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Contents
Preface
[ page vii]
part i
methodological orientation: harmonic analysis through listening
[1]
1 Foundational diatonic processes [3] 2 Surges 3 IV5–6 V 4 I5–6 II
[16] [24] [31]
5 Surging 6-phase chords [42] 6 Surges with ninths [50] 7 Colorful variants of II [60] 8 III along the path from I to V [69] part ii
masterpieces
[79]
9 Mendelssohn: Octet in E♭ Major (op. 20), movement 1 in response to Greg Vitercik and Benedict Taylor [81] 10 Mendelssohn: Song without Words in F Major (op. 85, no.1) in response to Allen Cadwallader [116] 11 Schumann: Warum? from Phantasiestücke (op. 12) in response to L. Poundie Burstein [127] “
”
12 Mendelssohn: Song without Words in A ♭ Major (op. 53, no.1) in response to Yosef Goldenberg [136] 13 Schumann: Three songs from Liederkreis (op. 39) in response to Charles Burkhart and David Ferris [146] v
vi
Contents
14 Schumann: Im wunderschönen Monat Mai from Dichterliebe (op. 48, no. 1) in response to Deborah Stein “
”
15 Schumann: Sonata in A Minor for Violin and Piano (op. 105) in response to Peter H. Smith [183] Notes [232] Select bibliography [271] Index of Mendelssohn s works [277] Index of Schumann s works [278] Index of names and concepts [279] ’
’
[171]
Preface
How did composers working just before or during the �rst half of the nineteenth century conceive of and apply harmony? My emerging answer to that question has by this point devoted due attention to the four superlative composers active in or near Vienna in the decades around 1800 (Harmony in Haydn and Mozart, Harmony in Beethoven, and Harmony in Schubert ), as well as to a wondrous expatriate Polish pianist/ composer in Paris a bit further into the century (Harmony in Chopin). Now it is time to assay what Mendelssohn and Schumann were accomplishing in various German locales. Though textbook and treatise authors of the era were active in building analytical systems to make sense of the contemporary harmonic practices (generally employing Roman numerals, as I relate in Thinking About Harmony ), their budding eff orts have been extensively transformed in my writings, in part because I incorporate notions proposed by later thinkers (Heinrich Schenker in particular) and in part through my willingness to jettison aspects of conventional modern harmonic analysis stemming from those early eff orts in favor of fresh and (I trust) improved ways of proceeding that may more fully unlock for us the processes these composers were pursuing. Though my work is intended mainly for graduate students and professional musicians, I hope that my recon�gured harmonic theory also will be introduced at the foundational level of instruction. Harmony in Beethoven off ers an inviting Harmonielehre that might aptly supplement any of the standard undergraduate harmony texts, giving initiates who may have become complacent or indiff e rent an eye-opening exposure to a new way of thinking about the topic. As a complement to the Harmonielehre, this volume opens with Harmonic analysis through listening (chapters 1 through 8), written in a way that should be accessible to undergraduates while concurrently off ering more seasoned readers plenty of rewarding content. It is curious yet true that, though music enters our consciousness through the ears, almost all of what you might draw upon to assist in developing your analytical capacities is absorbed through the eyes. I have taken the
vii
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Preface
unusual step of here introducing the foundations of my harmonic perspective through the act of listening to music. In contrast to passive reading about harmonic analysis, you will be invited to ponder questions that get to the heart of how a passage you listen to is conceived harmonically and realized in its details, and then to compare your responses to my suggestions. These featured excerpts may be accessed via audio examples available on this volume’s web page (www.cambridge.org .9781108418034). Rhythmic grids annotated with location symbols provide the means of identifying discrete moments within each sounding excerpt, so that both the questions and the responses can be crafted with speci�city. (It is important that you peruse my proposed responses in the endnotes even when you are sure that your own are correct, since I may introduce terminology or a strategy that will be needed in future responses.) I have indicated each question’s level of challenge by the number of bullets (•, ••, or •••) to the left of its identifying number, so that you have the option of pursuing only the easier questions during a �rst pass through the chapters, returning to the others later. Each listening excerpt is introduced by some preliminary commentary and the vocal generation of its essential features, focusing on the harmonic relationships that will be featured in what follows. Though you might be taken aback by my request that you proceed through eight chapters of a “scholarly ” book in this interactive mode, I hope that you will �nd it to be a transformative experience, touching on vital components of musical perception and comprehension that are di fficult to access through more conventional modes of author –reader interactions. This book ’s centerpiece is a Masterpieces section off ering detailed analyses of compositions by Mendelssohn and Schumann, featuring the tools that I advocate for harmonic analysis. Roman numerals generally are displayed in the context of Schenkerian graphs, which provide insights regarding harmony ’s hierarchical organization as well as on a range of other parameters. (During this portion of the book, some prior exposure to Schenkerian analysis is assumed, either through my Tonal Analysis: A Schenkerian Perspective, or by some other means.) As has been the case also in the earlier analytical volumes of my Harmony Project, I guide you through a direct comparison of each analysis with an interpretation by another prominent analyst (or sometimes two others), thereby deepening your perceptions regarding these works and highlighting what is at stake in the analytical process. (These alternative analyses all appear in publications that should be available at any collegiate music library. The critiques are set off from the main �ow of my analyses by shading.) Consequently, my
Preface
Harmony in . . . volumes not only point a way forward for the study of nineteenth-century music but also together comprise a unique and wideranging assessment of the state of tonal analysis in English-language scholarship over the past �fty or so years. Since my Masterpieces chapters already off e r substantial analytical challenges, I have not endeavored to extend the project ’s purview even further to incorporate assessments of publications in other languages. (Such works occasionally have been addressed in the endnotes.) Likewise some worthy analytical publications were passed over because they focus on issues only marginally related to harmony, making the sort of comparative analysis pursued here unworkable. Though I completed my �rst two Cambridge books without a clear sense of what ultimately was to emerge, or even awareness that something warranting being called a Harmony Project was in the works, by now my six monographs from Cambridge together constitute a bountiful and uni�ed body of analytical commentary on this important repertoire. I intend next to explore harmony in music after 1850, leading in due time to Debussy. I thank the University of Minnesota for granting me a sabbatical leave permitting a year of uninterrupted work on this volume and for the support of an Imagine Fund award that both covered the costs associated with the music examples and sound � les and allowed me to acquire books and to visit major research libraries. I am grateful to the New York Public Library, Astor, Lenox and Tilden Foundations, for allowing me to purchase on micro�lm and to make references to the Oster Collection: Papers of Heinrich Schenker. As in the earlier volumes of my Harmony Project, Peter Smucker has provided expert setting of the music examples.
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 CE>C. A black arrow may be used to indicate a descending-�fth 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.
ix
x
Preface
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, modi�ed 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, to the right corresponds to its third. If the chordal �fth, seventh, or ninth is altered, the analytical symbol will incorporate the 5♮ corresponding Arabic numeral, as in C Minor: II ♯ . (Arrow notation – here II➔ – off ers 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, C | F♯ B | E when an F♯-A♯-C♯ chord sounds with, rather than before, root B in a descending circle of � fths. 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♭-Bº-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. •
— — — —
–
Preface
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
anticipation closing zone chromatic passing note chromatic variant essential expositional closure essential structural closure half cadence imperfect authentic cadence incomplete neighboring note medial caesura neighboring note an individual pitch: passing note form: primary-theme zone perfect authentic cadence progression secondary-theme zone suspension transition wobble
xi
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Preface
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 measure beat. For example, the symbol 23 indicates the third beat of measure 2. Generally 2 the word “measure” will not precede the number. I regard measures in 2 6 and 8 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 signi�cant internal contrast. The symbol 15|16 indicates measure 16 along with its upbeat. When an x appears among the measure numbers in a music example, it signi�es either that the example’s content at that point does not actually sound but instead is suggested by the context or that the example displays a hypothetical continuation that the composer does not in fact pursue.
part i
Methodological orientation: harmonic analysis through listening
1
Foundational diatonic processes
Though any of the twelve pitch classes may sound during a tonal composition, certain pitches will be more prominently featured since in all cases a key will be established. For example, in A Major (the key of our �rst example, below) the pitches A, C ♯, and E are especially prominent, as members of the tonic triad. Their most frequent interactions will be with their diatonic cohorts B, D, F ♯, and G♯. The other � ve pitch classes (whose spellings will vary according to usage) may be deployed to add greater emphasis or variety (topics explored beginning in chapter 2), or instead to ful �ll subordinate embellishing or connective roles. During a harmonic progression di ff e rent pitches in turn come to the fore. For example, in the succession from V to I, the dominant’s E, G♯, and B at �rst will supersede even the tonic pitch A in prominence. With the resolution to I, A and C ♯ take over from G ♯ and B as highlighted pitches. Our �rst example lacks even that level of harmonic variety. Because of its unique location at the end of a ninety-measure composition, the tonic harmony is prolonged throughout. In that context the listener will focus especially on the deployment of the tonic triad’s three pitches (A, C ♯, and E) and on how Mendelssohn connects those pitches. Of course the pitch A, as the key ’s tonic, will sound – either in the melody or in the bass, or in both – when the greatest level of stability is desired. Though Mendelssohn here limits himself to one harmony, he projects the tonic triad ’s pitches in multiple registers.
1.1 Mendelssohn: Song without Words in A Major (op. 62, no. 6), mm. 83–90 As preparation for your exploration of audio example 1.1, sing arpeggiations of A, C♯, and E in all of its inversional arrangements, outlined below. Use a pitch pipe, an online pitch pipe, or a piano to establish the pitch A in your mind. 3
4
Harmony in Mendelssohn and Schumann
Start by singing A
C♯
<
<
E
high in your vocal range. (Use any solfege system you are comfortable with; or sing the letter names, substituting the single-syllable German “Cis” for the multi-syllable “C-sharp.”) Then, starting lower, sing E
<
A
C♯ <
E
<
A
C♯
E
C♯
<
followed by
and � nally A
<
<
low in your vocal range. You might also sing these pitches according to their scale degrees numbers: ^ 1 ^ 5 ^ 3 ^ 1
<
<
^ 3
^ 5
^ 1
< <
< <
^ 3
<
^ 5
^ 3
^ 1
^ 5
For future reference, here are syllables for sharp and �at pitches (departing from standard German practice for B since Germans instead use H) for readers who prefer to sing using note names: Cis Ces
Dis Des
Eis Es
Fis Fes
Gis Ges
Ais As
Bis Bes
(raised) (lowered)
Example 1.1 The work ’s concluding A Major tonic harmony, enlivened by arpeggiations and local chromaticism.
Indicate the scale degrees that sound at the � ve spots marked R. 1 2 •2. Indicate the scale degrees that sound at the top of the three chords marked Z. ••3. Though three distinct intervals occur at the spots marked W, they are all related. Building upon your response to question 1, indicate which two scale degrees sound in each instance, as well as what intervals those pitches form in each case. Brie�y explain how these intervals relate. 3 4 ••4. Among the eight pitches marked X or Y, three are chromatic. Which three? •1.
Foundational diatonic processes
1.2 Mendelssohn: Song without Words in A Minor (op. 53, no. 5), mm. 0|1–62 Over the past several centuries a large number of musicians have helped in establishing procedures for analyzing tonal music. Not surprisingly, there remain many areas of disagreement. Most analytical observations depend upon some foundational premises (developed, one might hope, through careful study of compositions that share speci �c stylistic traits). When practitioners who uphold contrasting premises study the same composition, alternative interpretations will likely emerge – sometimes even in coming to terms with the most elementary of musical utterances. Consider the tonic triad in A Minor: A-C-E. It may happen that the prolongation of the tonic is temporarily called into question through stepwise upward motion in two voices, resulting in the chord A-D-F. What if, immediately thereafter, A-C-E is restored? Though �gured bass numbers may provide a neutral accounting of this motion, as
565 343
, a consideration
of the internal chord’s genesis and role would lead to considerable controversy among analysts. Some would interpret the pitch D as a harmonic chordal root , generator of the concurrently sounding F and A. From that perspective, the passage might be analyzed as I IV I. Others would interpret the pitch D instead as a melodic embellishment of the tonic’s third: D as neighbor to C (and concurrently F as neighbor to E). From that perspective the tonic root A does not yield to any other harmony during A-D-F but instead perseveres despite the concurrent embellishment of both the chordal third and �fth. A single analytical label might be displayed: I perhaps forti�ed by Arabic numerals that provide a visual representation of the embellishment I
565 343
In this case the symbol 46 emerges through a linear initiative, not through chordal inversion. Likewise the A-C-E triad might be embellished by lower neighbors, as in G ♯-B-E, or by more complex combinations of neighbors, as in G♯-B-D-E or G♯-B-D-F. Though it may not always be possible to
5
6
Harmony in Mendelssohn and Schumann
draw a precise line between melodic embellishment and harmonic progression, in the perspective advocated in this study many local chordal interactions of this sort will not be interpreted harmonically. Audio example 1.2 o ff e rs opportunities to come to terms with local embellishing chords that are not harmonically motivated. None of the questions posed ask for a Roman numeral analysis, because that analysis would amount to no more than a prolonged I. Though this excerpt o ff e rs more chordal variety than does audio example 1.1, ultimately both in their own ways project a single harmony, the tonic. (Whereas audio example 1.1 occurs at the end of a composition, audio example 1.2 serves as an introduction.) To prepare for what you will hear, sing in turn two models of neighboring-note embellishment, beginning on a tonic A low in your vocal range: A A A
<
A A A
<
C
< D <
< < <
C C B
<
E < E
<
F
E
<
D
C
<
E
Then sing a combination of both neighboring-note embellishments: A A A A
<
C < B
< <
<
E
D <
< D <
C
F E
Finally sing a model in which three neighboring notes emerge concurrently: A A A
< <
C B
<
< <
C
E D
<
< G♯
< E
A
<
A
Foundational diatonic processes
Example 1.2 The composition’s introduction, bounded by A Minor tonic chords.
•1.
An A Minor tonic chord sounds during seven of the fourteen R segments. Which seven?5 •2. Downward stems are attached to fourteen of the noteheads in the grid above. Exactly how many of them correspond to the bass pitch A? 6 ••3. Inner-voice quarter notes C and E (both members of the tonic triad) sound with bass A at the downward-stem location within R 1. In the span from R 2 through R 13, only two other three-note combinations sound at downward-stem locations. Name those two combinations and indicate which locations correspond to each. Describe how those combinations relate to the tonic triad. 7 •••4. Throughout most of the excerpt, the upper-voice melody (corresponding to the notes with upward stems in the grid) follows the contour of the inner-voice pitches explored in question 3. Yet at three locations, upward motion among the inner voices coordinates with downward motion above. Name those locations, and describe the chord (the same in each instance) formed by the � ve sounding pitches above the bass.8
1.3 Schumann: “Die alten bösen Lieder ” from Dichterliebe (op. 48, no. 16), mm. 15|16–193 Analyzing the individual chords that constitute a progression warrants a careful consideration of their interactions with the chords that both precede and follow them. Many – perhaps all – chords commonly used in tonal compositions are susceptible to a range of deployments. There may be a tension between or among competing interpretations, leaving the listener in a state of uncertainty until further progress through the work provides, ex post facto, the context that helps clarify the roles the individual chords play. A chord in 46 position off ers special challenges for listeners, as well as special opportunities for composers. When, for example, a B-E-G ♯ chord sounds in an E Major context, the BE fourth formed with the bass may in fact represent the inversion of the tonic triad’s EB �fth, in which case
7
8
Harmony in Mendelssohn and Schumann
the chord (in second inversion) may convey a tonic function. Yet that sonority often functions in a quite di ff erent way, one in which B ( not E) is asserted as the root, while the E and G ♯ above delay (as suspensions, accented passing notes, or neighboring notes) the arrival of dominant chord members D ♯ and F♯, respectively. In a “left-to-right” hearing of a passage, one may reach a spot for which multiple equally viable continuations could be imagined. Only by taking what follows into account can one develop a well-considered conviction regarding how the chord in question might best be interpreted. The vocal melody in audio example 1.3 makes a surprising descending leap immediately after completing an ascending arpeggiation of E Major ’s tonic-triad pitches, from ^1 to ^ 8. To prepare for that encounter, sing ^ 1
<
^ 3
<
^ 5
<
^ 8
in E Major and then descend at random to ^ 1, or to ^ 3, or to ^ 5. Repeat the exercise in other major keys as well. Just before proceeding to audio example 1.3, perform the exercise again in the key of E Major.
Example 1.3 An internal phrase that brie�y tonicizes C♯ Minor’s mediant key, E Major.
•1.
•2.
•3. ••4.
••5.
In order, name the four pitches that are emphasized at locations R 1 through R 4. What is their relationship to the local tonic, E Major? 9 Within its context (as conveyed in question 1), what � gured bass numbers would correspond most aptly to what sounds at the downbeat of R 3 (mentally � lling out the chordal texture appropriately)?10 The chord at X reprises one of the four R chords. Which one?11 Especially since it is preceded by the chord at X, the chord at S1 initially might be interpreted as a restoration of one of the earlier R chords. Which one? If no more than a restoration is being accomplished, what harmony would be projected at that point? Through the reiteration of S1 at S2 and then the perhaps surprising continuation at S3, another interpretation of S 1 emerges. Discuss this context in terms of which pitch is asserted as the chordal root, and how that assertion a ff ects the harmonic analysis.12 Though the voice prolongs one pitch, the keyboard part begins a vigorous activity at T. What pitches other than the tonic ’s E, G♯, and B sound during this passage? What is their relationship to tonic pitches? Given the harmonic activity prior to T, would it seem more appropriate to deploy one or, instead, � ve Roman numerals to account for what transpires during the excerpt ’s � nal measure?13
Foundational diatonic processes
1.4 Mendelssohn: Song without Words in F♯ Minor (op. 30, no. 6), mm. 0|1–222 During a parallel period (one of music ’s most straightforward organizational schemes), two phrases sound in succession, with only the latter reaching the full closure generated by a perfect authentic cadence. In this scenario the �rst phrase (the antecedent) will come across as an incomplete musical utterance, thereby motivating the second try that will occur during the phrase that commences immediately thereafter (the consequent). Often the harmonic trajectory will be I –V followed by I–V–I (half cadence, then perfect authentic cadence). (Though usually at least one other harmony comes between I and V, in audio example 1.4 that is not the case. Also, because the example is in the key of F ♯ Minor and leading tone E ♯ is incorporated within the dominant, that chord ’s analytical symbol will appear as V♯.) The broad melodic trajectory supported by the period ’s harmonic progression often will take the form of ^ 3> ^ 2, ^ 3> ^ 2> ^ 1. Because a single harmony sometimes will span multiple measures, the melodic presentation of ^ 3 or ^ 2 might not coincide with the onset of its supporting chord. For example, a gradual arpeggiation up to ^ 3 might be a salient feature of an initial tonic harmony ’s presentation. Though a parallel period may serve as an independent musical entity, such a construction often serves as a component of a broader musical composition. The parallel period featured in audio example 1.4 constitutes the � rst part of a song, here preceded by a six-measure introduction. The dominant’s dissonant impact is here heightened through the incorporation of the chordal seventh and ninth. As preparation for your listening, sing the following alternation between tonic and dominant chordal arpeggiations: F♯ C♯
<
E♯
<
C♯
<
E♯
<
< <
E♯ E♯
<
<
B
< <
B B
A G♯ G♯
< < F♯
A G♯
< F♯
C♯ C♯
G♯
< F♯
A
<
A
<
D
9
10
Harmony in Mendelssohn and Schumann
Example 1.4 An introduction followed by a parallel period in F ♯ Minor.
••1.
•2.
•3.
••4.
••5. •6.
•••7.
••8.
••9.
••10.
The downbeat eighth note during R introduces the root of the F ♯ Minor tonic harmony. How are the three members of that harmony deployed during the remainder of R?14 As your answer to question 1 should indicate, the tonic harmony ’s F♯ and A are stated prominently during R. They are then repeated during the beats that follow. What two pitches emerge during X 1 (both in the melody and in the accompaniment) to serve as their immediate successors? 15 Though the two passages are very similar, the bass note during X2 (within the period’s antecedent phrase) is not the same as that during X1 (within the introduction). Name the bass pitch deployed in each instance, and indicate the term that often is used to describe how that of X1 functions.16 The harmony introduced during X 1 is intensi�ed through the introduction of a dissonant pitch at Y1 (repeated at Y2) and another at Z. Name, in order, these two dissonant pitches and indicate what intervals they form against dominant root C♯.17 Provide a detailed account of how the melody during W1 relates to R.18 Has the harmony changed at S, or instead has the preceding chord’s inversion changed? Indicate both what harmony is projected at S (using a Roman numeral) and that chord’s inversion (using conventional �gured bass numbers).19 The two measures that intervene between X1 and the onset of W1 do not have counterparts between X2 and the onset of W2. Explain what Mendelssohn does instead in the latter case. 20 Whereas W1 spans four measures, W2 spans � ve. Which one of W2’s measures most deserves to be regarded as an addition to what was presented in W1? What is the highest-sounding pitch during that measure, and what chromatic pitch is deployed?21 A suspension occurs at T, with resolution during X3. Using conventional �gured bass numbers (e.g., 9–8, 7–6, etc.), indicate the type of suspension that Mendelssohn deploys. Which of X3’s three pitches serves as the resolution? 22 A I–V♯–I harmonic progression often supports the descending melodic line ^ 3 >^ 2 >^ 1 . Precisely where do that line ’s A and G♯ sound during the antecedent
phrase? (Indicate locations within W1 and X2, respectively.) Likewise, where do those pitches sound during the consequent phrase, preceding the tonic arrival (supporting ^ 1 ) at U? (Indicate locations within W 2 and X3, respectively, noting that in this instance a descending registral shift occurs.) Given this state of aff airs, what cadence type concludes each phrase?23
Foundational diatonic processes
1.5 Mendelssohn: Song without Words in E Minor (op. 62, no. 3), mm. 0|1–82 From acoustics one learns that a sounding pitch C generates a range of partials: CC in C Major) became ubiquitous, con�rming the dominant root ’s prominence among the tonic’s partials. That root (^ 5), which of course generates its own set of partials (G
to ^ 2 during I to V might be supported in part by IV 7 emerging against prolonged soprano E, or by II supporting the onset of D. When the melody unfolds pitches of the tonic and the dominant – for example, CB – II may be deployed as support for the melody ’s D, with V delayed until the B. Though soprano D and bass G do not actually sound together in that context, one may regard the D of the D>B third as still in force once bass G and the melody ’s B arrive. Recognizing basic pitch patterns that recur again and again in tonal music is an important component of informed listening. In the case just described the foundational CE to DG expands to become CE (I) through DF (II in B
�rst inversion) to G (dominant).
Reinforce this conception by singing the
following arpeggiations � rst in C Major and then in other major keys: C G
<
< G
<
E
D C
F
<
< D
E
B
Then shift into minor, lowering the tonic’s third by a half step but retaining the leading tone:
11
12
Harmony in Mendelssohn and Schumann
G
< D
E♭
C
< D
E♭
<
F
< G
C
<
B♮
Conclude by singing this pattern in the key of E Minor, as preparation for audio example 1.5. Example 1.5 A four-measure introduction followed by the � rst stanza’s � rst phrase in E Minor.
•1. •2.
•3.
••4.
•5.
•••6.
•7.
Which two pitches of E Minor’s tonic triad are featured melodically during Q?24 Though in a higher register, the melody during R should come across as a response to that of Q. What harmony is being arpeggiated? What three pitches (in order) are deployed? Disregarding the registral contrast, what relationship is formed by the highest sounding pitch of Q and the highest sounding pitch of R? (Convey your answer as two scale degrees.) 25 Because Q and R are exactly equivalent rhythmically and both begin with an upbeat (triplets), what occurs at S will come across as an upbeat onset of the melody that appears over the next four measures. Yet harmonically it is closely related to what has just occurred during R. Name the two pitches that sound at S and indicate how that moment relates to what has preceded it. 26 The onset pitches of all seven of the melody ’s locations marked as T are members of the tonic triad. (The non-tonic context of T 7 will be explored below.) Which two consecutive T pitches might aptly be interpreted as a direct outgrowth of the introduction’s Q material? Which other T pitch presents one of Q’s notes in a higher register? 27 Compare the melodic embellishment that occurs between T2 and T3 with that between T3 and T4. Name the pitches employed.28 Had the tonic harmony been maintained for a bit longer, the melody pitch at T7 could have served as the culmination of a three-measure ascending arpeggiation of I. Yet concurrently with its arrival the harmony changes, converting T 7 into an embellishment of U1. How does T7 to U1 relate to content from the introduction? What bass pitch sounds against the melody ’s two pitches? Ultimately what harmony is projected during that beat? (Provide a Roman numeral and, if the chord is inverted, � gured bass numbers.) 29 If the melodic pitches of U1 and X had sounded where T 7 and U1 occur (that is, shifted one eighth note earlier), that beat’s harmony would have been enriched by the addition of its dissonant seventh. Yet because T 7 delays the arrival of U 1, X is pushed over to the next downbeat, thereby delaying the arrival of U 2. This situation is so common that chords like that at X have been given a special name. What is that name? What type of cadence concludes the phrase? 30
Foundational diatonic processes
1.6 Schumann: “Die alten bösen Lieder ” from Dichterliebe (op. 48, no. 16), mm. 1–73 The notion of harmonic progression is closely allied with the melodic �lling-in of the span between the tonic and dominant roots in the bass (usually ascending, as in C up to G in C Major, though sometimes descending). When D is placed between C and G, some manifestation of the supertonic likely will emerge. With F, the subdominant and the supertonic (inverted) both are viable. In either case the ascending �fth is segmented into a second plus a fourth, the latter of which may be further �lled in diatonically. For example, a C
13
14
Harmony in Mendelssohn and Schumann
Example 1.6 A brief introduction followed by the � rst vocal phrase in C ♯ Minor.
•1.
•2.
••3.
•4.
•5.
•6.
Describe the four principal characteristics of the �rst chord (R): its soprano pitch, its bass pitch, its quality, and the appropriate � gured bass numbers.31 The grid shows that the melodies during S1 and S2 are slightly at variance in terms of rhythm. How do they di ff er in terms of pitch?32 Whereas S1 is too sparse to convey any overt chordal contrast, the fourth and �fth vocal pitches within S2 are supported by a chord that di ff ers from what sounds before and after. (Allow half a measure for each chord to fully form, disregarding the neighboring-note embellishments.) What three pitch classes are members of the perimeter chords? What � ve pitch classes (segmented into four plus one) sound during the middle chord? 33 Compare the perimeter chord of S 2 and the chord at T. (Provide both Roman numerals and � gured bass numbers for both chords.) 34 What pitch sounds in the vocal line at U? What two harmonies (Roman numerals only) that precede the dominant might most likely be used to support that pitch in a progression in C♯ Minor? Which one does Schumann deploy here? 35 Analyze the two chords that create the phrase-ending cadence (W and X). What cadence type occurs?36
1.7 Schumann: “Ich will meine Seele tauchen ” from Dichterliebe (op. 48, no. 5), mm. 8|9 –122 Contrasting the situation with I and IV, the I and II triads share no pitch classes. Sing an arpeggiation of the succession I –II in the key of B Minor: B
<
D C♯
<
< E
F♯ < G
The strong contrast between chords can be eased if the supertonic’s seventh is incorporated. Sing
Of course, II 7 introduces a dissonant seventh (B) that normally would resolve downward by step. Fortunately that resolution pitch (here A ♯) is a member of the major dominant triad that generally follows the supertonic. Sing
Foundational diatonic processes
Example 1.7 The beginning of the binary form ’s A2 section in B Minor.
••1.
Which letter marks the location of a vocal pitch that serves as a chordal seventh? Is this dissonance suitably prepared and resolved?37 •2. What is the relationship between the keyboard bass and the vocal melody in the region from U to W? What harmony or harmonies are projected? 38 ••3. In coordination with other initiatives, the broad melodic trajectory during the excerpt’s harmonic progression (which is stated twice during the example) engages a foundational BC ♯>B. (The initial bass pitch D is well prepared by the presentation of the dominant in its 4 position immediately preceding the onset of the example.) Which three letters 2 in the grid correspond to the onsets of melodic pitches B, C ♯, and D, and which three correspond to the onsets of bass pitches D, C ♯, and B?39 •4. For good reason (as explored in question 1), the pitch A ♯ sounds at the onset of the V♯ harmony at T1. What occurs melodically and harmonically during the passage from T1 to T2.40
15
2 Surges
The very word chromatic implies a special coloration extending beyond a key ’s diatonic pitches. Often chromatic shifts emerge late in an individual harmony ’s prolongation, as the succession to its successor draws near. An individual harmony ’s particular evolution (over the course of two or more chords) gives the listener a strong hint of what will come next. In a surge, a harmony targets a speci �c successor through an appropriate utilization of chromaticism and dissonance. A surge may occur only when the roots of two successive harmonies form a descending perfect �fth (or ascending perfect fourth). In this chapter we explore one straightforward surge con�guration in two of its most common locations within tonal space: a surging I ➔ targeting IV (as in C-E♮-G-B♭ in C Major or C Minor); and a surging II ➔ targeting V (as in D-F♯-A♮-C). The voice leading from the surging chord to its successor will mimic that which transpires between V 7 and I – including various inversional alternatives such as a surging chord in 24 position resolving to a chord in 36 position. (More intense surges and supersurges will be explored in
16
later chapters.) In the perspective proposed here, the surging chord should not be interpreted as an actual dominant or labeled as V7. Instead it is a phase of I or of II that takes on the same outer form as V7. Depending on its location within tonal space and the mode, the chordal third and/or �fth may need to be raised chromatically, while the seventh may need to be lowered chromatically in order for the chord to precisely emulate V 7. It is important to maintain an awareness of where each root resides in relation to the prevailing tonic during a surge. Such information is lost in the common alternative method of analysis in which the surging tonic and supertonic chords instead are labeled in the keys of the chords to which they resolve (as is conveyed by the “applied dominant” symbols V7/IV and V7/V). A juxtaposition of labels such as I followed by V 7/IV conceals the fact that chromaticism is at play, taming this potent shift analytically to become a succession of diatonic chords in two related keys. In contrast, the surge labels ♭ that will be deployed here (for example, I 8– 7 or I ➔) succeed in conveying how a single harmonic function undergoes an internal evolution that makes the succession to its successor seem inevitable. In practice, composers exercised considerable freedom in this regard: I may proceed to IV without surging, and I➔ may target IV without a prior diatonic, consonant I.
Surges
2.1 Mendelssohn: Song without Words in E♭ Major (op. 38, no. 1), mm. 1 –5 Thinking in E♭ Major (the key of audio example 2.1), tonic E ♭-G-B♭ will surge toward the subdominant when D ♭ is added to the triadic pitches. Note in particular that the surging tonic ’s third G and seventh D ♭ form a diminished �fth that resolves into the subdominant ’s
C A♭
third (or, through
inversion, a D♭ to G augmented fourth that resolves into a
A♭ C
minor sixth).
Pay special attention to this relationship (highlighted by boxes) when singing the arpeggiations indicated below. Of course, an identical set of relationships prevails when V 7 resolves to I. Though not specially marked, the last two chords of this exercise present the very model upon which a surging tonic is based.
Example 2.1 The � rst phrase of composition in E ♭ Major.
••1.
The melody deploys � ve diff erent pitches during the span from R 1 through R 4. Name those pitches. How do they relate to the bass of measures 1 and 2? Also, how does the melody during the R 2 and R 3 beats relate to the bass during those same beats?1 •2. Omitting consideration of non-harmonic pitches and of inversion, what is the principal diff erence in pitch content comparing R 1 in measure 1 and R 2 through R 4 in measure 2? Name the pitch classes that are engaged at these two locations and provide a harmonic analysis that conveys their roles within the phrase. 2 ••3. Compare the melody during the three beats of S1 and S2 with that of the two beats of R 1 and R 2. Also compare those three S beats with the concurrently sounding bass pitches and with the melody during T 2 through U. 3 •4. A low E♭ sounds in the bass at the downbeat of each of the example’s measures. That pitch con�icts with the harmony being projected during measure 4. (Thus the E♭ should be interpreted as a pedal point.) Omitting consideration of E♭, what four pitch classes during measure 4 join forces to project a harmony? Provide an appropriate harmonic analysis for T 1 through U. What type of cadence occurs? 4
17
18
Harmony in Mendelssohn and Schumann
2.2 Schumann: “Es treibt mich hin” from Liederkreis (op. 24, no. 2), mm. 66|67 –74 Though the accidentals required will vary from one key to another ( ♮, ♯, or Ü for a raised pitch; ♮ , ♭, or º for a lowered pitch), the means of creating the particular type of surge for I ➔ featured in this chapter will always be the same, depending on the key ’s mode: in a major key, a chromatically lowered minor seventh is added to a diatonic major triad; in a minor key, a diatonic minor seventh is added to a triad whose third is chromatically raised (converting it from minor to major quality). These adjustments result in a chord containing a diminished �fth (or its inversion, the augmented fourth) that resolves into the subdominant’s root and third. In the key of B Minor, diatonic B-D-F♯ requires two adjustments to evolve into this form of I ➔ surge: the chordal third D must shift to D ♯, and seventh A must be added. Sing the following arpeggiated chords, paying special attention to the diminished �fth of I➔ and its resolution during IV. (These pitches are displayed within boxes.)
Example 2.2 The coda of a song in B Minor.
•1.
Schumann conveys most of the chords within the excerpt as a melodic anticipation at the end of a measure followed by the full chord ’s gradual emergence during the �rst two eighth notes of the next measure. Instances of this process beginning at S 1 and at S2 project the tonic harmony. How do those two statements of the tonic relate? 5 •2. The chords initiated at R 1 and at R 2 embellish the tonic chords S 1 and S2. Which four pitch classes are used in their formation? Indicate appropriate �gured bass numbers for both. 6 •3. Compare the chords that emerge at S 2 and at S 3, indicating what two shifts transpire in the pitch content, what general term is used to indicate this transformation, what harmony is being targeted, and how the two chords may be analyzed using a Roman numeral and other symbols. 7 •4. Provide a careful harmonic analysis for the passage from T through W. Indicate what type of cadence occurs?8
Surges
2.3 Mendelssohn: Song without Words in A Major (op. 53, no. 6), mm. 106–113 Because the roots of I and IV span the interval of an ascending fourth (or descending �fth), they relate exactly as do the roots of V and I and thus are susceptible to connection via a surge. In a major key the tonic chord’s major quality already makes the succession to IV a favored option (engaging the half-step ascent from the tonic’s third to the subdominant’s root). With the addition of a minor seventh, a dissonant diminished �fth will resolve to the root and third of IV. When singing the following arpeggiated chords, be particularly attentive to the interactions among the boxed pitches, emphasizing the C ♯F♯ resolutions.
Another type of tension (followed by resolution) results from embellishments such as passing notes and suspensions, a classic instance being the cadential
6 4
resolving into a dominant 35 . Yet if the dominant will be
introduced in an inversion, the notes of a cadential 46 may occur in an “inversion” as
into
6 3
or
5 3
well (or, one may say that the notes have been unfurled
position while retaining their tendencies toward stepwise
downward resolution). That is the case in the relationships formed by the boxed pitches in the following arpeggiated chords. It is as if E were the low note of both the fourth and �fth chords, inducing 6>5 and 4>3 resolutions.
19
20
Harmony in Mendelssohn and Schumann
Certainly responses to tonal musical phenomena will vary among analysts. To some, this passage would contain a succession from IV to I (in �rst inversion) prior to the dominant ’s arrival. Yet many analysts would hear IV proceeding instead to V, announced by the sounding of root E (in the chordal interior) but not fully in place until accented passing note C ♯ resolves to B and suspension A resolves to G ♯. Example 2.3 An eight-measure phrase in A Major at the onset of the coda.
•1.
•2.
••3.
•4.
•••5.
•••6.
•7.
The tonic chord at the onset of R 1 concludes the broader composition’s main harmonic trajectory, sealed by a PAC in A Major. The coda here begins with a tonic-reinforcing progression. In that context, what Roman numerals pertain to the chords at S 1 and at U 1–U2? Given the excerpt ’s initial tonic and these two chords, what harmony would one expect to hear between S1 and U1–U2? At what point does that harmony sound in its root position?9 Assess the transformation of the tonic between R 1 and R 3. Spell out the chords at the endpoints of that trajectory (one with three pitch classes, one with four) and propose a suitable harmonic analysis to convey the progression from these two chords to S1.10 The tonic prolongation during the excerpt’s �rst four measures reaches its principal interior chord at R 2, which targets the tonic restoration at R 3 (explored in question 2). Name the four pitches that constitute R 2, carefully distinguishing between the pitches that congeal to form this chord and the tonic pedal A that persists throughout the passage. Also indicate in order the three pitches that come between R 1’s initial bass A and R 2’s bass E.11 Though the chord at S2 is closely related to its predecessor at S 1, something has changed. What?12 The notion of interval inversion sometimes creates unexpected compositional opportunities. Whereas DE inversion may substitute. Yet if that happens, the large interval of a seventh often would be broken up into smaller components. First, name in order the three pitches that sound in the bass between D and E in the vicinity of S1 through T3. Second, how might one interpret the chord at T 1 if bass E were sounding already by that point? Third, can you hear the passage as a succession from IV to (embellished) V even if bass E is delayed until T 3?13 Your answer to question 5 should have revealed the deployment of chromaticism in the bass during the span from T 1 to T2. Another chromatic pitch emerges in that vicinity as well. Name that pitch and explain its role.14 How is the phrase’s concluding tonic chord embellished in the melody at U1?15
Surges
2.4 Schumann: “Ein Jüngling liebt ein Mädchen” from Dichterliebe (op. 48, no. 11), mm. 4|5–82 The tonic triad ’s root and third may be embellished by concurrent lower and/or upper neighboring notes. Use the following series of arpeggiations in E♭ Major to explore how this works. E♭ D < E♭ E♭ D < E♭
< G < F < < G < F < A♭ < < G < F < A♭ < < G <
B♭ B♭ B♭ B♭ B♭ B♭ B♭
Though the I and II triads have no pitches in common, the voice leading between those harmonies often does achieve a sense of connection through the deployment of the supertonic’s seventh, which is also the root of I. In the arpeggiations below, note how at �rst the high E ♭ is a stable chordal element, but that upon the arrival of root F it attains a downward resolutional tendency, ful�lled by the dominant ’s third, D. (Focus especially on the boxed E♭>D descending second.)
The same trajectory may be projected more intensively if the supertonic surges: the raising of the supertonic’sthirdtoA♮ creates an AE ♭♮ diminished �fth that resolves to the dominant’s
D B♭
third. Two sets of arpeggiations are
provided below. In the �rst, the diatonic II7 evolves into II➔ (via the shift from A♭ to A♮, displayed within boxes); in the second, the II➔ surge emerges at the onset of the supertonic function, with no diatonic predecessor.
21
22
Harmony in Mendelssohn and Schumann Example 2.4 The E♭ Major song’s � rst vocal phrase, which follows after an introduction that traverses an identical chordal path.
•1.
Hear how the chord during R 2 restores the pitches that sounded at R 1, resulting in the prolongation of the tonic harmony into the excerpt ’s third measure. At the midpoint (S), common tone B ♭ persists against three pitch classes that serve as neighbors to tonic chord members. What neighboring note sounds in the low bass? What other neighboring notes sound in the piano accompaniment (one doubled by the voice)? What � gured bass numbers correspond to the chord at S? 16 •2. Considering only the melody, the measure labeled R 1 projects a chordal skip downwards from one tonic chord member to the next, whereas the measure of R 2 and T pursues that agenda in the ascending direction. In order, name the tonicchord pitches involved.17 ••3. The last of the four pitches described in question 2 is not supported by the tonic harmony (as was the second). Instead, another chord in which it serves as a member emerges during T. Is this chord consonant or dissonant? Is it diatonic or chromatic? Is it surging? If so, what harmony is being targeted? Suggest both an appropriate Roman numeral (in the key of E♭ Major) and �gured bass numbers for this chord. (As is always an option, here the chordal �fth is omitted. A suspension delays the full sounding of the chord until the measure ’s � nal eighth note.)18 •4. Spell and analyze the chord that sounds at U. Which pitch sounds in the bass, and which pitch is sung?19
2.5 Schumann: “Aus alten Märchen” from Dichterliebe (op. 48, no. 15), mm. 8|9–162 Though its wide range may be a challenge for some voices (in which case a few notes may be imagined rather than sung), the following arpeggiation outlines essential features of the excerpt by Schumann that will be explored below. Note especially that the pitches forming the descending span 5>4>3> 2 in E Major are displayed within boxes. Though one should not accent these notes in performance, do consider how that basic line serves as a unifying force within the excerpt, even if on occasion another chord member reaches higher. ^
^
^
^
Surges
Example 2.5 The E Major song ’s �rst vocal phrases, which follow after an introduction that traverses the same chordal path.
••1.
The excerpt may be broken down into � ve segments, as follows: – –
the prolongation of the initial tonic, with emphasis on melodic pitch B (= 5 ). an interior melodic space supported by non-tonic harmonies, between the ^
initial melodic B ’s prolongation and the arrival of G ♯ (= 3 ). – the return of the tonic, now supporting G♯. – the upward arpeggiation of an octave (G♯
^
20
Indicate which of the letters in the grid correspond to each of these � ve segments. B •2. How is the tonic’s E �fth conveyed melodically during the span from R 1 through R 3?21 •3.
Some analysts would label the chord at S1 as IV (despite the lack of a dominant successor). Instead, develop an interpretation that regards it as a melodic embellishment of the tonic. Supply an analytical symbol that uses both Roman and Arabic numerals.22 •4. Provide a harmonic analysis for the four chords from R 4 through U 1, making sure to allow each chord to fully form through the sounding of its bass note late within each beat.23 •5. Though the tonic harmony prevails throughout the passage from U2 through both U3 and U4 to goal U5, its inversion shifts several times. Indicate the appropriate � gured-bass numbers for each of these four locations. 24 •••6. Though the foundational harmonic trajectory of chords U5 and X is among tonal music’s most common, the intervening chords W 1 through W3 are susceptible to two highly contrasting analytical interpretations. The matter hinges on whether the chord at W1 is interpreted as the onset of the harmony that comes to rest at X or instead as an unfurled predecessor of the chord that sounds in a more normative con�guration at W2. (W1, W2, and X all deploy the same three pitch classes.) In such cases it is useful to write down analytical notation for both hypotheses, so that their merits and de�ciencies may be thoroughly examined. To come to terms with the �rst of two hypotheses for this passage, analyze the chords from W1 through X as a foreground harmonic progression in the tonicized key of B Major. (Four Roman numerals will be required.) Then shift to the hypothesis that the chord at W 1 is unstable, initiating a tendency that is repeated and more normatively conveyed by the chord at W2, which resolves conventionally as embellishment of the chord at W3. In this reading the chord at W 3 would be regarded as the principal harmonic link between U5 and X. (The chord at S 3 functions in a manner similar to that at S 1: as an embellishment of the chords that surround it.) To come to terms with this hypothesis, supply a harmonic analysis that deploys exactly three Roman numerals (all in E Major) for the passage from U5 through X.25
23
3
IV5–6 V
Whether accomplished vibrantly through a surge or more modestly as a consonant diatonic succession, a progression ’s passage from an initiating tonic to the subdominant represents signi �cant progress, in that IV is a mere step away from the dominant that most progressions sooner or later will attain. In this scenario the composer ’s harmonic concern shifts from generating the momentum to launch the progression on its ascending root trajectory to a nuanced steering through a more delicate operation: that of leading from IV to V, a chord that shares no pitch classes with IV. Without intervention a chord rooted on 4 instead might project a tendency to proceed upwards another fourth, to the subtonic. (In C Major or C Minor, a C ➔ F opening gesture could in fact proceed as F ➔ B♭ ➔ E♭. Mediant E♭ might then serve as an intermediary between the initial tonic and an upcoming dominant.) Generating e ff ective harmonic progressions occasionally involves mitigating certain potentialities for a given chord so that it may function e ff ectively within a speci �c desired trajectory. Two factors often help steer IV toward V: sti �ing its surge potential and introducing a common tone with V. This may be accomplished by raising IV ’s � fth up a step in a 5–6 shift. (In C Major, that would result by either juxtaposing F-A-C and F-A-D or by adding D as a fourth pitch class against a prolonged F-A-C.) If nothing further transpires before the dominant sounds, then the added pitch may be regarded as a nonharmonic intermediary between IV and V (in the manner of an anticipation) rather than as a supertonic root. In chapter 5 a more assertive role for that pitch, warranting the deployment of a II numeral, will be explored. ^
3.1 Schumann: “Es treibt mich hin” from Liederkreis (op. 24, no. 2), mm. 59–66
24
Thinking hierarchically, some musical sonorities result from a collection of passing and/or neighboring notes that, though they congeal into a
IV 5–6 V
chord, do not project a distinct harmonic function. In such cases supplying a Roman numeral impedes comprehension, because the chord ’s context does not ful�ll the implications of the analytical symbol. Consider how a tonic harmony may be prolonged through the juxtaposition of its pitches in two di ff erent positions. Sing an arpeggiation of B Minor’s tonic harmony � rst in its 36 position and then in its 46 position, as follows: D
<
F♯ F♯
< <
B B
<
D
Next add passing notes at the edges of the texture, diatonically � lling in the bass D
Next create a full-�edged passing chord to come between the two presentations of the tonic.
As the tonic proceeds to its successor – here the subdominant – a similar juxtaposition of pitches in two distinct inversions may transpire. Sing the following arpeggiation of � ve chords representing the harmonic succession from I (the �rst three chords) to IV (the last two chords).
Finally make an added-sixth addition to the IV harmony and then proceed to V♯, noting how the common tone C ♯ serves both as IV ’s added sixth and as V ♯’s �fth.
25
26
Harmony in Mendelssohn and Schumann
Example 3.1 The song’s � nal vocal phrase, in B Minor.
••1.
Often one harmonic function will be conveyed through a set of interrelated chords, some of which will project pitches from that harmony while others serve as connectors or as embellishment. The trajectories of the exposed outer voices from R 1 through R 2 and between T1 and T2 reveal two contrasting ways in which such projections may be accomplished. First, a ffirm the tonic presence at R 1 and R 2 by indicating the � gured bass numbers that reveal how pitch classes B, D, and F♯ are arranged at those two points. Second, indicate how the vocal melody and the piano bass relate during this passage. Do they work in parallel or in contrary motion? What vertical intervals are formed by these two lines at those two locations? Then make a similar assessment of the passage from T1 to the downbeat of T2 (at this point not considering the further development later in the T2 measure). What �gured bass numbers should be applied? What Roman numeral? How do the outer voices relate? 1 •2. One of the most fascinating (and sometimes challenging) aspects of harmonic analysis is that the same chordal constructions may function in contrasting manners, depending upon the tonal context. For example, the chord at R 2 often sounds in a context in which the bass note F ♯ is asserted as the dominant root, causing the B and D above to resolve downwards to the dominant ’s third and �fth. That is not the case at R 2, where F♯-B-D instead projects the tonic harmony in its second inversion. Likewise the chord at S might have played a signi �cant harmonic role if what follows next had in fact projected a dominant harmony. Since that is not the case, the chord at S serves more humbly as a passing chord connecting two tonic chords. Name the four pitch classes that sound at S, and indicate the � gured bass numbers that correspond to that chord. 2 •3. From question 1 we come to understand that the parallel motion that has prevailed between the vocal melody and the piano bass comes to an end through the melody ’s ascent against the bass’s descent between T1 and T2. Yet something quite interesting happens during the latter measure: the vocal line leaps downwards to the pitch that would ful�ll the parallel-motion trajectory. Name that pitch, and explain its role within the chord in which it resides. 3 •4. Assess the contrasting roles of the same pitch classes at R 2 andatU1. Then analyze the passage from U 1 through W, indicating what cadence type is deployed. 4
IV 5–6 V
3.2 Mendelssohn: Song without Words in G Minor (op. 19, no. 6), mm. 30–34 When IV serves as the principal intermediary between I and V ♯, both a surge (between I and IV) and a 5 –6 shift (between IV and V ♯) may transpire. Sing the following chordal arpeggiations as presented, and then sing each line backwards (that is, as G>D>B ♭, etc.). The subdominant’s 6-phase pitch, A, is displayed within a box.
Example 3.2 A phrase near the end of a composition in G Minor.
•1.
•2.
•3.
•4.
••5.
Compare the chordal pitch content during R 1 with that during R 2 and also with that during R 4.5 From the answer to question 1, it is apparent that a tonic function is asserted from R 1 through R 4. Yet often during such expanses some embellishment provides a contrast to the persistent sounding of the prolonged chord. What three non-tonic pitches sound at S1 (and again at S2)? (Hint: all three pitches serve as neighbors to tonic chord members.) 6 Over the course of R 1 through R 4 it becomes clear what chord Mendelssohn intends for the location marked T 1. How does the chord at T 1 ful �ll the resolutional tendencies that precede it? Provide a harmonic analysis for the passage from R 1 through T1.7 Any chord is susceptible to a transformation resulting in a surge targeting a successor rooted a perfect � fth lower. How might the chord at T 1 have been so transformed? In this case Mendelssohn elects not to proceed in that direction (which would launch a circle of �fths), but instead treats the chord at T 1 as the principal intermediary between I and V ♯ within a progression in G Minor. Comparing the chords at T 1 and T2, explain what Mendelssohn does to assure that the progression will lead straightforwardly to V ♯. Provide suitable analytical symbols for what happens from T 1 to T2.8 What two pitches sound on the beat at U1? What harmony emerges over the course of that beat? What type of cadence is projected between U 2 and W?9
27
28
Harmony in Mendelssohn and Schumann
3.3 Schumann: “Am leuchtenden Sommermorgen” from Dichterliebe (op. 48, no. 12), mm. 22–61 The foundational state of a 5 –6 shift model would proceed from a chord in 5 3
position to one in
6 3
position. Sing the following arpeggiated chords,
during which IV 5–6 in B♭ Major conforms to that model.
Chordal unfurlings add variety to harmonic progressions. The unfurling of IV’s 6-phase chord (such as E ♭
5 3
position
(C
Signi�cant intervals within a composition often will be �lled in by diatonic or chromatic passing notes. Connective chords may emerge at such locations. Retaining an emphasis upon the E ♭>C bass and B ♭
IV 5–6 V Example 3.3 A composition in B♭ Major’s � rst vocal phrase.
•1.
•2.
•3.
•••4.
•5.
What four pitch classes are deployed during the beat marked Q to lead decisively into the tonic harmony at R?10 Does the tonic prolongation during the measure labeled R include the addition of a minor seventh (A♭), inducing a surge toward IV? 11 What is the relationship between the chords that sound during the beats labeled S1 and S2?12 The piano sounds a chord with bass E♭ and soprano B ♭ at S1. First indicate the pitches to which those lines move at S2. Then name the connective pitches that sound in those voices at T. Finally, indicate which two other pitch classes sound within the chord at T. 13 Provide a harmonic analysis of the phrase’s concluding chords (U and W), indicating whether they ful�ll the expectations established by the harmonic trajectory from R through S 2.14
3.4 Schumann: “Ich grolle nicht” from Dichterliebe (op. 48, no. 7), mm. 1–42 An important factor in hearing how harmonic progressions work is to be able to come to terms with various layers of embellishment or alteration that modify a foundational progression. In the arpeggiations that follow, such a foundational progression gradually is transformed through the incorporation of multiple musical devices. Begin by singing the foundational progression, as follows: F
< G
A <
< B
C C
< <
C
E
<
G
E
<
G
D <
Now more gradually phase in the subdominant, with a descent in thirds between the tonic and subdominant roots, as follows:
F
< G
A A <
< < B
C C C
< < <
C
E F
<
G
E
<
G
D <
29
30
Harmony in Mendelssohn and Schumann
Next expand the subdominant through the addition of its 6 phase, as follows:
F F
< < G
A A A <
C C C C
< < < B
< < < <
C
E
D D <
<
G
<
G
F
E
Finally modify IV ’s 6-phase chord through the incorporation of chromatic pitch A ♭ (borrowed from C Minor), as follows:
Example 3.4 The opening phrase of a song in C Major.
•1.
From bottom to top, what three pitches sound at the onset of Q? Which of the intervals formed by those pitches is featured ( �lled in by a passing note) in the melody during R? 15 •2. What harmony emerges at S1? How does the piano bass during the span from S 1 to S 2 relate to the vocal melody that began at R?16 ••3. The chord that sounds at S3 has the important task of supporting the word “Herz” (heart), poetically regarded as the organ responsible for love. In this case that heart is breaking (“bricht” at location U). Two separate musical devices are deployed by Schumann to help convey that unfortunate state – one represented by the soprano pitch at S3, the other by the fact that that pitch persists at T1 despite the altered harmonic context. Before assessing those distinctive features, explain how the chord at S 3 may be interpreted as representing a frequently encountered phenomenon that comes between IV (at S1 and S2) and V7 (at T1 and T2). Then indicate what special and less frequently encountered devices Schumann deploys at S 3 and at T 1 to heighten the emotional impact of the passage.17
4
I5–6 II
Though not emphasizedin the historical literature on harmony, it appears that one of the salient features of harmonic practice by Mendelssohn and Schumann is, as it were, the interchangeability of parts during the progression from I to V. The ascending-�fth root trajectory ’s division into a fourth followed by a second or, instead, into a second followed by a fourth not only involves the selection of diff erent harmonies to intervene between the perimeter points, but also reveals how a range of related procedures may work in the same way regardless of where within tonal space they are deployed. Thus the same sort of surge that transpires between I and IV when IV is selected may emerge between II and V when II is selected. Likewise the IV-to-V and I-to-II trajectories bring on the same sorts of 5 –6 shifts and corollary connective chords. Consequently this chapter, which assesses how II may serve as the principal intermediary between I and V, o ff ers little in the way of new ideas, but instead considers how what we explored in the context of IV in chapter 3 may be called into service when the fourth and second that together constitute the ascending �fth from I to V are presented in the opposite order. It is very important to keep in mind that this II is not derived from IV. Instead of conceiving of the tonal system symmetrically, with the dominant a �fth above and the subdominant a �fth below the tonic, the tonal system is here regarded as unidirectional, with the principal harmonic path of tonal music being the ascent of a �fth from the tonic root to the dominant root and then back again. Along that path, II and IV are equally viable and distinct intermediary options.
4.1 Schumann: “Ich wandelte unter den Bäumen ” from Liederkreis (op. 24, no. 3), mm. 13|14–223 A phrase’s initial tonic harmony often is given a chance to settle in before the harmonic progression gets underway in earnest. Embellishing chords that feature neighboring notes of tonic chord members or passing notes that connect two diff erent tonic chord members may be deployed. Sing the followingarpeggiated chords, noting howtheinternal chordsembellishtheperimeter tonic arpeggiations. Project bass A♯ as the lower neighbor to the B Major tonic root and soprano C♯ as a passing note between the tonic chord ’s B and D♯.
31
32
Harmony in Mendelssohn and Schumann
The following arpeggiations project the basic progression I II V in B Major. That progression accommodates variable levels of dissonance. In this case the tonic ’s octave (B) is retained against supertonic root C ♯, resulting in II 7. (This B resolves appropriately to A ♯ at the onset of V.) Likewise the supertonic third E is retained against dominant root F ♯, resulting in V7. One further dissonance emerges as well: whereas in con ventional voice leading the supertonic’s �fth (G♯) would descend to the dominant’s root (F♯), in this case the voice leading does not succeed in achieving that goal, descending only as far as G ♮, the minor ninth of V ♮ 79 .
It is very common for the succession from I to II to transpire as I 5–6 II. Incorporate I6 into your arpeggiations according to the grid provided below.
Almost any whole step motion in tonal music might on occasion be �lled in melodically as two half steps. Sing the arpeggiations below, in which the tonic’s 5–6 shift (F♯
I 5–6 II
Example 4.1 The second of a song in B Major’s four stanzas.
•1.
•2.
••3.
•4.
•5.
What is the relationship between the chords at R 1 and the onset of R 2? How does the chord at Q 2 serve as a connector between those two points? How do the chords at Q1 and Q2 relate?1 What interval is traversed in the vocal melody from R 2 through the onset of R 3? How does this melody relate to that which transpires from R 1 through R 2?2 How is the tonic chord transformed between R 2 and R 3? What role does chromaticism play in this process?3 All of the pitch classes that sound during the measure of R 4–5 match those that sound at the onset of R 3 except for one: the last vocal pitch (doubled by the piano), at R 5. What is that pitch, and what dissonant interval does it form against the initial G♯?4 What harmonic labels correspond to the chords at S and at T? (Hint: allow the chord during the measure labeled as T time to fully take shape. Five diff erent pitches sound in an ascending arpeggiation in the chordal interior.) 5
4.2 Schumann: “Berg’ und Burgen schau’n herunter” from Liederkreis (op. 24, no. 7), mm. 4|5–12 Though a neighboring note sometimes transpires quickly as a local embellishment, often such notes congeal within a chordal formation. Such chords may serve as embellishments of other chords, rather than asserting a harmonic function. When singing the arpeggiated chords below, interpret B and D as upper neighbors to the tonic root and third, respectively, and later G ♯ and B as lower neighbors.
Whereas the tonic harmony ’s 5–6 shift (E to F ♯ in A Major) often facilitates the traversal of the harmonic succession from I to II (chords whose triads share no common tones), the inclusion of the supertonic ’s seventh (A) adds another link between those two chords. Sing the
33
34
Harmony in Mendelssohn and Schumann
following arpeggiated chords, which convey the progression I 5–6 II♯37 V, noting the F♯ and A common tones between I 6 and II♯37 .
The trajectory from I 6 to II ♯7 may undergo evolution through the addition of pitch E (a passing note between F ♯ and D♯) and the chromatic shift of C♯ to C ♮ (a borrowing of A Minor ’s tonic third). Pay special attention to these initiatives while singing the following arpeggiations:
Example 4.2 A song in A Major’s � rst phrase, which follows after a four-measure introduction.
••1.
E
What harmony is conveyed at R 1, R 2, and R 3? Against a persistent A �fth (with pedal function), other pitch classes take on chordal roles during the beats marked Q1, Q 2, and Q3. Carefully explain each chord ’s role. (Explore the multiple phases of Q2.)6 •2. What change in pitch content emerges in the vicinity of R 4? How might this change be conveyed using the analytical notation of harmonic analysis?7 •3. First, what harmonies sound at the phrase’s perimeters (R 1 and T)? Given that trajectory and the shift addressed in question 2, what chordal root would you expect to �nd in the vicinity of location S? Is the chord that emerges there consonant or dissonant? Diatonic or chromatic? Provide a suitable analytical label for this chord in the context of A Major. 8 •••4. Though Schumann might have proceeded directly from the chord at R 4 to that at S, in this case the former chord evolves in two distinct ways (at R 5) before its successor is introduced. Explain how the chord at R 5 relates to that at R 4.9
I 5–6 II
4.3 Mendelssohn: Song without Words in D Major (op. 85, no. 4), mm. 2 –5 Composers often construct multifaceted harmonic progressions by expanding upon foundational progressions in various ways. To establish an orientation for one such expansion, sing the following arpeggiations, which project a I 5–6 II V harmonic trajectory. D D A
<
C♯
<
< < E E
F♯ F♯ <
< < G
<
A < A
B B
The second chord among the following arpeggiations unfurls I 6 into its 35 position. The second and third chords develop the soprano melody into a multi-chord arpeggiation of the tonic ’s three members: AC ♯>A (likewise within boxes), supported by II V.
Further re�nement results from connecting I 5 and the unfurled I6 by means of a connective chord (with passing notes C ♯ and E). In addition, II may be presented in its �rst inversion to bring the bass in close proximity to the following dominant’s root. Sing the following arpeggiations, focusing especially on these new initiatives:
35
36
Harmony in Mendelssohn and Schumann
Example 4.3 A composition in D Major’s � rst phrase, which follows after a onemeasure introduction.
•1.
The phrase’s initial tonic harmony extends from R 1 through R 4. The outer voices at two locations therein create an
D F♯ F♯ D
voice exchange. Which locations? A
connective chord comes between those two points. What pitch classes constitute that chord, and what is that chord ’s � gured bass?10 •2. The voice exchange addressed in question 1 projects a DA melodic trajectory concludes the excerpt. List all nine pitches that appear in the melody during locations S and T (through the end of the excerpt) and indicate how each either serves as a member of the prevailing harmony (which harmony?) or performs an embellishing role (what type of embellishment?). 13
4.4 Mendelssohn: Song without Words in A♭ Major (op. 38, no. 6), mm. 1 –53 During a I IV V I progression certain initiatives may emerge in predictable ways. I might surge as the succession to IV draws near, while a 5 –6 shift may transpire between IV and V. Sing the following set of arpeggiations, in which those optional features are incorporated. Pay close attention to how the 8>♭7 of I (A♭>G♭) leads downwards to the subdominant ’s third (F) and how IV’s 6-phase pitch (B♭) is retained as the dominant ’s �fth. (These pitches appear within boxes.)
I 5–6 II
Some chords work at a very local level, embellishing or connecting more foundational chords. The second and fourth chords in the following set of arpeggiations play such roles. Note especially how the emergence of a tonic surge may be accomplished by moving each triadic pitch up a third by step: that is, root to third (A ♭
To prepare for a more elaborate progression that follows, �rst sing some foundational arpeggiations that project I 5–6 II V, noting how the tonic ’s 6phase chord may emerge when the arpeggiated tonic ’s � fth, E♭, ascends to F (as shown within boxes).
When a phrase proceeds from I to V, it is very common for the foundational melodic trajectory to transpire as 3> 2. That second often will be embellished by means of local descents of a third, here C>A ♭ (supported by I 5–6) followed by B ♭>G (supported by II V). In the set of arpeggiations that follows, both of those thirds are � lled in by a passing note. (Focus on the melodic trajectory of the boxed notes, observing that the initial C is reinstated after the C>B ♭>A ♭ descent prior to the shift to B ♭.) ^
^
37
38
Harmony in Mendelssohn and Schumann
Example 4.4 The � rst phrase of a composition in A♭ Major.
••1.
••2.
••3.
•4.
•••5.
A melody often will weave back and forth between two individual strands. In this excerpt’s melody, the pitches at R 1 and at U2 not only participate in establishing the tonic harmony but also serve as the starting points for two distinct strands that persist throughout the excerpt. Name these two third-related pitches, and then indicate what other third-related pairs of pitches continue these two strands at locations W1–W2, R 2–R 3, and S–T2. (The pitches in question will not necessarily sound at the onset of the region marked by the letter designation.) 14 The only pitch to sound in the bass during the span from P through R 2 is A♭, which serves as a pedal point. Consequently the harmonic progression that transpires there will come across as working closer to the musical surface than does the broad phrase-de�ning progression projected by S and T 1–2. Provide a harmonic analysis of that local progression, focusing on the chords at six locations: R 1, U 2, W 1, W 2, X, and R 2.15 Though the chords at both Q1 and Q2 serve as connectors between two tonic chords, their manners of embellishment are contrasting. Explain what occurs in both cases, indicating which pitch classes form the connective chords and how those pitches function.16 The phrase’s foundational harmonic progression transpires after the tonic prolongation of P through R 2 concludes. How does the chord at R 3 relate to that at R 2? What Roman numerals correspond to the harmonies of S and T 2?17 The chord at location Q3 serves as a local connector between the chords at R 2 and R 3. What pitch classes sound within this connective chord? The chord on the beat at location T1 often sounds near a cadence. Explain how it usually functions, and comment on the less common turn of events near the end of the T1 beat, just prior to the resolution to the chord at T 2.18
4.5 Mendelssohn: Song without Words in A Major (op. 102, no. 5), mm. 1–7 As an initial orientation, sing arpeggiations of the progression I5–6 II➔ V in A Major, as follows:
I 5–6 II
A A
<
E <
B
< E
< F♯ F♯ <
A A A
< < G♯
C♯ C♯
< <
D♯
< <
B
<
By presenting the tonic ’s 6-phase chord in a 35 unfurling (as in A-C ♯-E to F♯-A-C♯-F♯), the bass attains some space (A>F ♯) that may be �lled in by a passing note. In the set of arpeggiations that follows, that passing G ♯ is complemented by chromatic passing note E ♯, which connects 5-phase E and 6-phase F♯. These arpeggiations also feature a further expansion of the 6-phase chord through the addition of bass passing note E (thus producing a chord in 24 position), which motivates the presentation of II➔ in 56 position.
Example 4.5 A composition in A Major’s opening phrase.
•1.
••2.
•3.
•••4.
•5. •6.
•7. ••8.
39
How do the tonic chords at the downbeats of R 1 and R 2 diff er? How do those at the downbeats of R 1 and R 3 di ff er?19 Name the � ve bass pitches that sound during the span from R 3 through T. (Each is a half note, sounding for one full measure.) 20 What is the relationship between the tonic harmony (R 1 through R 3) and the chord at S1?21 The sonority at X incorporates both a retained tonic pitch A in the alto register and three other pitches that form a connective chord that targets the upcoming chord at S1. (One of X’s pitches, in the tenor register, is chromatic.) Name those three pitches.22 What � gured bass numbers pertain to the chord at S 2?23 What consonant, diatonic chord often would serve as the successor to the chord at S1? In what two ways does the chord of T represent an evolved state of that successor? Provide a suitable analytical symbol for the chord at T. 24 What � gured bass numbers pertain to the chord at T? 25 Explain the rationale for Mendelssohn’s deployment of the pitches D ♯ and D♮ in the vicinity of U1 and U2.26
E
40
Harmony in Mendelssohn and Schumann
4.6 Mendelssohn: Song without Words in E Major (op. 38, no. 3), mm. 7 –14 As an initial orientation, arpeggiate the progression I5–6 II V (with unfurled I6), as follows:
A
< B
C♯ C♯ <
<
E E < D♯
<
< < F♯ F♯
G♯ G♯
<
B
Now add a surging connective chord between I 5 and I6.
Finally, arpeggiate the initial tonic harmony as a chord in 36 position, and descend by step (parallel 36 chords) until the connective chord is reached, as follows:
I 5–6 II
Example 4.6 The song in E Major ’s � rst phrase, which follows after a six-measure introduction.
••1.
•2.
•3.
••4.
••5.
•6.
Four chords stand out as projectors of the excerpt’s foundational harmonic progression. Analyze the progression represented by the chords at the following locations: R 3, U,W, and X1. Also comment on the melodic trajectory projected by those chords (taking into account that a descending registral shift occurs). 27 Near the end of the introduction that precedes this excerpt, the pitches C♮, D♯, F ♯, and A sound in the range from one to two octaves above Middle C. Explain how the soprano pitches that sound at locations R 1, R 2,andR 3 relate to those earlier pitches.28 A root-position tonic chord sounds at locations R 1, R 2,andR 3, each witha diff erent soprano pitch. Which of those three chords sounds at R 4? What happens in the meantime, at S? Carefully describe the relationship between chords R 3 and R 5.29 From question 1 we understand that the chord at U is closely related to the initial tonic of R 1 through R 5. Often a connective chord will intervene between those two more foundational chords. That connective chord might relate back to the initial tonic, or it might instead target the succeeding chord. The second alternative prevails with the chords at T5 and U. Name the pitch classes employed in both chords, and explain how the former may be said to “target” the latter.30 In questions 3 and 4, the roles of chords R 5 and T5 within the broader harmonic trajectory have been assessed. Both of those chords sound in �rst inversion. What voice-leading procedure does Mendelssohn deploy in the vicinity of locations T 1 through T4 to connect those two more foundational points?31 5 The harmony that concludes the phrase’s progression (at X1) is introduced in its 3 position, suitable for a cadence. (What type of cadence occurs?) Yet by the measure’s end this chord has been forti �ed by two dissonant pitches that help motivate the return of the tonic harmony for the phrase that begins just after this excerpt. Those two pitches are featured in the melody at X 2 and X3. Name the two pitches, and indicate what intervals they form with the chordal root. 32
41
5
Surging 6-phase chords
Many thousands of musicians have created harmonic analyses over the past several centuries. As numerous textbooks created during this period attest, a wide range of analytical symbols – not necessarily the Roman numerals that are deployed here – have been called into service. Certainly disagreements are to be expected in this undertaking, especially since the composers whose music we analyze generally did not give us much guidance regarding how they thought about harmony. The analytical perspective advocated here is notable for its sparse deployment of Roman numerals. Perhaps already these procedures have proven to be insight-enhancers for some readers, though others might be resisting them. (Many of the chords that are described as “connective,” “embellishing,” or “passing” would be awarded a harmonic label by most modern analysts.) Likewise in a diatonic context a 5 –6 shift here generally will not trigger a new Roman numeral: adding an A to a C-E-G tonic chord in C Major does not necessarily imply that the root has shifted from C to A. Instead, the A often will be interpreted as a dissonant addition to the stable tonic pitches, in the manner of an anticipation of the following II chord’s �fth. Yet if certain other factors come into play, then the balance between the maintenance of C as root and a shift to A will tip in favor of the latter, in which case a two-tiered analytical symbol such as C Major:
I5−−−−−−−−−−−−−−−− 6 (= VI➔)
II
will be employed. The factor that triggers the VI ➔ interpretation is, of course, the emergence of the chromatic pitch C ♯. Chords that are spelled as C♯-E-A or C♯-E-G-A and that resolve to D-F-A project a strong sense of a descending-�fth root succession (A to D). Consequently the VI➔ label (or, with greater precision, VI ♯ or VI ♯37 ) will be introduced within parentheses below the Arabic 6 of the I 5–6 label. Such surges of the tonic 6-phase chord off er composers a wider range of intensity with which to work in formulating their harmonic trajectories. (Surges of even greater intensity will be explored in chapters 6 and 7.) Likewise IV 5–6 might evolve in a way that 42
Surging 6-phase chords
would make the symbol II ➔ (or II♯ or II ♯37 ) appropriate. In this context II emerges out of IV, contrasting the supertonic deployments explored in earlier chapters.
5.1 Mendelssohn: Song without Words in B♭ Major (op. 85, no. 6), mm. 14–171 First sing a foundational set of arpeggiations corresponding to the progression I5–6 II V I, as follows:
In the following set of arpeggiations, the tonic ’s 6-phase chord (which in this case incorporates 6 in addition to 5) evolves in two ways: �rst, through an unfurling that places G in the bass; second, through the chromatic shift of B ♭ to B♮, thereby generating a surge targeting the II chord that follows. The succession from II to V is facilitated by the emergence of II ’s �rst inversion, placing bass E ♭ and F in a stepwise relationship.
43
44
Harmony in Mendelssohn and Schumann Example 5.1 The � rst stanza’s � nal phrase in a composition in B ♭ Major.
•1.
•2.
•3.
••4.
•5.
What bass pitch sounds on the downbeat of each of the excerpt’s measures: at R 1, S1, T1, and U? Though the harmonies are not necessarily fully in place at these downbeats, what foundational harmonic progression is suggested by these bass notes?1 Each of the excerpt’s �rst three measures engages in a di ff e rent sort of internal initiative. Perhaps the most straightforward is that which transpires between S1 and S 2. How are those chords related? Also explain how both F♯ and F ♮ may occur in close proximity in the melody during this measure. 2 The internal initiative between T1 and T2 likewise is frequently encountered. How are those chords related?3 In relation to the chordal root B ♭, what Arabic numerals correspond to the soprano pitches occurring on the beats at R 1 and R 2? What bass note sounds at R 2? What chromatic event occurs during the beat of R 2? Drawing upon these individual pitch initiatives, provide a coherent narrative concerning the harmonic trajectory from R 1 through S1.4 What cadence type concludes the excerpt, at U?5
5.2 Mendelssohn: Song without Words in A♭ Major (op. 53, no. 1), mm. 3 3–72 A 5–6 shift applied to a subdominant harmony may come about not only through the literal ascent from a �fth to a sixth above the subdominant root, but also by means of a descent from that root ’s octave to the sixth. The following set of arpeggiations emphasizes that melodic trajectory.
The expanded set of arpeggiations below develops the progression in two ways: �rst by moving from the tonic root position to �rst inversion,
Surging 6-phase chords
with parallel tenths in the outer voices; and second by allowing IV ’s 6phase chord to surge in its approach to V. The latter deploys chromatic D ♮ to � ll in a D ♭
Further re�nements in the progression result from the deployment of a connective connective chord chord between between the root-positio root-position n and �rst-inversion tonic chords at the onset (retaining the use of tenths between the outer voices) and allowing allowing the tonic to surge in its approach to the subdominant. subdominant. In addition, addition, 5–6 a passing note (C) �lls in the descent from 8 to 6 during IV . Sing the follo followi wing ng set set of arpe arpegg ggia iati tions ons,, keep keeping ing in mind mind how how these these vari variou ouss evolu evolutio tions ns and expansio expansions ns relate relate to the more more foundat foundation ional al progre progressio ssions ns you sang earlier.
45
46
Harmony in Mendelssohn and Schumann Example 5.2 A composition in A ♭ Major’s � rst phrase, which follows after a brief introduction.
••1.
••2.
••3.
••4.
•5.
First, First, compare compare the chords chords at locations locations R 1 and R 2. Second, assess the role of the chord prolonged for a full measure at Q. Third, explain how the chord at R 3 relates to what has preceded it. 6 Explai Explain n how the partic particula ularr invers inversion ion of the chord chord at R 2 aff ects ects the invers inversion ion of the resolution chord at S 1. If the chord during R 2 is to resolve appropriately, what relationship must prevail between the melody ’s two pitches during S1? Is there any precedent within the excerpt to help the listener listener in appropriately interpreting interpreting 7 that relationship? Name the six melodic melodic pitches pitches that sound sound during during S1 through S3. Which two of those six pitches play the most foundational role? If that is so, then suggest a harmo harmonic nic label label (with (with app append endage agess to the right right of the Roman Roman numera numeral) l) that that 8 conveys what transpires during these beats. Though Though the chord that that congeals congeals during during S3 is incomplete (with the pitch D♭ that sounded during S 1 and S2 absent), it is diatonic. At S 4 the situation changes. (Again one pitch, now B ♭, is absent.) Explain the chordal evolution at this point. 9 As was the case case also also at at R 2, S 1, and S3, the melody ’s second pitch at T serves as the chord member. What harmony emerges during T? 10
5.3 5.3 Schu Schuma mann nn:: “Allnächtlich im Traume ” from Dichterliebe (op. 48, no. 14), mm. 0|1–111 As an initial orientation, sing a set of arpeggiations that corresponds to the harmonic progression I IV 7 V I, as follows: B
< E
B
<
D♯
<
F♯ < F♯ F♯
< G♯ < <
B B
< A♯
<
< D♯ < D♯ C♯
B
Now expand these arpeggiations to include a I ➔ IV surge, the addition of IV’s 6 phase (asserted as II ➔), and the �lling-in of a C♯>B>A♯ third in the melody between II ➔ and V, as follows:
Surging 6-phase chords
Finally, further develop the initial tonic by ascending gradually from B to D♯ in the melody melody,, using using a proced procedure ure often often referr referred ed to as reachi reaching-o ng-over ver:: descend from B to A ♯, supported by an embellishing chord; then, without chang changin ingg chor chords ds,, allow allow C♯ to reac reach h ove over A♯; then then desce escend nd from from C♯ toBforthe tonic’s restor restorati ation; on; �nally, nally, withou withoutt changi changing ng chord chords, s, allow allow D♯ to reac reach h over over B.
Example 5.3 A song in B Major ’s opening stanza.
•1.
•2.
•3.
••4.
••5.
The tonic tonic harmo harmony ny ’s root and �fth (B and F ♯) are maintained as pedal points throughout R 1, Q, and R 2. What pitches sound above those pedal points during Q? What ascending melodic interval (a component of the tonic triad) is traversed in the piano melody (for the most part doubled by the voice) during this passage?11 What What pitc pitch h soun sounds ds in the the melo melody dy at S1? What What harm harmon onyy supp suppor orts ts that that pitc pitch? h? What What sort of chordal evolution occurs between S 1 and S2? What descending descending melodic melodic interval is traversed between S 1 and T, complementing the ascending interval discussed in question 1?12 Compare Compare the the chords chords at R 2 and R 3. How is the tendency introduced at R 3 ful�lled by the succession to the chord at U 1?13 Two initiativ initiatives es transp transpire ire concurre concurrentl ntlyy at U2 – one diatonic, one chromatic. Explain how these initiatives suitably connect the chords at U 1 and W1–2.14 Explai Explain n how the melody melody pitch pitch that sounds sounds on the beat at W 1 functions in the context of the progression from U 2 through through W2. Especially Especially consider issues relating to register (where within the vocal range a pitch sounds), taking into account that the text being projected at this point reads as follows: “und lautaufweinend stürz’ ich mich zu deinen süßen Füßen ” ( “and sobbing audibly I throw myself upon your charming feet ”).15
47
48
Harmony in Mendelssohn and Schumann
5.4 Mendelsso Mendelssohn: hn: Song Song without without Words Words in B Minor (op. 30, no. 4), mm. 111–1171 First sing a set of arpeggiations that projects I IV V♯37 I in B Minor, as follows: B < D < F♯ < B E < G < B < E F♯ < A♯ < C♯ < E B < D < F♯ < B < D Now sing arpeggiations that introduce a surge: I ➔ IV. In a temporary major-mode in �ection, allow the subdominant to be projected as a chord of major quality (E-G ♯-B).
In the next set of arpeggiations, concurrently rescind IV ’s major quality (by lowering G ♯ to G♮) and incorporate the 6-phase pitch C ♯. Also embellish the dominant by means of a cadential cadential 46 chord.
Surging 6-phase chords
Example 5.4 A phrase near the end of a compositio composition n in B Minor. Minor.
•1.
Though Though several B major chords sound in the measures measures preceding preceding this excerpt, the cadence at location U con�rms that B Minor prevails as the tonal center. In that context, propose precise Roman numeral labels for the chords at R and at the onset of S1.16 •••2. Name Name the � ve bass pitches that sound during the span from S 1 through T1. One of tonal music’s most intriguing features (and greatest analytical challenges) concerns the variable ways in which individual pitches may function. Consider the bass pitch at Q2. One analytical hypothesis (which will be countered by a better one in question 3) would propose that Q 2 serves as the onset of the dominant. If that is so, then how might one convey the relationship between S 1 and Q1 leading up to Q2? What pitch sounding at Q2 con�icts with a dominant reading, and how might it behave if the dominant interpretation is to be successful? How could the bass pitch at S2 be understood as conforming to this dominant reading? 17 •••3. Several Several factors argue argue against the hypothesis hypothesis explored explored in question question 2. An alteralternative hypothesis would propose that the bass pitch at Q2 serves as a passing note: that the line ascending in half steps from S 1 through S2 is an indivisible by the arrival of the dominant root at T 1 (with the dominant unit, followed unit, followed by the harmony fully falling into place during T 2). Strong support for that reading comes from a melodic line in the alto register that coordinates with the bass line from S1 through S 2. What pitches constitute that line, and how does it relate to the bass? What four pitch classes (two of which sound at Q 2 but then are followed by rests) should be understood to constitute the chord at S 2? How does the chord at S 2 relate to that at S 1? Finally, how should the chord at Q 1 be interpreted in the context of this hypothesis? 18 ••4. In its its cont contex extt the the down downbe beat at melo melody dy pitc pitch h at T1 would would genera generate te the expect expectati ation on of a speci�c pitch at T2. Name those two pitches. Something vastly di ff erent erent occurs on the downbeat at T2. What pitch sounds at that point? What is its role within the harmonic context? 19
49
6
Surges with ninths
Because music is an art that deeply touches the emotions, a tonal composer’s palette of available chordal constructions o ff ers many options. The chords with intense potency generally will contain at least one chromatic pitch or at least one dissonant pitch. Or, both of those characteristics may prevail concurrently. Since by their very nature surges are among the key emotive players in a harmonic progression, the level of potency conveyed in their forward thrust may be adjusted with great precision. In earlier chapters we saw how a minor triad may be chromatically adjusted through the raising of its third and how a minor seventh may be added. Now we up the ante: a minor or major ninth may intensify the surge ’s drive toward its successor. The behavior of a chordal ninth di ff ers to some extent from that of a chordal seventh. Whereas the seventh, once integrated into a chord as a member (rather than as a � eeting passing note), generally will prevail until that chord resolves, the ninth may resolve within the chord: that is, 9 –8 (a descending resolution by step within the chord) is an option unavailable to 7. This gives rise to the interpretation of the ninth as a displacement of an octave doubling of the root (8). In the context of V proceeding to I in C Major, the dominant G-B-D may be forti �ed not only by seventh F, but also by ninth A or A♭. When a ninth sounds, the chord might be presented as B-D-F-A(♭) – that is, with A(♭) instead of , rather than in addition to, root G. Yet G remains the unsounded root of B-D-F-A( ♭). A bullet symbol ( •) will be deployed in the harmonic analyses to indicate such an absent root (here as V(♭ )). Any surge may evolve so as to emulate this potently dissonant dominant. Thus during the succession I 5 6 II in C Major the tonic 6-phase chord (C-E-A) might transpire in a context in which the pitch A is asserted as an intermediate root, fostering a local succession from VI to II. To surge, VI➔ must sound with a raised third (A-C ♯-E). The forward thrust is enhanced when the minor seventh is added (A-C ♯-E-G). Yet four new possibilities emerge upon the addition of a ninth: that ninth might be 9
7 •
–
50
Surges with ninths
major (A-C♯-E-G-B) or minor (A-C♯-E-G-B♭), and its addition might coordinate with the omission of the chordal root (C ♯-E-G-B or C♯-EG-B♭). Likewise during IV 5 6 V, the surging subdominant 6-phase chord (= II➔) might appear as D-F ♯-A, D-F♯-A-C, D-F♯-A-C-E, D-F♯-A-C-E♭, F♯-A-C-E, or F♯-A-C-E♭. (To con�rm your understanding, also spell out all the surge spellings for I ➔ targeting IV.) Whereas the Arabic numerals, accidentals, and bullet symbol to the right of a Roman numeral are capable of indicating which of these options is deployed with precision, the convenient right-pointing arrow refers to this general class of chords without distinguishing among the variants. Though in many cases only one surging chord will sound, certainly it is possible that multiple variants will be juxtaposed; for example, with the –
gradual addition of the seventh and then the ninth to a major triad (II
9 7—– ♯3——
),
or with the softening of a chord ’s impact through a 9 –8 resolution within 9–8 7— ♯3—
the chord (II
).
6.1 Schumann: “Und wüssten’s die Blumen” from Dichterliebe (op. 48, no. 8), mm. 34–37 Sing a set of arpeggiations in which the melody ’s 3> 2> 1 trajectory in A Minor is embellished by an incomplete upper neighbor (D), supported by the subdominant. ^
^
^
Now expand the phrase ’s initial tonic through a CC neighboring motion in the melody. Lead from C to D via a chromatic C ♯, with upward propulsion generated by C ♯’s dissonant interactions with G and with B ♭, and then proceed from D back to C, with downward propulsion generated by D’s dissonant interaction with G ♯.
51
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Harmony in Mendelssohn and Schumann
Example 6.1 The � nal measures of a song in A Minor.
•1.
The excerpt deploys only four bass pitch classes. That which sounds at R 1 is notated as a half note (maintained as a pedal point against the chordal progression in the upper voices), thus persisting until its reiteration at R 5. The second sounds brie�y during U, the third in multiple registers at W 1 2, and the fourth at X. For now omitting consideration of what happens between R 1 and R 5, provide a harmonic analysis for this foundational progression. 1 ••2. This excerpt concludes the song’s coda, which occurs after the singer has completed delivering the text. Two measures before the excerpt begins, what sounds at R 1 had joined with the singer’s �nal pitch (an A) to project a PAC ’s concluding minor tonic (in this case with omitted third and �fth). Both immediately after that PAC and at this excerpt ’s onset, a sudden build-up of tonal energy results from the introduction of pitches that dissonate against root A or with one another. Name the melodic pitch that sounds at the onset of locations R 2, R 3, and R 4, and then provide a complete list of the intervals that these pitches form against the bass and with one another. 2 ••3. Provide a detailed harmonic analysis for the progression that transpires above bass pedal point A over the span from R 1 through R 5.3 –
6.2 Mendelssohn: Song without Words in A Major (op. 53, no. 6), mm. 11–18 When a broad melodic contour proceeds directly from 3 to 2 (leading even^
^
tually to 1), II often will support 2 initially. Though this 2 may be maintained ^
^
^
during the following V, a local descent to 7 is a frequently encountered alternative. Sing the following set of arpeggiations, based on that trajectory. ^
Surges with ninths
A wondrous though challenging aspect of tonal harmony is the notion that a pitch might convey multiple meanings, with only the continuation following a chord clarifying what structural role has been ful �lled. Consider the shift from an A-C♯-E tonic to what might be spelled as A-C♯-E-G♮-B♭. Given that spelling, we would regard the chord to be functioning as I ➔, targeting IV. In that case, major third C♯ would ascend to D, while minor seventh G ♮ would descend to F♯ and minor ninth B ♭ would descend to A. Yet an alternative spelling for the chord (used by Mendelssohn in the example to be explored below) would be A-C ♯-E-G♮-A♯. In that case the A serves as a pedal point in con � ict with the emergence of an F ♯➔ chord (tonic A’s asserted and surging 6 phase) projected by its upward-resolving major third (A ♯), a neutral �fth (C♯), and downward-resolving minor seventh (E) and minor ninth (G ♮). Sing the following set of arpeggiations twice. First sing the �rst two chords as notated but conceive of the second chord as being spelled using a B♭ rather than an A ♯. Thereafter improvise a continuation that proceeds to IV, followed by V and I. Then sing the set of arpeggiations as notated, noting the vastly di ff erent outcome if B ♭ is interpreted instead as A♯. (A C ♯-to-B suspension resolution transpires as well.)
In the set of arpeggiations that follows, a dominant (which one might imagine was attained as the goal of the phrase preceding the excerpt) lingers at the onset of the new phrase, preceding the A tonic ’s arrival. This dominant is embellished by two upper neighboring notes: A embellishing the dominant’s third, G♯, in the bass; and F ♯ embellishing the dominant’s root, E, in the soprano.
53
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Harmony in Mendelssohn and Schumann
Example 6.2 A composition in A Major’s second phrase: a consequent phrase cadencing on I.
•1.
•••2.
••3.
Preceding this excerpt an antecedent phrase cadences on an E-G♯-B dominant harmony during its eighth and �nal measure. In a modest blurring of the boundary between phrases (but with Q1 clearly positioned as the �rst of eight consequent-phrase measures), that dominant persists at the consequent phrase’s onset. Where does tonic A-C ♯-E arrive? What are the appropriate �gured bass numbers for the dominant that precedes that tonic at the phrase ’s onset?4 Though listeners will expect the G♯ leading tone to resolve to tonic A, the pitch A that sounds at Q2 should not be interpreted as that resolution. Instead, V 7 persists through Q3, with the chord at Q 2 embellishing – rather than resolving – the dominant. Spell out the pitches that constitute the dominant harmony at Q 1 and Q3 (omitting the persistent local neighboring embellishment provided by A♯), and then assess what happens at Q2. (Hint: only the outer voices shift at that point.) 5 The consonant tonic chord that �nally arrives at R 1 is prolonged through R 2. Some analysts would interpret the intervening chords at S1 and S2 as local embellishment of the tonic, whereas others would deploy a V label, proposing a local I V I harmonic progression as a means of projecting the phrase’s initial tonic. Again not considering the persistent neighboring embellishment (now D ♯), what two pitches sound in addition to triadic E-G♯-B during S1 2, and what roles do they perform? 6 For the moment omitting consideration of the chord at R 3, what harmonic progression concludes the excerpt (from T1 through W)? Note that a chromatic shift occurs at T2. After spelling out the chords of T 1 and T2 (again omitting consideration of the persistent neighboring embellishment, now C♯), assess how this shift participates in a broader voice-leading initiative that transpires in the alto register.7 The harmonic trajectory from the chord at R 2 to the chord at T 1 encourages a speci�c connective voice-leading operation. In general, what pitch might be added to the three chord members of R 2 in that process? Now spell out that proposed chord, arranging its four pitch classes in a stacked-thirds formation. Next raise one of those pitches so as to create a surge, targeting the chord at T 1. Finally, assess how the chord during R 3 extends beyond that level of intensity.8 –