II. Diatonic Polyphony and Functional Harmony

# 19.1 Introduction

In Chapter 18 we discussed the various types of seventh chords that one encounters in tonal Western art music. One of these types occurs far more frequently than any of the others: the major-minor seventh chord, typically built on scale degree $\hat5$. In this chapter, you will learn about the dominant-seventh chord, its inversions, and the characteristic voice-leading one encounters as it resolves by falling-fifth root motion to the tonic.

# 19.2 Construction

The dominant seventh chord is constructed by adding a diatonic seventh (scale degree $\hat4$) to the dominant triad.

The following example shows a dominant seventh chord in C major in an SATB setting:

The construction of the V7 is the same in minor:

As with Example 19–1, Example 19–3 shows the construction of the dominant seventh chord as a major triad on scale degree $\hat5$ with an added diatonic seventh. Remember the necessary leading-tone adjustment for scale degree $\hat7$ in dominant chords in minor keys (G to G# in this case). The following example shows a dominant seventh chord in A minor in SATB setting:

Activity 19-1

Activity 19–1

Each of the following V7 chords is presented in SATB setting and is missing one note. Provide the missing note as directed for each of the exercises.

### Question

What pitch in the alto voice will complete this V7 chord in F major?

Hint

This V7 chord is missing scale degree $\hat7$.

E

### Question

What pitch in the soprano voice will complete this V7 chord in C minor?

Hint

This V7 chord is missing scale degree $\hat4$.

F

### Question

What pitch in the bass voice will complete this V7 chord in A major?

Hint

This V7 chord is missing scale degree $\hat5$.

E

### Question

What pitch in the tenor voice will complete this V7 chord in B minor?

Hint

This V7 chord is missing scale degree $\hat7$.

A#

Activity 19-2

Activity 19–2

In this activity, you will build V7 chords in various keys starting with the root.

### Question

What is the root of a V7 chord in G major?

Hint

Remember, the root of a V7 chord is scale degree $\hat5$.

D

### Follow-up question

Complete the V7 chord by adding the upper voices.

Upper voices should consist of F#, A, and C.

### Question

What is the root of a V7 chord in G minor?

Hint

Remember, the root of a V7 chord is scale degree $\hat5$.

D

### Follow-up question

Complete the V7 chord by adding the upper voices. (Remember to raise the leading tone in minor keys.)

Upper voices should consist of F#, A, and C.

### Question

What is the root of a V7 chord in Eb major?

Hint

Remember, the root of a V7 chord is scale degree $\hat5$.

Bb

### Follow-up question

Complete the V7 chord by adding the upper voices.

Upper voices should consist of D, F, and Ab.

### Question

What is the root of a V7 chord in E minor?

Hint

Remember, the root of a V7 chord is scale degree $\hat5$.

B

### Follow-up question

Complete the V7 chord by adding the upper voices. (Remember to raise the leading tone in minor keys.)

Upper voices should consist of D#, F#, and A.

# 19.3 Tendency tones in the V7 chord

There are two strong tendency tones in the V7 chord: scale degrees $\hat7$ and $\hat4$. These two tendency tones form a tritone—a dissonance that requires resolution.

Activity 19-3

Activity 19–3

It is important that you be able to recognize the tendency tones present in a V7 chord and treat them accordingly. In this activity, you will identify the tendency tones and the interval they form.

### Question

Identify the two tendency tones in the following V7 chord (scale degrees $\hat7$ and $\hat4$):

G# and D

### Follow-up question

What interval do these two tendency tones form?

G# and D form a diminished fifth (d5).

### Question

Identify the two tendency tones in the following V7 chord (scale degrees $\hat7$ and $\hat4$):

A and Eb

### Follow-up question

What interval do these two tendency tones form?

A and Eb form a diminished fifth (d5).

### Question

Identify the two tendency tones in the following V7 chord (scale degrees $\hat7$ and $\hat4$):

E# and B

### Follow-up question

What interval do these two tendency tones form?

E# and B form an augmented fourth (A4).

### Question

Identify the two tendency tones in the following V7 chord (scale degrees $\hat7$ and $\hat4$):

F# and C

### Follow-up question

What interval do these two tendency tones form?

F# and C form a diminished fifth (d5).

Scale degree $\hat7$, the leading tone, pulls strongly upward toward scale degree $\hat1$, which is only a half step away. (Despite this strong pull, the voice containing the leading tone does not always resolve directly to the tonic. These exceptional cases are discussed below.) Scale degree $\hat4$, the other tendency tone, pulls strongly downward to $\hat3$, its half-step neighbor. These dual tendencies create an urgent need for resolution in a dominant seventh chord. The following example demonstrates the conventional resolutions of tendency tones $\hat4$ and $\hat7$ to $\hat3$ and $\hat8$:

In this case, the augmented fourth formed by $\hat4$ and $\hat7$ resolves outward to a sixth.

Note: You may wish to refer back to the chapter off viio chords (Chapter 16) where tritone interval progressions are explored in greater depth. It is worth pointing out, too, that a V7 chord takes all of the pitches of a viio chord and adds scale degree $\hat5$. Because these two chords are so similarly constructed, they are often found in similar contexts and function in similar ways.

Activity 19-4

Activity 19–4

In this activity, you will resolve the tendency tones from the V7 chords of the previous chapter.

### Question

Resolve the two tendency tones in the following V7 chord:

Hint

Remember, scale degree $\hat7$ tends to resolve to $\hat1$, and scale degree $\hat4$ tends to resolve to $\hat3$.

### Question

Resolve the two tendency tones in the following V7 chord:

Hint

Remember, scale degree $\hat7$ tends to resolve to $\hat1$, and scale degree $\hat4$ tends to resolve to $\hat3$.

### Question

Resolve the two tendency tones in the following V7 chord:

Hint

Remember, scale degree $\hat7$ tends to resolve to $\hat1$, and scale degree $\hat4$ tends to resolve to $\hat3$.

### Question

Resolve the two tendency tones in the following V7 chord:

Hint

Remember, scale degree $\hat7$ tends to resolve to $\hat1$, and scale degree $\hat4$ tends to resolve to $\hat3$.

There remain, however, two other notes in the V7 chord: the root ( $\hat5$) and the fifth ( $\hat2$). These two voices, forming a perfect fifth in the V7 chord, usually resolve in similar motion to an octave. This 5–8 motion is one of the basic interval progressions outlined in Chapter 12. The following example shows the basic interval progressions in the upper and lower voice pairs:

As described in Chapter 12, four-part harmony is an extension of three-part harmony which, in turn, is built from combinations of basic interval progressions. The voice leading in Example 19–7 can be explained in this manner. The outer voices form the primary interval progression of a third expanding to an octave. The tenor, then, supports the soprano with a 6–8 progression and the alto harmonizes with the tenor in parallel thirds (3–3). Looking at the progression this way, we can see that the augmented fourth between the alto and soprano is a resultant interval.

In the example above, you might have noticed that the resolution chord has three roots, a third, and no fifth. This voicing of the I chord is common at the end of a musical idea. This type of voice-leading, with both chords in root position, provides a strong sense of repose and, thus, closure.

Examples 19–5 through 19–7 show the resolution of a V7 chord in C major. The same rules apply to dominant seventh chords in minor keys. Example 19–8 shows a V7 chord in C minor resolving to the tonic harmony:

Note that all the same voice-leading patterns appear: the augmented fourth (tritone) formed by F and B§ resolves outward to a sixth (a major sixth in minor, because scale degree $\hat4$ must now resolve a whole-step down to $\hat3$), $\hat2$ resolves stepwise to $\hat1$, and $\hat5$ leaps down to $\hat1$.

Note: Incomplete chords such as those shown in Example 19–7 and Example 19–8 are common in progressions moving from the dominant to the tonic. Generally speaking, though, composers tend to avoid two incomplete chords in a row. In other words, incomplete V chords are usually followed by complete I chords and incomplete I chords usually come after complete V chords.

Activity 19-5

Activity 19–5

In this exercise, you will complete the resolution of the previous activities to the I chord.

### Question

Taking your answer from the previous activity, complete the resolution to the I chord by providing pitches for the bass and alto:

Hint

Remember, both scale degrees $\hat2$ and $\hat5$ will resolve to $\hat1$ as V7 moves to I.

### Question

Taking your answer from the previous activity, complete the resolution to the I chord by providing pitches for the bass and soprano:

Hint

Remember, both scale degrees $\hat2$ and $\hat5$ will resolve to $\hat1$ as V7 moves to I.

### Question

Taking your answer from the previous activity, complete the resolution to the I chord by providing pitches for the bass and tenor:

Hint

Remember, both scale degrees $\hat2$ and $\hat5$ will resolve to $\hat1$ as V7 moves to I.

### Question

Taking your answer from the previous activity, complete the resolution to the I chord by providing pitches for the bass and tenor:

Hint

Remember, both scale degrees $\hat2$ and $\hat5$ will resolve to $\hat1$ as V7 moves to I.

The voice-leading conventions described above are extremely common, even in non-SATB textures. Consider the following example:

There are two instances of V7 resolving to I in this excerpt and in both cases the chord members resolve as expected. In m. 2, the tritone-forming pitches (D and Ab ) are found in the right hand of the piano part and resolve inward to form a third. (The upper part of this progression is doubled in the upper vocal line.) Scale degree $\hat5$ appears in the bass and leaps up to Eb while scale degree $\hat2$ resolves down by step to the tonic in the lower vocal line. The same voice-leading appears in m. 3, though here several small adjustments have been made: the bass leaps down instead of up and the common tone Bb is sustained as V7 resolves to I. (Note, too, that the penultimate note in the upper vocal line—a Bbreaks up the parallel octaves with the top notes of the piano part.)

# 19.4 Inversions

The V7 chord often appears in inversion. While the preferred resolutions of the tendency tones generally remain the same regardless of the position of V7, the resolution of $\hat5$ and $\hat2$ vary somewhat, depending on context. Consider the following example, where a dominant seventh chord in first inversion resolves to the tonic triad:

In this example, both tendency tones resolve as expected: $\hat7$ to $\hat1$ in the bass and $\hat4$ to $\hat3$ in the soprano. As in Example 19–7, $\hat2$ resolves to $\hat1$. In this case, however, because the root of the V7 chord ( $\hat5$) is not in the bass, it is sustained as a common tone between the two chords. Because of its smoothness, this is the preferred voice-leading.

The resolution of the dominant seventh in second inversion follows the same voice-leading patterns as Example 19–10: $\hat2$ resolves to $\hat1$ (now in the bass), $\hat5$ is held as a common tone, and the tendency tones resolve as expected:

Example 19–12 shows the resolution of the remaining position of the dominant seventh chord:

The third inversion of the dominant seventh chord is a special case. In a V4/2, the chordal seventh is exposed in the bass. This makes it very audible and therefore powerful. Consequently, it is generally reserved for circumstances where heightened musical expression is appropriate. Because of the tendency of $\hat4$ to resolve to $\hat3$, the chord of resolution is necessarily in first inversion (I6). It should be noted that V4/2 moving to I6 is the least stable formation of the common V7–I progression and therefore typically leads to more music instead of ending a musical thought.

Note: Conventions for resolving V7:

1. The tendency tones typically resolve as expected with $\hat7$ moving to $\hat1$ and $\hat4$ moving to $\hat3$,
2. similarly, $\hat2$ tends to resolve to $\hat1$, and
3. $\hat5$ is typically held to promote smooth voice-leading (this is possible in every inversion of the dominant seventh, but not in root position where the bass must leap from $\hat5$ to $\hat1$).
Activity 19-6

Activity 19–6

So far in this chapter, the activities have focused on resolving dominant seventh chords in root position. Dominant seventh chords frequently appear in inversion, however, and it is important that you be able to resolve these chords as well. In this activity, you will resolve an inverted dominant seventh chord according to the guidelines outlined above.

### Question

Identify the leading tone in the following V6/5 chord:

D (bass)

### Follow-up question

Resolve the leading tone according to the guidelines outlined above.

Hint

Remember, the leading tone tends to resolve to the tonic.

### Question

Now identify the tendency tone (scale degree $\hat4$):

A (tenor)

### Follow-up question

Resolve scale degree $\hat4$ according to the guidelines outlined above.

Hint

Remember, scale degree $\hat4$ tends to resolve to scale degree $\hat3$.

### Question

Because this dominant seventh chord is in inversion, we can retain the root as a common tone as we resolve to I. Identify the root of the following V6/5 chord:

Bb (soprano)

### Follow-up question

Hold the root as a common tone into the I chord.

Hint

Remember, because the dominant seventh chord is in inversion, we can retain the root as a common tone into the I chord.

### Question

Now there is only one voice to be resolved. Resolve scale degree $\hat2$ according to the guidelines outlined above.

Hint

Remember, scale degree $\hat2$ tends to resolve to the tonic.

The following example shows a pair of dominant seventh chords in different positions resolving in a conventional manner to the tonic:

In Example 19–13 we see two dominant sevenths resolving to the tonic: first a V4/2 in m. 2 and then a V6/5 in m. 6. In both cases, the chordal seventh (C) resolves down by step to scale degree 3 (Bb), the leading tone (F# ) resolves up by step to scale degree $\hat1$ (G), and the common tone (D) is sustained. The only difference between the two resolutions is that scale degree $\hat2$ (A) leaps up to $\hat5$ (D) in mm. 2-3 but steps down to $\hat1$ (G) in m. 6.

The following excerpt also features several dominant sevenths, though here the resolutions break with convention:

In this excerpt, we find three dominant sevenths resolving to the tonic: a V4/3 in the pickup measure, a V6/5 in m. 2, and a root-position V7 in m. 3. Of the three resolutions, the V6/5 moving to I is the most conventional. In the other two resolutions, the chordal seventh (Ab) is found resolving up by step to scale degree $\hat5$ (Bb). In non-SATB settings such as this, one often encounters composers going against the conventions outlined above. The voice-leading described earlier in this chapter is far more common, but one should keep in mind that it is not universal.

# 19.5 Other leading tone resolutions

Despite the strong upwards pull on the leading tone, there are occasions where it does not resolve to scale degree $\hat1$. Consider the following resolution of V7 to I:

In this case, the alto has $\hat7$ in the V7 chord. Instead of moving as expected to $\hat1$, the alto leaps down to $\hat5$. This is permissible for two reasons. Most importantly, the soprano begins on $\hat2$, just above the leading tone in the alto. When the soprano resolves downward from $\hat2$ to $\hat1$, we hear the alto’s leading tone as if resolving to the same $\hat1$. With the soprano acting as a surrogate resolution for the leading tone, the alto is free to leap to $\hat5$.

The result of this $\hat7$ to $\hat5$ motion is a complete triad in the resolution. Whereas in Example 19–7, the dominant seventh resolved to a I with three roots, a third, and no fifth, Example 19–15 illustrates resolution to a fuller sonority.

Occasionally, as in the following two examples, the leading tone leaps to a pitch other than scale degree $\hat1$ without another voice fulfilling the surrogate duty:

In Example 19–16, the tenor has the leading tone (B) in the V chord at m. 8. Instead of resolving upwards to scale degree $\hat1$ (C), the tenor leaps down to scale degree $\hat5$ (G). This is very similar to Example 19–15 but in this case, the voice immediately above (the alto) is not acting as a surrogate resolution to $\hat1$. Instead, the soprano resolves to the necessary C, but an octave higher! In Example 19–17, the tenor has the leading tone (G#). In this case, the leading tone jumps up to scale degree $\hat3$ (C#). As in Example 19–16, the missing tonic appears an octave higher in the soprano. In either case, the unresolved leading tone appears in an inner voice where it is not so easily noticed.

Note: Typically, the tendency tone $\hat7$ is required to resolve to $\hat1$ in a V7 chord. Occasionally, however, the voice singing $\hat7$ may leap to $\hat3$ or $\hat5$. Sometimes, as in Example 19–15, another voice can act as a surrogate resolution. However, as Examples 19–16 and 19–17 illustrate, this surrogate resolution need not always be in the correct register.

It should be noted that these resolutions—particularly the progression in Example 19–17—are far less common that those in which the leading tone resolves up by step. As a rule of thumb, you should use them in your own partwriting exercises only when necessary.

# 19.6 Summary

In this chapter we have discussed the various configurations of one of the most important harmonic idioms in tonal music: V7 to I. The voice-leading of these various configurations is determined primarily by the presence of tendency tones $\hat7$ and $\hat4$, as well as a preference for smoothness in voice-leading to the resolution. The dominant seventh chord may appear in any of its four positions, each of which leads to characteristic resolutions. While the conventions for resolution have been given here as simplified rules, it is important to remember that basic interval progressions and dissonance treatments are still the guiding criteria of voice-leading.