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3
Triads and Seventh Chords
Triads and seventh chords are the basic harmonies of most Western music.
Triads
Seventh Chords
Triad construction
Seventh chord construction
Triad qualities
Seventh chord qualities
Natural (white-key) triads
Natural (white-key) seventh chords
Triads in inversion
Seventh chords in inversion
Triads in Major and Minor Keys Roman numerals
Seventh Chords in Major and Minor Keys Roman numerals and inversions
Roman numerals and inversions
TRIADS TRIAD CONSTRUCTION
A triad consists of three different pitches: a fifth divided into two thirds, or two thirds triad consists stacked to make a fifth. Triads can appear on three consecutive lines or spaces on the staff. When a triad is stacked in thirds, the lowest note is the root root,, the middle note is the third third,, and the highest note is the fifth fifth.. 3.1
TRIAD QUALITIES
Triads are classified c lassified by quality quality:: depending on the qualities of the thirds and fifths they contain, triads may be diminished diminished,, minor , major , or augmented augmented.. You can refer to a # triad by its name and quality, quality, for example, C -major triad or D-minor triad.
Triads
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3.2
Chord symbols identify symbols identify the root and quality of a triad. Diminished triads are indicated indicated with a degree symbol ( ) after the root, minor triads with a lowercase m, and augmented triads with a plus sign ( ). Major triads are indicated with just their root.
NATURAL (WHITE-KEY) TRIADS
Knowing the natural triads — without without accidentals — can can be helpful in identifying triad quality. 3.3
Every triad uses one of those seven seven groups of letter names: CEG, DFA, DFA, EGB, FAC, FA C, GBD, ACE, BDF. BDF. To To spell a triad, tri ad, start star t with a white-key white-k ey triad and, if i f necess necessary, ary, add an accidental to match the root requested. Then check the intervals of the triad, adding accidentals as needed for the proper quality of third and fifth. 3.4
TRIADS IN INVERSION
Triads can be arr anged in a variety of ways, from three notes played played with one hand at the piano to being spread out over an entire orchestra. However However they are arranged, ar ranged, the lowest sounding note of a triad is called the bass bass;; any one of a triad’s three notes can sound in the bass. The bass note of a triad determines its position position.. When the root of a triad is in the bass, the triad is in root position. position . When the third of a triad is in the bass, the triad is in first inve inversion rsion.. When the fifth of a triad is in the bass, the triad is in second inversion. inversion. It does not matter which notes are on the top or in the middle of the chord: the position is determined solely by the bass. 38
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3.5
Root position Root in bass
First inversion Third in bass
Second inversion Fifth in bass
Root position Root in bass
First inversion Third in bass
Second inversion Fifth in bass
Triad positions are commonly labeled with a stack of two Arabic numbers, or a figure figure:: 53 = root position; 63 = first inversion; 64 = second inversion. These numbers correspond to the inter vals formed above the lowest lowest sounding note. 3.6
Arabic numbers indicate the position of the triad: 5 3 = root position 6 3 = first inversion 6 inversion ersion 4 = second inv
TRIADS IN MAJOR AND MINOR KEYS ROMAN NUMERALS
Within a major or minor key, Roman numerals — corresponding corresponding to the root — identify identify triads. Major triads are indicated with uppercase Roman numerals; lowercase Roman numerals indicate minor triads; and lowercase Roman numerals numerals followed by a degree sign ( ) indicate diminished triads. (Augmented triads require accidentals and occur only under special, rare conditions).
Triads in Major and Minor Keys
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3.7
In every major key, there are three major triads (I, IV, V), three minor triads (ii, iii, vi), and one diminished triad (vii ).
In every minor key, there are three major triads (III, VI, VII), three minor triads (i, iv, v), and one diminished triad (ii ).
In minor keys, the dominant and subtonic harmonies usually include raised 7ˆ from the harmonic minor scale, creating a leading tone (a semitone below the tonic). (The raised 7ˆ is not ordinarily used in the III triad.) 3.8
When 7ˆ is raised from subtonic to leading tone (as in the harmonic minor scale), v becomes V and VII becomes vii .
ROMAN NUMERALS AND INVERSIONS
A Roman numeral numeral can be combined with a figure that consists of Arabic numbers to show the root, quality, quality, and position of a triad. 3.9
For triads in root position, the figure is usually omitted. A Roman numeral without any figure is interpreted to mean 53.
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For triads in first inv inversion, ersion, 63 is usually abbrevi abbreviated ated to 6.
For triads in second inv inversion, ersion, 64 appears with the Roman numeral and is not abbrevi abbreviated. ated.
SEVENTH CHORDS SEVENTH CHORD CONSTRUCTION
A seventh chord can chord can be understood as either a triad plus a seventh over over its root or a triad tri ad with an additional third stacked on top of its fifth. Seventh Seventh chords can be written on four consecutivee staff lines or four consecutive spaces. When a seventh chord is stacked in consecutiv thirds, the lowest note is called the root, followed by the third , the fifth, and the seventh. 3.10
SEVENTH CHORD QUALITIES
Like triads, seventh chords are classified by quality. quality. Depending on the qualities of the triads and sevenths they contain, seventh chords may be fully diminished (diminished diminished (diminished triad + diminished sev seventh), enth), half-diminished (diminished triad + minor seventh), seventh), minor (minor half-diminished (diminished triad + minor seventh), dominant (major triad + minor seventh), or major (major (major triad dominant (major + major seventh). As with triads, you can refer to a seventh chord by its root and quality. 3.11
Chord symbols: 7 = fully diminished; 7 = half-diminished; m7 = minor seventh; 7 = dominant; maj7 = major seventh
Seventh Chords
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NATURAL (WHITE-KEY) SEVENTH CHORDS
Knowing the qualities of natural seventh chords — without without accidentals — can can be helpful in identifying seventh chord quality. 3.12
Every seventh chord uses one of those seven groups of letter names: CEGB, DFAC, EGBD, FACE, GBDF, ACEG, BDFA. To spell a seventh chord, start with a white-key seventh chord and, if necessary, add an accidental to match the root requested. Then check the intervals of the seventh chord, adding accidentals as needed for the proper quality of third, fifth, and seventh. seventh. 3.13
SEVENTH CHORDS IN INVERSION
Like triads, seventh chords can appear in inversion as well as root position; any of the four notes of a seventh chord can sound in the bass. A figure (stack of three Arabic 7 6 6 numbers) is used to identify these inversions: 53 = root position; 53 = first inv inversion; ersion; 43 = 6 second inv inversion; ersion; 42 = third inversion. 3.14
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SEVENTH CHORDS IN MAJOR AND MINOR KEYS ROMAN NUMERALS AND INVERSIONS
For seventh chords as for triads, a combination of a Roman numeral and a figure (stack of Arabic numbers) indicates the root, r oot, quality, quality, and position. Here are the most common seventh chords and inv inversions: ersions: 3.15
In every major key, ii7 is minor, IV 7 is major, V 7 is dominant, and vii 7 is half-diminished.
3.16
In every minor key, ii 7 is half-diminished, and iv 7 is minor. The seventh chords on 5ˆ and 7ˆ usually use the raised 7, 7ˆ , the leading tone, from the harmonic minor scale; thus V 7 is dominant, and vii 7 is fully diminished.
Seventh Chords in Major and Minor Keys
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review and interact POINTS FOR REVIEW
• Depending on the qualities of the thirds and fifths they contain, triads may be diminished, minor, major, or augmented. • Triads may appear in three positions: root position ( 53 , root in bass), first inversion ( 63 , third in bass), or second se cond inversion ( 64 , fifth in bass). • Roman numerals combined with figures (stacks of Arabic numbers) identify the root (as a scale degree in a major or minor scale), quality, and inversion of a triad or seventh chord. • In minor keys, 7 is usually raised in the V and vii triads and seventh chords. • Depending on the qualities of the triads and sevenths they contain, seventh chords may be fully fu lly diminished, half-diminished, minor, dominant, or major. • Seventh chords may appear in four positions: root position ( 7, root in bass), first inversion ( 65 , third in bass), second inversion ( 43 , fifth in bass), or third inversion ( 42 or 2, seventh in bass).
TEST YOURSELF 1.
Identify each triad with its root and quality. quality.
2.
Write each triad in root position.
3.
Identify each sev seventh enth chord with its root and quality. quality.
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4.
Write each sev seventh enth chord in root position.
5.
Use a Roman numeral with a figure to identify each triad or seventh chord in the key indicated.
6.
Write each triad or seventh seventh chord in the key indicated. Use accidentals rather than key signatures.
Know It? Show It! Focus by by working through the tutorials on: • Recognizing triad qualities and writing triads • Inv Inverting erting triads and writing triads from figures • Recognizing seventh seventh chord qualities q ualities and writing seventh chords • Inv Inverting erting seventh chords and writing seventh chords from figures Learn with inQuizitive. inQuizitive. Apply what you’v you’vee learned to complete the assignments: • Identifying triad quality
• Identifying seventh chord quality
• Writing triads triad s
• Sev Seventh enth chords by root and quality
• Triad inversions
• Seventh-chord inversions
• Triads in major and minor keys
Seventh Chords in Major and Minor Keys
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r e t p a h c
6
Harmonic Progression
Harmonies in tonal music follow conventional progressions.
Beginning and Ending Phrases
Melody Harmonization
Authentic and half cadences
Matching chords to the melody
Perfect and imperfect authentic cadences
Voice leading Conventional harmonic progressions
Harmonic Patterns T D T (Tonic Dominant Tonic) –
–
–
–
T S D T (T (Tonic-Subdominant-Dominant-T onic-Subdominant-Dominant-Tonic) onic) –
–
–
BEGINNING AND ENDING PHRASES AU TH EN TI C AN D HA LF CA DE NC ES
A phrase is the basic unit of tonal music, akin to a sentence in language. Within a phrase is phrase, harmonies generally occur in conventional progressions. Typically, phrases begin with a root-position I triad. Even more standard is the harmony har mony found at the end of the phrase, or the cadence. Phrases almost always conclude either with a root-position V or V 7 chord leading to root-position I, or with a root-position V. A cadence consisting of V or V 7 moving to I is an authentic cadence ( cadence (AC AC); ); a cadence ending with a V triad is a half cadence ( ). Because they end on a stable tonic harcadence (HC HC). mony,, authentic cadences generally mony gener ally sound more conclusive than half cadences.
Beginning and Ending Phrases
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6.1
Beethoven, Beethov en, String Quartet Quartet in B Major Major,, Op. Op. 130, ii
Half cadence ( cadence (HC HC): ): The first phrase ends with rootposition V. Both phrases begin with a root-position I triad.
Authentic cadence (AC AC): ): The second phrase ends more conclusively with a V – I progression.
PERFECT AND IMPERFECT AUTHENTIC CADENCES
Authentic cadences are further categorized by the final final note note in the melody melody.. An authentic cadence that ends with 1ˆ in the melody is a perfect authentic cadence ( cadence (P PAC AC). ). An ˆ ˆ authentic cadence that ends with 3 or 5 (the third or fifth of the I chord) in the melody is an imperfect authentic cadence ( ). Perfect authentic cadences tend to sound cadence (IAC IAC). more conclusive than imperfect authentic cadences. 6.2
Mozart, Variations Variations on “La Belle Françoise,” Françoise,” K. 353 Imperfect authentic cadence ( cadence (IAC IAC): ): The first ˆ phrase ends with V – I, I, and with 3 in the melody.
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Perfect authentic cadence ( cadence (P PAC AC): ): The second 7 ˆ phrase ends with V – I, I, and with 1 in the melody.
As you will see later, there are some other types of cadences; nevertheless, the HC, PAC, PAC, and IAC are by far the most common. Also, it should be noted that harmonies alone do not determine where cadences occur : cadences appear only at the ends of phrases, which are determined not only by the chords that are used, but also by features of the rhythm and melody. melody.
HARMONIC PATTERNS Compared to the beginning and end, the middle of a phrase offers a wider variety of harmonic possibilities. Choosing the proper order for chords in the middle of phrases can be challenging, and will be a primary focus of Units 3 and 4. As you will see, each chord fits into one of a few possible categories, either Tonic, Dominant, or Subdominant. You already know the terms tonic, subdominant, and dominant to apply to I, and IV, and V, but the categories of Tonic, Dominant, and Subdominant include more than these three chords, as you will see. These basic categories in turn help determine the order in which chords progress. T D T (TONIC DOMINANT TONIC) –
–
–
–
A particularly common pattern patter n involves involves a stable Tonic chord moving to an unstable Dominant and then back to a Tonic (T (T – D – T). Different individual chords belong to the functional categories of Tonic and Dominant. The Tonic chord in the T – D – T progression must be a triad (not a seventh chord), and it can be in root position or (especially if it appears in the middle of a phrase) first inversion (I6; it may not appear appear as 6 6 a second-inversion chord (I 4), since I 4 is an unstable harmony. The Dominant chord may be V, V 7, or (especially if it appears in the middle of a phrase) an inversion (like V 6), as well as other similar harmonies that will be discussed in Unit 3. The Tonic-Dominant-Tonic pattern
6.3
Tonic harmonies: I or 16 (not I I64) Dominant harmonies: such as V, V 7, and V 6 T stability `
D harmonic tension
T resolution
6.4 SOME EXAMPLES OF CHORD PROGRESSIONS THAT FOLLOW THE
T D T P A T T E R N : –
–
4
I – V – I
I – V7–I
I– V6–I
I– V 3 –I6
T DT
T DT
T DT
T DT
–
–
–
–
–
–
–
–
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Within the T – D – T pattern, a chord may repeat or move to another chord within the same category before progressing onward. 6.5
Two or more tonic chords may appear in a row; two or more dominant chords may appear in a row.
6.6
“Let all on Earth their voices voices raise” (from Hymnal of the Episcopal Church)
The chord progressions in this excer pt follow the standard Toniconic-D Dominantominant-T Tonic pattern.
T S D T (TONIC-SUBDOMINANT-DOMINANT (TONIC-SUBDOMINANT-DOMINANT-TONIC) -TONIC) –
–
–
Another harmonic pattern inv involves olves a Tonic chord that moves through a Subdominant chord to a Dominant and back to a Tonic (T (T – S – D – T). Like the Tonic and Dominant categories, the Subdominant category includes a number of chords: IV, IV, ii6, and other chords to be discussed later. 6.7
The Tonic-Subdminant – Dominant-Tonic pattern Tonic: I or 16
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Dominant: V and similar
Subdominant: IV and similar
harmonies, such as
harmonies, such as ii 6
V 7 and V 6
T
S
D
T
stability
leads to dominant
harmonic tension
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6.8 SOME EXAMPLES OF CHORD PROGRESSIONS THAT FOLLOW THE 4
T S D T P A T T E R N : –
–
–
I – IV – V – I
I–ii6– V7–I
I–IV– V 3 –I
I –ii 6 – V – I 6
I–ii6– V6–I
T SDT
T S D T
T S D T
T SDT
T S D T
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
A Subdominant chord may repeat or be follow followed ed by another Subdominant chord before progressing to a Dominant. 6.9
Two or more Subdominant chords may appear in a row.
Although a Subdominant often leads to a Dominant, the reverse is not true: true: in four-part harmony, it is very unusual for a Dominant to move to a Subdominant, as in I – V V – IV IV – I or I – vii vii 6 – ii ii6 – I. I. 6.10
I – V V – IV IV – I T – D – S – T
I – vii vii 6 – ii ii6 – I T – D – S – T
In standard four-par four-partt harmo harmony ny,, a Dominant chord does not move to a Subdominant-type chord. Poor
T – D – T and T – S – D – T do not exhaust the possibilities for harmonic progressions. For instance, another particularly common chord progression is I – IV IV – I (Tonic – Subdominant – Tonic, Tonic, see Chapter 16). Nonetheless, the harmonic structure of most tonal music may be understood as framed by a series of T – D – T and T – S – D – T patterns.
Harmonic Patterns
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Beethoven, Variation Variationss in G, WoO 77
6.11
Phrase begins with I.
Phrase ends with V – I. I. Progressions follow either the T – D – T or T – S – D – T pattern.
MELODY HARMONIZATION One way to enhance your your understanding of harmonic progressions is to harmonize melodies. In a melody harmonization, you are g ive iven n a melody with a simple rhythm and directed to supply a harmony for every note (or almost every note), using standard voice-leading and harmonic procedures. You begin such an exercise by identifying the key and determining the scale degrees of the melody in that key. You then locate the cadences and determine a proper bass line and Roman numerals for the cadences, and finally determine the Roman numerals and bass line for the rest of the harmonies by choosing appropriate chords. Strategies for developing the skills for harmonizing melodies are discussed in detail starting in Unit 3. In each case, the chords chosen for the harmonization must include the notes found in the melody, melody, allowing for good voice-leading and har monic progressions. 6.12
Task: Harmonize this me lody by providing a bass line and Roman numerals.
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The following harmonization of the melody is good: the notes of the melody appear in each of the chords chosen to harmonize them, there are no voice-leading voice-leading errors, and the chord progression follows conventional conventional harmonic practice, with an appropriate chord progression at the cadence. 6.13
(1) melody notes match chosen chords; (2) voice leading is good; (3) uses conventional harmonic progression. Good
After choosing the harmonies and writing the bass line, you can fill in the inner inner voices, paying attention to chord construction (see Chapter 4) and voice leading (see Chapter 5). 6.14
Realization follows proper chord Realization construction and voice leading. Good
MATCHING CHORDS TO THE MELODY
In harmonizing a melody, you must make sure that each note belongs to the chord chosen to harmonize it. 6.15
In C major, V = G – B – D; D; I6 = C – E – G (with E in bass).
The note E (3) 3ˆ ) is not in V. Poor
The note D (2) 2ˆ ) is not in I6. Poor
The note must be part of the chosen chord.
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VO IC E LE AD IN G
In harmonizing a melody, you should follow voice leading and chord construction guidelines, such as avoiding parallel fifths and avoiding doubled leading tones. 6.16
The chords chosen to harmonize the me lody create parallel octaves. octaves.
CONVENTIONAL HARMONIC PROGRESSIONS
Finally, the harmonization should follow conventional Finally, conventional harmonic progressions, using patterns such as T – D – T or T – S – D – T and ending each phrase with a cadence. 6.17
Use T – D – T and T – S – D – T Use T patterns and end with a cadence.
Progression mov moves es from a Dominant to a Subdominant chord (ii6). Poor
Phrase ends on IV instead of root-position V or I. Poor
review and interact POINTS FOR REVIEW • Phrases most often begin with a root-position I chord, and end with a cadence on either a root-position r oot-position V, V, or a root-position V (or V 7) that leads to a root-position I. • A cadence ending on a root-position V is known as a half cadenc cadence e ( HC). (HC ). • A cadence that ends V – I or V7 – I is known as an authentic cadence ( cadence (AC AC). ). An authentic cadence that ends with 1ˆ in the soprano is a perfect authentic cadence (PAC AC); ); an authentic cadence that ends with 3ˆ or 5ˆ in the melody is an imperfect authentic cadence ( cadence IAC). (IAC ).
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• The ordering of harmonies within a phrase follows conventional progressions, including Tonic – Dominant – Tonic (T (T – D – T) and Tonic – Subdominant – Dominant – Tonic (T (T – S – D – T). • Chords in the Tonic category are I and I6; chords in the Dominant category include V, V7, and V6; chords in the Subdominant category include IV and ii 6. • In a good melody harmonization, the chord chosen for each note of the melody should include the melody note, conform to voice-leading guidelines, and result in a chord progression that follow followss the conventions of harmony harmony..
TEST YOURSELF 1.
In the examples below, below, do the phrases (each ending is marked by a fermata) end with PACs, IACs, or HCs?
2.
Why are the following phrase endings (indicated by fermatas) not conv conventional entional cadences?
3.
Which of the following follow a Tonic – Dominant – Tonic chord progression, which follow a Tonic – Subdominant – Dominant – Tonic progression, and which follow neither? (a) I – V V – I
(b) I – I – V V – V V6 – I
(c) I – V V – IV IV – I
(d) I – ii ii6 – V V – I
Melody Harmonization
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4.
Which of the following are good harmonizations of the given melodies? If the harmonization is not good, what is the p roblem with it?
Know It? Show It! Focus by by working through the tutorials on: • Recognizing cadences • Understanding standard harmonic patterns • Harmonizing melodies Learn with inQuizitive. inQuizitive. Apply what you’v you’vee learned to complete the assignments: • Beginning and Ending a Phrase • Melody Harmonizations: Preparatory Exercises • Harmonic Functional Categories: T, T, S, D
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r e t p a h c
12 6
6 V 5 and
4
V 5 and V 2 are inversions of V 7 that embellish tonic harmony: 6 4 V 5 leads to I, V 2 leads to I 6. Harmonic Progressions 6
Voicee Lead Voic L eading ing in FourFour-Part Part Har Harmon monyy
4
V 5 and V 2 as Embellishing Harmonies
Figured Bass
HARMONIC PROGRESSIONS V 65 and V 42 are the first and third inversions of V 7, respectively re spectively.. 12.1
V 65 and V 42 are inversions of V 7.
Like other Dominant harmonies, V 65 and V 42 lead toward the tonic chord. Since the leading tone is in the bass of V 65 and must resolve up by step, V 65 resolves to I in root position (I), not first first inversion (I6). Similarly, Similarly, since the chordal c hordal seventh seventh in the bass of V 4 4 to I in root position. 2 must resolve down by step, V 2 resolves to I6, not to
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4 V 2
12.2
Haydn, Sonata in C, Hob. XVI:35, i V 65 and V 42 are Dominant harmonies that lead to Tonic (I or I6) with stepwise motion in the bass.
V 65 leads to I, as the leading tone in the bass resolves up.
V 42 leads to I 6, as the chordal 7th in the bass resolves down.
Poor
V 65 may not move to I6.
Poor
V 42 may not move to I.
V 65 may follow any of the harmonies discussed in the previous chapters (I, I6, V, V 7, and V 6). 12.3
Beethoven, Symphony No. 9, iii
V 65 may follow V or V 6.
V 65 also may lead to V 7 in root position or in inversion. V 65 may not be directly followed by V or V 6, however, since if it did its chordal seventh would not be able to resolve down by step.
Harmonic Progressions
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12.4
Handel, Violin Violin Sonata in E, HWV 373, 373, iii
V 65 may followed by V 7.
Poor
12.5
V 65 may not be be followed by a V triad.
V 42, too, may follow follow any of the harmonies discussed in the previous chapters. It is especially common for V 42 to follow root-position V. V 42 should not precede another dominant harmony, harmony, however: however: the chordal seventh in the bass is so prominent that V 4 2 should resolve directly to I6. 12.6
Haydn, Menuett, Hob. IX:11/2
V 42 may follow another V or V 7 chord.
12.7
V to V 42 — resulting resulting from a passing tone in the bass — is is very common. Good
6
Poor
V 42 may not be be followed by
V or V 7; V 42 must lead straight to I 6.
4
V 5 A N D V 2 A S E M B E L L I S H I N G H A R M O N I E S The bass motions involving V 65 – I and V 42 – I6 often resemble neighbor-tone or incomplete neighbor-tone motions. This is because V 65 and V 42 are relatively unstable tonally and their basses resolve by step to notes of the tonic triad. Thus, much as neighbor or incomplete neighbor tones embellish a g iven note, note, so V 65 and V 42 may be regarded as embellishing a Tonic harmony. 132
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12.8
Similarly, these V 65 and V 42 chords embellish the I and I 6, to which they resolve by step in the bass.
12.9
Haydn, Variations faciles
The stepwise motions in the bass of V 65 – I and V 42 – I6 embellish the tonic harmony. harmony.
Like other inversions of tonic and dominant harmonies, V 65 and V 42 may be used anywhere within the phrase except for the cadence, where V or I is required. Indeed, since a cadence must involve involve root-position dominant or tonic, inversions earlier within the phrase are extremely helpful in promoting variety and providing an interesting bass line.
as Embellishing Harmonies
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12.10 Good Embellishing harmonies appear at the beginning and middle of the phrase; V and I in root position appear at the cadence.
Root-position V – I motions are overused in the first parts of the phrase; inverted chords appear at the cadence. Poor
V O I C E L E A D I N G I N F O U R - P A R T H A R M O N Y In four-part harmony the upper voices typically move move smoothly within V 65 – I and V 42 – I6 progressions, with the chordal seventh resolving down by step and the leading tone resolving up by step. Usually none of the notes (not even the chordal fifth) of V 65 or V 42 is omitted in four-part harmony, and thus usually none of the notes in the chord is doubled. 12.11
Upper voices usually move move by step or common tone in V 65 – I and V 42 – I6 progressions.
Progressions that alternate V 65 – I and V 42 – I6 are common, and often feature voice exchanges with the melody, embellishing the tonic harmony.
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V 42 – I6 may also support a leap in the melody moving in contrary motion to the bass.
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FIGURED BASS 6
In figured bass, V 65 is indicated either with the numbers 53 or (more commonly) 65 placed below the leading tone in the bass. Note that the fifth above the bass in this case is diminished, not perfect: however, as always, you should assume that a note needs no accidental unless an accidental is expressly indicated by the figures. 12.12
The hese se fig figur ures es . . .
may ma y be re real aliz ized ed li like ke th this is . . .
. . . bu butt no nott li like ke th this is!!
Unless indicated by the figures, do not raise 5 above the bass to create a perfect 5th. Poor
6
V 42 in figured bass is indicated either with the figures 42 or (more commonly) 42 placed below 4ˆ in the bass. The fourth above above the bass of V 42 is a leading tone and thus must be raised in minor keys. In figured bass, this raising of the fourth above above the bass is indicated by placing a sharp or natural next to the number 4, or else with a diagonal slash through or plus sign or attached to the number 4. 12.13
This figured bass in C major . . .
may be realized . . .
In A minor, a sharp is required . . .
while C minor requires a natural.
The sharp or natural sign next to, a slash through, or a plus sign attached to the 4 indicates that this interval above the bass is to be raised.
Figured Bass
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review and interact POINTS FOR REVIEW • V65 and V 42 are inversions of V 7; they are Dominant harmonies. • V65 resolves to I; V 42 resolves to I6. • V65 may follow another Dominant harmony. V 65 may also be followed directly by V 7 or an inversion of V7, but it may not be be followed by V or V 6. • V42 may follow another Dominant harmony. V 42 may not be be followed by by another V or 7 6 V , however, however, but rather must resolve directly to I . • Do not use V 65 or V42 at cadences.
TEST YOURSELF 1.
In the example below: Label the chord with a Roman numeral in the key indicated.
a.
2.
b.
Which of the following Tonic harmonies could follow this chord: I or I6? Which of the following Dominant harmonies could follow this chord (choose all that apply): V, V, V 6, 4 V 7, or V 2?
c.
Which of the following harmonies could precede the chord (choose all that apply): I, I6, V, V 7, or V 42?
In the example below: a.
Label the chord with a Roman numeral in the key indicated.
b.
Which of the following harmonies could follow this chord (choose all that apply): I, I6, V, V 6, or V 7?
c.
Which of the following harmonies could precede the chord (choose all that apply): i, i6, V, V 7, or V 65?
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CHAPTER 12
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3.
Below is a melodic phrase in D major. a.
4.
Which of the asterisked notes could be harmonized with V 65? Which of the asterisked notes could be harmonized V 42? (Hint: the chord chosen should not create a poor doubling.)
b.
What harmonies should you use in m. 4?
c.
In which measure could you place a voice exchange between the bass and melody?
What notes are in the following chords, as indicated by the figured basses?
Know It? Show It! Focus by by working through the tutorials on: • Writing and resolving V 65 and V 42 • Realizing figured bass with V 65 sand V 42 Learn with inQuizitive. inQuizitive. Apply what you’v you’vee learned to complete the assignments: • Spelling Chords
• Melody Harmonization
• Realizing Roman Numerals
• Composition
• Realizing Figured Bass
• Analysis
• Error Identification
review and interact
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