II. Diatonic Polyphony and Functional Harmony

# 18.1 Introduction

If we compare the act of musical composition to cooking, we may think of triads as being analogous to the basic ingredients in a dish. A good chef can produce a delicious meal using just a few simple ingredients and a composer can write a compelling piece of music using only triads. Occasionally, however, both chef and composer might require something a little more exciting. A chef might add some flavorful spices to a dish and a composer might add some extra pitches to their triads, thereby broadening the range of expressive sonorities.

A seventh chord consists of a triad with an added pitch sounding a seventh above the root. Because seventh chords contain four distinct pitches and by definition include a dissonant seventh, they offer richer harmonies than their triadic counterparts. It is this very dissonance, however, that makes the voice-leading of seventh chords a matter requiring special attention.

This chapter will present the various categories of seventh chords and familiarize you with their construction. A more specific discussion follows, touching on the commonly used seventh chords and the reasons why other seventh chords are not used.

# 18.2 Construction and types of seventh chords

Seventh chords are built by extending triadic construction to include a fourth voice. A triad consists of two stacked thirds. A seventh chord simply adds a diatonic third above the fifth of the triad—or, in other words, a seventh above the root. In the following example, a D-minor triad becomes a seventh chord with the addition of the pitch C:

Whereas a triad may be consonant, a seventh chord is inherently dissonant. The added pitch forms a seventh with the root of the chord and must be treated carefully. We will return to this matter shortly.

The following examples show the diatonic seventh chords of C major and C minor respectively. Like triads, the quality of a seventh chord built on any particular scale degree depends on whether the key is major or minor. (Note that in Example 18–3 we use the harmonic minor for the chords built on scale $\hat5$ degrees and $\hat7$. For more information on the harmonic minor, refer to Chapter 16.)

As you can see from Examples 18–2 and 18–3, the Roman numerals used to label seventh chords are the same as those of the corresponding triads (which are shown with open noteheads in each chord). To distinguish a seventh chord label from that of a triad, we add a 7 to the right of the Roman numeral and understand that it is shorthand for 7/5/3. I7 refers to the diatonic seventh chord built on scale degree $\hat1$, ii7 to the chord built on $\hat2$, and so on.

Activity 18-1

Activity 18–1

In this activity, you will be presented with a triad in SATB setting. Change one of the pitches in the upper voices to transform the triad into a seventh chord. Then, identify the seventh chord with Roman numerals.

### Question

Move one of the upper voices to change the triad into a seventh chord:

The soprano should be changed from F# to E.

### Follow-up question

Give this new chord a Roman numeral.

iiø7

### Question

Move one of the upper voices to change the triad into a seventh chord:

The soprano should be changed from F to Eb.

### Follow-up question

Give this new chord a Roman numeral.

V7

### Question

Move one of the upper voices to change the triad into a seventh chord:

The alto should be changed from E to D.

### Follow-up question

Give this new chord a Roman numeral.

V7

### Question

Move one of the upper voices to change the triad into a seventh chord:

The soprano should be changed from G# to F#.

### Follow-up question

Give this new chord a Roman numeral.

viiø7

Below each line of Roman numerals in Examples 18–2 and 18–3 is another line of letters and symbols. These markings indicate the intervallic content of the chord and in doing so describe the quality. For the chords labeled with letters, the first describes the quality of the triad (“M” for a major triad; “m” for a minor triad) and the second indicates the quality of the seventh (again, “M” for a major seventh; “m” for a minor seventh). You will find two other symbols as well. These symbols are used for seventh chords built on diminished triads: ø indicates a half-diminished seventh chord (a diminished triad with a major seventh) and o indicates a fully-diminished seventh chord (a diminished triad with a minor seventh). The following table summarizes the various types of commonly encountered seventh chords:

Table 18–1.
Name: Quality of Triad: Quality of Seventh: Symbol:
major-major seventh chord major major MM
major-minor seventh chord (see note) major minor Mm
minor-minor seventh chord minor minor mm
half-diminished diminished minor ø7
fully-diminished diminished diminished o7

Note: The major-minor seventh chord is a special case in tonal Western art music. It has a distinctive sound and most listeners associate this particular quality with chords built specifically on the dominant scale degree ( $\hat5$). For this reason, the term “dominant seventh chord” is often used interchangeably with “major-minor seventh chord.”

Activity 18-2

Activity 18–2

In this activity, you will examine the intervallic content of various seventh chords by identifying the quality of the triad and the quality of the seventh. (For each question, the options for triad quality are “major,” “minor,” and “diminished.” The options for seventh quality are also “major,” “minor,” and “diminished.”)

### Question

The quality of the triad is          . The quality of the seventh is          .

The viio7 chord in G minor is a fully-diminished seventh chord. The triad is diminished and the seventh is also diminished.

### Question

The quality of the triad is          . The quality of the seventh is          .

The IV7 chord in G major is a major-major seventh chord. The triad is major and the seventh is also major.

### Question

The quality of the triad is          . The quality of the seventh is          .

The V7 chord in C minor is a major-minor seventh chord. The triad is major and the seventh is minor.

### Question

The quality of the triad is          . The quality of the seventh is          .

The ii7 chord in D minor is a minor-minor seventh chord. The triad is minor and the seventh is also minor.

# 18.3 Inversions of seventh chords

As with triads, seventh chords may also be written in inversion. Because there are four distinct pitches in a seventh chord, there are, accordingly, four possible positions (determined, again, by the bass note). The following example shows the four positions of a seventh chord built on D:

As with triads, inverting a seventh chord alters the intervallic relationships between the upper voices and the bass. The notation for labeling seventh chords indicates the intervals formed with the bass, although abbreviated notation is often used. For example, a seventh chord in first inversion contains the intervals of a sixth, a fifth, and a third above the bass. As with triads, the figures for seventh chords are often abbreviated. Rather than write three numerals every time (6/5/3), the convention is to assume the third and simply write: 6/5. The following table summarizes the figured-bass signatures of the inversions of seventh chords, and gives the notational short hand in the rightmost column:

Table 18–2.
Position Chord Member in the Bass Intervallic Content Figured Bass Short Hand
root position

root 7/5/3 7
first inversion

third 6/5/3 6/5
second inversion

fifth 6/4/3 4/3
third inversion

seventh 6/4/2 4/2 or 2
Activity 18-3

Activity 18–3

In this activity, you will be presented with a series of seventh chords in SATB setting. For each exercise, choose the appropriate figured bass signature (7, 6/5, 4/3, or 4/2) to represent the inversion of the chord.

### Question

Which figured bass signature would be used to represent this chord?

Hint

Remember the common abbreviations for figured bass signatures. Only one of the four options makes sense with the given intervals above the bass.

7

### Question

Which figured bass signature would be used to represent this chord?

Hint

Remember the common abbreviations for figured bass signatures. Only one of the four options makes sense with the given intervals above the bass.

6/5

### Question

Which figured bass signature would be used to represent this chord?

Hint

Remember the common abbreviations for figured bass signatures. Only one of the four options makes sense with the given intervals above the bass.

4/3

### Question

Which figured bass signature would be used to represent this chord?

Hint

Remember the common abbreviations for figured bass signatures. Only one of the four options makes sense with the given intervals above the bass.

4/2

As shown above, figured bass for seventh chords may be combined with Roman numerals. The following example adds Roman numerals in C major to the seventh chords shown in Example 21–13 and uses the common figured-bass abbreviations from Table 18–2:

Since the seventh chords in Example 18–4 are built on D (scale degree $\hat2$ in C major), they are given the Roman numeral ii. In each case, the four notes are written as closely as possible on the staff. The following example, on the other hand, shows the four positions voiced in SATB format, spaced out across a grand staff:

Note that each chord shown in Example 18–6 is just one possible voicing. Many other voicings are possible for each inversion.

Activity 18-4

Activity 18–4

In this activity, you will be asked to identify various seventh chords and their inversions.

### Question

What Roman numeral should appear in place of the question mark? Be sure to indicate the inversion in your answer.

Hint

In this key, which scale degree is the root of the chord? Which member of the chord is in the bass?

iiø6/5

### Question

What Roman numeral should appear in place of the question mark? Be sure to indicate the inversion in your answer.

Hint

In this key, which scale degree is the root of the chord? Which member of the chord is in the bass?

V6/5

### Question

What Roman numeral should appear in place of the question mark? Be sure to indicate the inversion in your answer.

Hint

In this key, which scale degree is the root of the chord? Which member of the chord is in the bass?

viio7

### Question

What Roman numeral should appear in place of the question mark? Be sure to indicate the inversion in your answer.

Hint

In this key, which scale degree is the root of the chord? Which member of the chord is in the bass?

V4/2

Activity 18-5

Activity 18–5

In this activity, you will build various types of seventh chords in different keys.

### Question

Write a viio7 chord in E minor in four-part SATB voicing.

D# in the bass with F#, A, and C in the upper voices in any arrangement.

### Question

Write a iiø6/5 chord in G minor in four-part SATB voicing.

C in the bass with A, Eb, and G in the upper voices in any arrangement.

### Question

Write a V4/3 chord in A major in four-part SATB voicing.

B in the bass with E, G#, and D in the upper voices in any arrangement.

### Question

Write a V4/2 chord in Bb major in four-part SATB voicing.

Eb in the bass with F, A, and C in the upper voices in any arrangement.

# 18.4 Preparing and resolving seventh chords

As mentioned earlier, the characteristic feature of a seventh chord is the dissonant seventh formed with the root. This dissonance is unstable and requires resolution. Chordal sevenths almost invariably resolve down by step. This can be explained by considering the origin of the seventh chord. Example 18–5 shows a common cadential pattern where the octave above the bass in the V chord (scale degree $\hat5$) steps down through a passing tone to scale degree $\hat3$. Over time, this passing tone became incorporated into the chord (as shown by the arrow).

In the previous section we saw that seventh chords can be categorized according to their intervallic content. However, not all seventh chords are treated equally. Seventh chord built on scale degree $\hat1$, for example, are rare as the dissonant seventh would undermine the stability of the tonic triad. When a I7 chord does occur, it is usually the result of a melodic phenomenon and should be analyzed as a triad with a nonharmonic tone. Seventh chords built on scale degrees $\hat2$, $\hat3$, $\hat4$, $\hat5$, $\hat6$, and $\hat7$, occur more frequently in tonal music and the rules for approaching and resolving them are similar.

The following example shows a typical progression involving a seventh chord—in this case, a ii6/5 chord:

Note that the seventh of the ii6/5 chord (C in the soprano voice) is prepared as a common tone by the preceding I chord. As described above, the seventh of a seventh chord is a dissonance and typically originates as a melodic event. In this case, the C sounds and resolves like a suspension. The preparation of a chordal seventh as a common tone with the preceding harmony provides smooth voice leading into a seventh chord. Stepwise motion to the chordal seventh is a common alternative, and frequently appears when common-tone preparation is impossible. Chordal sevenths are seldom approached by leap as this would overemphasize the dissonance.

Activity 18-6

Activity 18–6

In this activity, you will be asked to complete a progression from I to ii6/5.

### Question

In the following example, which voice will contain the seventh of the ii6/5 chord?

Hint

Remember that the seventh of the ii6/5 chord should be prepared as a common tone if possible.

The tenor will prepare the seventh of the ii6/5 as a common tone G from the I chord:

### Follow-up question

Complete the ii6/5 by adding the two remaining voices.

### Question

In the following example, which voice will contain the seventh of the ii6/5 chord?

Hint

Remember that the seventh of the ii6/5 chord should be prepared as a common tone if possible.

The soprano will prepare the seventh of the ii6/5 as a common tone Eb from the I chord:

### Follow-up question

Complete the ii6/5 by adding the two remaining voices.

### Question

In the following example, which voice will contain the seventh of the ii6/5 chord?

Hint

Remember that the seventh of the ii6/5 chord should be prepared as a common tone if possible.

The soprano will prepare the seventh of the ii6/5 as a common tone A from the I chord:

### Follow-up question

Complete the ii6/5 by adding the two remaining voices.

### Question

In the following example, which voice will contain the seventh of the ii6/5 chord?

Hint

Remember that the seventh of the ii6/5 chord should be prepared as a common tone if possible.

The alto will prepare the seventh of the ii6/5 as a common tone F from the I chord:

### Follow-up question

Complete the ii6/5 by adding the two remaining voices.

Seventh chords typically resolve by falling-fifth (or rising-fourth) root motion. In other words, a seventh chord will typically resolve to the sonority whose root is a fifth below (or a fourth above) its own. In Example 18–6, the ii6/5 chord (whose root is D) resolves to V (whose root, A, is a fifth below). Note that the falling-fifth root motion is not affected by the fact that the ii6/5 chord appears in inversion.

As a dissonance, the seventh of any seventh chord requires resolution. Because of its descending passing-tone origin, the seventh almost always resolves down by step. In the tenor voice of Example 18–6, the seventh of the ii6/5 chord steps down to B in the following V chord.

Activity 18-7

Activity 18–7

In this activity, you will continue the I–ii6/5 progressions from the Activity 18–5 by adding a V chord.

### Question

Where should the chordal seventh of the ii6/5 (G) chord resolve to?

Hint

Remember, the chordal seventh must resolve down by step.

The chordal seventh resolves down by step to F#.

### Follow-up question

Complete the V chord by adding the resolution of the chordal seventh and the two remaining voices.

### Question

Where should the chordal seventh of the ii6/5 (Eb) chord resolve to?

Hint

Remember, the chordal seventh must resolve down by step.

The chordal seventh resolves down by step to D.

### Follow-up question

Complete the V chord by adding the resolution of the chordal seventh and the two remaining voices.

### Question

Where should the chordal seventh of the ii6/5 (A) chord resolve to?

Hint

Remember, the chordal seventh must resolve down by step.

The chordal seventh resolves down by step to G#.

### Follow-up question

Complete the V chord by adding the resolution of the chordal seventh and the two remaining voices.

### Question

Where should the chordal seventh of the ii6/5 (F) chord resolve to?

Hint

Remember, the chordal seventh must resolve down by step.

The chordal seventh resolves down by step to E.

### Follow-up question

Complete the V chord by adding the resolution of the chordal seventh and the two remaining voices.

Example 18–6 demonstrates the most common preparation and resolution of a chordal seventh using a ii7 chord as an example, but this treatment can be used for any seventh chord. Consider the following example:

Example 18–7 shows a progression where a vi7 chord, prepared by a iii chord, resolves to a ii chord. Again, we see the falling-fifth motion between the root of the vi7 chord (A) and the resolution ii chord (D). The seventh of the vi7 chord (G) is prepared as a common tone in the preceding iii chord, and resolved downwards by step to F. These same rules may be used for any other seventh chord. A iii7 chord, for example, typically resolves to vi. (These two seventh chords, vi7 and iii7, occur less frequently than other seventh chords. When they do, they are usually found in root position.)

Note: Because chordal sevenths are inherently dissonant, they are typically treated with great care. Keep the following guidelines in mind when approaching and resolving seventh chords as you write music and complete exercises in this style:

• Chordal seventh should be prepared as a common tone: Ideally, a chordal seventh should be prepared as a common tone by the preceding harmony in order to lead as smoothly as possible into the dissonance. If the seventh cannot be prepared as a common tone, approach by step is the next best alternative. Leaping to the chordal seventh should be avoided.

• Chordal seventh descends by step: Because of the origin as accented passing tones, chordal sevenths must always resolve downwards by step.

• Falling-fifth root motion: In most cases, the root of the chord of resolution will be a fifth below the root of the seventh chord.

Now consider the following example (Example 18–8b clarifies the voice leading in the first three chords)

The ii6/5 chord in m. 2 is prepared and resolved exactly in the manner described above. The chordal seventh (Eb ) is prepared as a suspension by the preceding I chord. It then resolves down by step to D in the following V chord, whose root (Bb ) is a fifth down.

# 18.5 Specific seventh chords and their functions

Some seventh chords behave in predictable ways, performing the same musical functions again and again in different musical contexts. In the following sections, we will explore the specific roles played by a pair of commonly encountered seventh chords: the supertonic seventh chord and the subdominant seventh chord. The dominant seventh chord and leading-tone seventh chords are special cases and will be discussed on their own in Chapter 19 and Chapter 20, respectively.

# 18.6 The supertonic seventh chord (ii7 in major; iiø7 in minor)

The supertonic seventh chord (ii7 in major; iiø7 in minor) is one of the most commonly encountered seventh chords. As discussed above, seventh chords frequently resolve by falling-fifth (or rising-fourth) root motion. The ii7 chord, then, typically moves to the dominant. (We will discuss the relationship between the supertonic and dominant in greater detail in Chapter 24.) The supertonic seventh chord may appear in any position, but first inversion (ii6/5) is most common. Example 18–9 shows the progression used earlier in which a ii6/5 chord, prepared by I, leads to V:

As mentioned above, the rules for proper approach and resolution of the ii6/5 chord are all in place: the chordal seventh is prepared as a common tone, the seventh chord resolves by falling-fifth root motion, and the chordal seventh resolves downwards by step.

The ii6/5 chord may also move to a dominant with suspensions in the upper voices. Example 18–10 follows the same progression seen in Example 18–9, but adds two nonharmonic tones above the V chord (E and C), delaying the arrival of the chordal third and fifth (D and B) until a beat later. (This particular figuration is commonly known as a “cadential 6/4.” We will discuss it in further detail in Chapter 23.) Note that the suspended fourth above the bass (C in the tenor) delays the obligatory descending stepwise resolution of the chordal seventh:

Finally, the supertonic seventh chord can also appear in root position. Though occurring less frequently than when it is in first inversion, the root-position supertonic seventh chord is another possible lead-in to V.

As in the examples above, the seventh of the ii7 chord is held over as a common tone from the I chord (this time in the soprano). In Example 18–11, though, the third of the ii7 chord (F) appears in an upper voice instead of the bass and is therefore not obligated to step up to the root of the V chord (see F–G in the bass of Example 18–9). Instead, it is held as a common tone, and thereby ends up preparing the seventh of the V7. Because of this, ii7 typically moves to a V7 chord instead of a triad. Note, too, the proper resolution of the seventh of the ii7 chord: the C in the soprano steps down to the leading tone (B) of the V7 chord.

The following excerpt combines elements of Example 18–9 and Example 18–11:

The chordal seventh of the ii4/2 chord—the D in the bass voice—is prepared as a suspension by the preceding tonic harmony. The chordal seventh then steps down to C# as ii4/2 moves to V6/5 where again the chordal seventh is suspended from the previous chord—in this case the G in the soprano voice.

Supertonic chords in second inversion (ii4/3) occur from time to time as well. When they do, they tend to follow the same conventions described above.

# 18.7 The subdominant seventh chord (IV7 in major and iv7 in minor)

The diatonic seventh chord built on scale degree $\hat4$—the subdominant seventh chord (IV7 in major; iv7 in minor)—is closely-related to the supertonic seventh chord differing only by one member. Because of this similarity, it too typically leads to a dominant harmony, despite the fact that its root lies just a step below $\hat5$ instead of a fourth or fifth away.

By far, IV7 appears most frequently in root position. The following example shows the typical voice leading in the progression I–IV7–V:

Aside from the lack of a falling-fifth root motion, you should be able to recognize most of the same conventions from Example 18–6. The seventh of the IV7 chord (E) is prepared by common tone from the preceding I chord. As the harmony changes on the third beat, the seventh resolves downward by step—in this case to D, the fifth of the V chord. Because the seventh chord does not resolve by falling root-motion, one exception to conventional voice-leading can be found in the tenor voice. Note how the tenor leaps from A down to D as the IV7 moves to V. This leap is necessary in order to avoid what would otherwise have been parallel fifths between the tenor and alto had the tenor moved to the nearest member of the V chord (D). The result of the exceptional voice-leading is a doubled fifth in the V chord.

Activity 18-8

Activity 18–8

In this activity, you will complete a I–IV7–V progression in four voices. In each exercise, the voicing of the I chord has been given to you. (Remember, the seventh of the IV7 chord must be prepared as a common tone and must resolve downwards by step. Also, be sure to avoid parallel fifths in the move from IV7 to V.)

### Question

Complete the following progression by filling in the remaining notes for the upper voices:

### Question

Complete the following progression by filling in the remaining notes for the upper voices:

### Question

Complete the following progression by filling in the remaining notes for the upper voices:

### Question

Complete the following progression by filling in the remaining notes for the upper voices:

# 18.8 Summary

Seventh chords lend variety to the tonal landscape, offering richer, fuller textures than their triad counterparts by adding dissonance. They may be built on any scale degree. However, a I7 chord would undermine the importance of the tonic harmony and should therefore be analyzed as a triad with a nonharmonic tone.

There are five different seventh chord qualities. Three of them include a perfect fifth between the root and fifth: minor seventh (MM7: a major triad with an added major seventh above the root), minor seventh (mm7: a minor triad with an added minor seventh above the root), and major-minor seventh (Mm7: a major triad with a minor seventh, sometimes referred to as a “dominant seventh”). The two remaining seventh chord qualities are based on diminished triads. The half-diminished seventh chord (ø7) adds a minor seventh to a diminished triad while the fully-diminished seventh chord (o7) adds a diminished seventh to a diminished triad.

Because of the added dissonance, seventh chords must be treated carefully. To avoid overemphasizing the dissonance, chordal sevenths are ideally prepared by common tone with the preceding chord or through stepwise motion. Seventh chords typically resolve through falling-fifth root motion. In other words, the root of the chord of resolution will be a fifth below (or a fourth above) the root of the seventh chord. Chordal sevenths have their origin as passing tones. Because of this, they almost invariably resolve down by step.

Some seventh chords perform specific and predictable roles in tonal Western art music. The supertonic and subdominant seventh chords, for example, typically lead to dominant harmonies.