (F Minor), 213–232 Barcarolle op. 60 (F♯ Major), 233–252 Étude op. 10, no. 2 (C Minor), 145–156 Grande Valse brillante op. 18 (E♭ Major), 253 Mazurkas op. 6, no. 1 (F♯ Minor), 32, 43, 71, 73–74 op. 6, no. 2 (C♯ Minor), 4–5, 7, 43, 73–74 op. 6, no. 3 (E Major), 106–109 op. 6, no. 4 (E♭ Minor), 22–23, 42–44, 264 op. 6, no. 5 [a.k.a. op. 7, no. 5] (C Major), 5–6, 43, 44–45 op. 7, no. 1 (B♭ Major), 6–7, 43, 74, 255 op. 7, no. 2 (A Minor), 26–27, 43, 64–65, 160 op. 7, no. 3 (F Minor), 95–98, 123 op. 7, no. 4 (A♭ Major), 16–17, 43, 74–75 op. 17, no. 1 (B♭ Major), 91–95 op. 17, no. 2 (E Minor), 27–29, 43, 45–47 op. 17, no. 3 (A♭ Major), 23–24, 43, 67 op. 17, no. 4 (A Minor), 29–30, 43, 77 op. 24, no. 1 (G Minor), 109–111 op. 24, no. 2 (C Major), 7–8, 43, 79–81, 269 op. 24, no. 3 (A♭ Major), 8–9, 14, 43, 47–49 op. 24, no. 4 (B♭ Minor), 9–10, 12, 43, 81–84
op. 30, no. 1 (C Minor), 96–98 op. 30, no. 2 (F♯ Minor), 10–12, 43, 49–50, 259 op. 30, no. 3 (D♭ Major), 6, 12–13, 43, 50–52 op. 30, no. 4 (C♯ Minor), 11, 98–101 op. 33, no. 1 (G♯ Minor), 17–18, 43, 52–53, 273 op. 33, no. 2 [a.k.a. op. 33, no. 3] (C Major), 24–25, 43, 53–54 op. 33, no. 3 [a.k.a. op. 33, no. 2] (D Major), 25, 43, 67–70 op. 33, no. 4 (B Minor), 130–133 op. 41, no. 1 [a.k.a. op. 41, no. 2] (E Minor), 18–20, 43, 54 op. 41, no. 2 [a.k.a. op. 41, no. 3] (B Major), 116–119, 273, 274 op. 41, no. 3 [a.k.a. op. 41, no. 4] (A♭ Major), 119–120 op. 41, no. 4 [a.k.a. op. 41, no. 1] (C♯ Minor), 20–21, 43, 56–58 without opus 42A (A Minor), 101–104 without opus 42B (A Minor), 32–35, 43, 58–60 op. 50, no. 1 (G Major), 35–37, 43, 84 op. 50, no. 2 (A♭ Major), 37–39, 43, 86 op. 50, no. 3 (C♯ Minor), 111–116 op. 56, no. 1 (B Major), 11, 13–14, 43, 86–90 op. 56, no. 2 (C Major), 15, 43, 60–62, 265 op. 56, no. 3 (C Minor), 133–136 op. 59, no. 1 (A Minor), 136–142 op. 59, no. 2 (A♭ Major), 120–124 op. 59, no. 3 (F♯ Minor), 124–129 op. 63, no. 1 (B Major), 104–106, 283 op. 63, no. 2 (F Minor), 31, 43, 62–63 op. 63, no. 3 (C♯ Minor), 39–41, 43, 63–64 Nocturne op. 27, no. 1 (C♯ Minor), 157–165
Preludes op. 28, no. 4 (E Minor), 166–167, 176–186 op. 28, no. 9 (E Major), 166–176 op. 28, no. 15 (D♭ Major), 283 op. 28, no. 22 (G Minor), 187–197 op. 45 (C♯ Minor), 198–212 Scherzo op. 31 (B♭ Minor), 254
Index of names and concepts Aldwell, E., 167, 173, 176, 273 antecedent/consequent, 21, 22–23, 25, 26, 29, 30, 31, 41, 58, 62, 65, 67, 77, 86, 108, 116, 122, 158, 172, 187, 189, 191, 216, 220, 262, 266 antipode, 13, 14, 26–27, 131, 141, 151, 194, 220, 254 applied dominant, 18, 255, 280 arrow symbols (➔ and ⇨), 4, 12, 13–14, 255 augmented sixth chords, 12, 14, 132, 150, 183, 212, 248, 265, 266 Beach, D., 257 Beethoven, L. van, 198 Bellman, J., 254 Boulanger, N., 263 bullet symbol, 7 Burkhart, C., 266 Catel, C.-S., 275 chromatic variant, 48, 63, 67, 69–70, 88, 114, 116, 123, 164, 246, 259–260, 283 circle of fifths, 10, 13, 27, 29, 32, 39, 41, 43, 48, 49, 50, 52, 59–60, 65, 67, 81, 84, 88, 90, 94, 96–98, 99, 101, 105, 116, 118, 119, 123, 124, 128, 129, 135, 149, 150–151, 162–164, 171, 172, 173, 204, 206, 217–218, 219, 221, 237, 240, 242, 244, 248, 258, 259, 260–261, 267, 269, 274 circle of thirds, 199, 205, 219 collision, 7, 39, 48, 101, 109, 110, 134, 153, 171, 173, 265, 277, 281, 283, 284 common-tone diminished seventh chord, 155, 263, 272 Cone, E. T., 255, 280 Cortot, A., 273 Delacroix, E., 198
dominant emulation, 4 Edlund, B., 167 Eibner, F., 256–257 Eigeldinger, J.-J., 198–212, 273 Ekier, J., 266, 273 elision, 6, 8, 9, 18, 31, 35, 39, 48, 73, 81, 86, 94, 111, 123, 137, 150, 201, 206, 229, 231, 237, 255, 257, 261, 266, 267, 278 embellishing chord, 9, 17, 20, 30, 31, 45, 47, 54, 63, 73, 75, 79, 81, 84, 88, 95, 96, 99, 101, 104, 108, 109, 111, 116, 120, 122, 123, 124, 126, 128, 129, 134, 136, 142, 145, 150, 153, 163, 183, 186, 190–191, 196, 199, 205, 211, 214, 215, 216, 218, 221, 228, 229, 231, 234, 242, 246, 253, 258, 263, 264, 265, 277 enharmonic equivalence, 14, 67, 70, 77, 79–81, 88, 101, 110, 115, 116, 123, 124, 129, 131, 150, 153, 155, 161, 167, 171, 173, 176, 183, 205, 206, 207, 208, 211, 212, 220, 223, 245, 255, 263, 264, 265, 266, 267, 271, 273, 281, 283 equal subdivisions of the octave, 173, 208, 223, 231 essential dissonance, 233 Gołąb, M., 263, 270 hidden fifths, 258 Hood, A., 187–197, 270 hypermeter, 116, 118 idiosyncratic progression, 79, 175, 176, 237 incidental dissonance, 153, 233, 281, 284 interruption, 21–23 Jackendoff, R., 166 Kallberg, J., 260 Kinderman, W., 254 Klein, M., 265, 279 Kopp, D., 254
Korsyn, K., 254 Krebs, H., 254 Laufer, E., 213–232, 260, 261, 264 Leichtentritt, H., 279 Lerdahl, F., 166–186 Lester, J., 255, 257 London, J., 167, 180–181, 185–186, 276 lower-third chord, 69, 246 lowered supertonic see ♭II Lydian mode, 79 McCreless, P., 262 Mehrdeutigkeit, 148, 194, 268, 277 modal mixture see parallel keys modulo 7 vs. modulo 12, 70, 81, 101, 115–116, 123, 200, 205–206, 207, 281 Morgan, R. P., 280 Mozart, W. A., 264 multiple meaning see Mehrdeutigkeit Neapolitan sixth see ♭II obstinate progression, 13, 70, 115, 174, 176, 177, 193, 200, 205, 206, 219, 220 Oster, E., 271 Oster Collection, 254, 271, 272, 273, 276 parallel fifths, 29, 178, 232, 258 parallel keys, 42, 45, 56, 70, 77, 94, 116, 123, 132, 136, 161, 163, 274 parallel octaves, 13, 54, 67 parallel progression, 77, 101, 177, 179, 182, 198–199, 220, 233, 237, 275, 281, 282 parenthetical passage, 122, 165, 205, 228, 231, 264 passing chord, 177, 218, 257, 275
peculiar juxtapositions, 63 Phipps, G. H., 145–156 Picardy third, 86, 129, 135 reaching-over, 11, 14, 15, 32, 41, 95, 249, 267 registral shift, 4, 29, 47, 49, 83, 116, 168, 215, 218, 233, 234, 242, 244–245, 252 Rink, J., 233–252, 262, 270 Rischel, G., 279 Rodman, R., 167, 180–181, 185–186, 276 Rothstein, W., 255, 262, 280 Salzer, F., 157–165, 258, 263 Samson, J., 3 Schachter, C., 167, 173, 176, 181, 185–186, 254, 256, 265, 273, 276, 281 Schenker, H., 145, 152, 167, 169, 185, 200, 253–254, 255–256, 257, 260, 262, 264, 265, 268, 269, 270, 271, 273, 274, 275, 276, 278, 280, 283 Schoenberg, A., 145, 147, 262, 283 Schubert, F., 261, 263, 278 Sechter, S., 145, 148 seismic shift, 133–135, 141, 142, 151, 152, 153, 267, 269 sequence, 4, 11, 31, 59–60, 64, 79–81, 106, 114, 122–123, 128, 129, 141, 150, 169, 170, 174–175, 176, 193, 206, 207, 208, 237–239, 259, 267, 268, 273 Smith, C. J., 198–212 species counterpoint, 4, 5, 10, 12, 16, 29, 54, 256 Starobinski, G., 198 Stein, D., 278, 279 surge, 8–9 Suurpää, L., 280 Swoboda, A., 270
tonic pillar, 3, 91, 259 tonicization, 42, 45, 47, 53, 54, 60, 73, 75, 79, 83, 86, 88, 96, 99, 101, 106, 108, 114, 128, 150, 160, 164, 166, 194, 196, 203, 205, 210, 213–214, 215, 216, 217, 218, 219, 221, 224, 225, 226, 228–229, 241, 244–245, 250, 253, 260, 261, 262–263, 271, 280, 281, 283 twelve-note chromatic space see modulo 7 vs. modulo 12 Tymoczko, D., 257, 258, 261, 274, 275 unfurling, 6, 53, 54, 58, 63, 79, 99, 104, 106, 111, 115, 163, 168, 176 upper-third chord, 53, 54, 81, 99, 106, 109, 114–115, 161, 163, 164, 193, 214, 215, 221, 223, 228, 241, 242–244, 246, 282, 283 voice exchange, 30, 39, 161, 162, 194–195, 264, 284 Wagner, R., 181 Weber, G., 275, 279 wobbly note, 15, 19, 24, 27, 31, 32, 39, 48, 50, 53, 58–59, 69, 73, 86, 88, 99, 104, 114, 115, 116, 122, 131, 136, 141, 157, 163, 164, 171, 200, 203, 207, 212, 218, 220, 237, 241, 251, 260, 262, 264, 267, 273, 279 Yip, J., 261 5–6 shift (5- and 6-phase chords), 5, 7–8, 24, 25, 30, 37, 44, 45, 47, 49, 52, 54, 56, 64, 69, 70, 75, 79, 84, 86, 88, 94, 96, 98, 110, 111, 115, 122, 124, 126, 132, 133, 135, 141, 163, 168, 169, 170, 172, 174, 176, 177, 182, 194, 214, 218, 221, 223, 226, 228, 229, 231, 232, 233, 234, 237, 239, 241, 246, 251, 253, 254, 258, 259, 264, 265, 266, 269, 271, 276, 283 ♭II, 26–27, 31, 58, 69–70, 75, 88, 99, 130–131, 133, 150, 151, 153, 157, 176, 194–195, 196, 197, 200–201, 203, 207, 212, 218, 223, 241, 251, 267, 270, 271, 284
