III. Modulation and Chromatic Harmony

# 32.1 Introduction

The example below shows an excerpt from a string quartet. Notice the intriguing chromatic sonority in m. 5:

Following a IV6 chord in m. 4, the outer voices expand in contrary motion to form an augmented sixth (Ab in the bass with F# in the treble). As the sonority moves to V in the following measure, we see that the outer voices both resolve outward by semitone to G. Just as a leading tone lies a half step away from the tonic, Ab and F# both lie a half step away from G. We may think of them as dual leading tones to scale degree $\hat5$, since each approaches its destination with half-step motion. The only difference between these notes and a typical leading tone is that in this case one of the notes (Ab) moves in the opposite direction.

Of course, this type of sonority could never occur diatonically. No two diatonic pitches will produce an augmented sixth. Nevertheless, chromatic sonorities containing an augmented sixth appear quite frequently. As you will see in this chapter, there are several types of chromatic sonorities characterized by the presence of an augmented sixth, appropriately referred to as augmented sixth sonorities. As seen in Example 32–1, augmented sixth sonorities characteristically function as pre-dominant chords and usually lead to dominant harmony. Like other chromatic sonorities, augmented sixths can have a striking effect that composers exploit in order to heighten dramatic tension or highlight important structural moments.

After discussing the general structure and derivation of augmented sixth sonorities, we will look at the three common types and their function in tonal music. We will then examine several complex uses of this type of sonority.

# 32.2 Structure and derivation

Augmented sixth sonorities are derived by chromatically altering a common basic interval progression. (See Chapter 12 for more on how basic interval progressions lie at the base of all voice-leading.)

Example 32–2a shows the familiar basic interval progression of a major sixth expanding to an octave, as it might appear in the common progression iv6–V (in this case, in A minor). Here, the lower voice descends to $\hat5$ by semitone while the upper voice ascends by whole tone to the same scale degree. Raising scale degree $\hat4$, as in Example 32–2b, will produce an augmented sixth. Now both voices are only a semitone away from their respective destinations. Example 32–2c fills out the sonority with an inner voice. Augmented sixth sonorities invariably include scale degree $\hat1$a major third above the bass—which moves to the leading tone in the ensuing dominant harmony.

As Example 32–2 demonstrates, augmented sixth sonorities may arise from chromatic alterations of pre-dominant chords. They retain that function and most commonly lead to the dominant. In Example 32–2, for instance, we see that raising the root of a iv6 chord creates an augmented sixth with the bass. The tritone between $\hat1$ and # $\hat4$ is another characteristic dissonance of all augmented sixth sonorities. Rather than undermine the function of the iv chord, the chromatic pitch in fact intensifies the pre-dominant function. The dual contrary-motion voice-leading by semitone to $\hat5$, combined with the dual contrary-motion resolution of the tritone between $\hat1$ and # $\hat4$ (also by semitone), drives augmented sixth sonorities powerfully toward the dominant.

Augmented sixth sonorities also occur in major contexts. There, they require an extra accidental to lower scale degree $\hat6$ so that it is a semitone away from $\hat5$. Example 32–3 reproduces Example 32–2c in A major. As you can see, the augmented sixth requires an accidental to lower the F# ( $\hat6$ in A major) to F§, a semitone above $\hat5$:

(For the sake of consistency, we will here use b $\hat6$ to generically refer to the pitch a semitone above $\hat5$, even though minor keys require no additional accidental and sometimes a natural sign is used in major keys.)

Activity 32-1

Activity 32–1

Augmented sixth sonorities arise from chromatic alterations of predominant chords. Alter one of the pitches in each of the following progressions to change the subdominant chord to an augmented sixth sonority. (Remember, two accidentals are needed for augmented sixths in major keys.)

### Question

Alter the pitches as necessary in the following iv6–V progression in D minor to transform the predominant chord into an augmented sixth sonority.

Hint

Scale degree $\hat4$ needs to be raised to form an augmented sixth with the bass.

G must be replaced with G#.

### Question

Alter the pitches as necessary in the following iv6–V progression in B minor to transform the predominant chord into an augmented sixth sonority.

Hint

Scale degree $\hat4$ needs to be raised to form an augmented sixth with the bass.

E must be replaced with E#

### Question

Alter the pitches as necessary in the following iv6–V progression in Eb major to transform the predominant chord into an augmented sixth sonority.

Hint

Scale degrees $\hat4$ and $\hat6$ need to be adjusted to form the augmented sixth.

Ab must be replaced with A§ and C with Cb.

### Question

Alter the pitches as necessary in the following iv6–V progression in A major to transform the predominant chord into an augmented sixth sonority.

Hint

Scale degrees $\hat4$ and $\hat6$ need to be adjusted to form the augmented sixth.

F# must be replaced with F§ and D with D #.

Raised scale degree $\hat4$ (# $\hat4$) appears in other chromatic harmonies as well, most notably in applied chords. (See Chapter 27 for more on applied chords.) In V7/V, for example, # $\hat4$ acts as a temporary leading tone to $\hat5$. But # $\hat4$ never appears in conjunction with b $\hat6$ in an applied chord to V, nor should you interpret the presence of # $\hat4$ in an augmented sixth as tonicizing V. Augmented sixth sonorities, as chromatic pre-dominants, emphasize the arrival of the dominant but do not tonicize it.

Augmented sixth sonorities usually appear with b $\hat6$ in the bass, often with # $\hat4$ in the treble to emphasize the chromatic expansion to the octave. Other positions are possible, but occur less frequently. That said, augmented sixth sonorities with other scale degrees in the bass should not be considered “inversions” since b $\hat6$ is not a “root” in the same sense as the root of a triad or seventh chord.

Activity 32-2

Activity 32–2

In each of the following progressions, identify the pre-dominant chord as either an augmented sixth sonority or an applied chord.

### Question

In the following progression in D minor, is the chord marked with a question mark an augmented sixth sonority or an applied chord?

Hint

Remember, the presence of an augmented sixth frame—#4 and (b)6indicates an augmented sixth sonority.

augmented sixth sonority

### Question

In the following progression in D minor, is the chord marked with a question mark an augmented sixth sonority or an applied chord?

Hint

Does the chord in question include an augmented sixth? What does that tell you?

applied chord

### Question

In the following progression in D minor, is the chord marked with a question mark an augmented sixth sonority or an applied chord?

Hint

Does the chord in question include an augmented sixth? What does that tell you?

applied chord

### Question

In the following progression in D minor, is the chord marked with a question mark an augmented sixth sonority or an applied chord?

Hint

Remember, the presence of an augmented sixth frame—#4 and (b)6indicates an augmented sixth sonority.

augmented sixth sonority

# 32.3 Types of augmented sixth sonorities

There are three varieties of augmented sixth sonorities, each containing a different “filling,” so to speak, within the framework of the augmented sixth. These varieties are identified with geographical names—Italian, French, and German—none of which is historically or geographically justifiable. The names are widely used, however, and we will use them here since they permit easy identification.

It is important to remember that augmented sixths are embellishing sonorities, not structural chords. They cannot be constructed purely from diatonic notes and therefore cannot be goals of modulation. Like auxiliary sonorities—another type of chord arising from voice-leading procedures—augmented sixths are a combination of simultaneous melodic embellishments. The different types listed below occur with enough frequency to merit discussion, but their differences simply arise from combinations of nonharmonic tones. Though the inner-voice filling may vary, it is the augmented sixth between b $\hat6$ and # $\hat4$ that gives the sonority its aural signature and requires the most attention.

# 32.4 Italian augmented sixths

The simplest type of augmented sixth sonority is the Italian. In addition to # $\hat4$ and b $\hat6$ forming the augmented sixth framework, this sonority contains one other pitch a diatonic major third above the bass (scale degree $\hat1$), as seen in Example 32–2c. The Italian augmented sixth sonority is sometimes referred to as the augmented 6/3. This does not imply that the chord is a triad in first inversion. Rather, it simply indicates the presence of a third and a sixth above the bass.

Note: You may occasionally see augmented sixths indicated by a bass figure six with a slash through it:

This is a common figured bass convention. The slash indicates that the sixth above the bass should be raised by a semitone: in this case requiring D# instead of D§.

Other music theory texts include a superscript “+” sign to emphasize that the sixth is augmented: It+6. In this chapter we will use abbreviations of the geographic nicknames combined with bass figures. In other words, “It6 is short for “Italian augmented sixth.”

The following example shows an Italian augmented sixth sonority in a musical context:

In this excerpt, we find an arpeggiation of a VI chord in mm. 56–58. We expect this pattern to continue in m. 59, but encounter there an E# where the arpeggiation of G-major harmony in mm. 56–58 points toward a G. The substitution of E# (scale degree # $\hat4$) for G creates a dissonant augmented sixth with the bass G (scale degree $\hat6$). The sonority is filled in with a B in the tenor (a major third above the bass) and all three voices resolve, as expected, to a dominant in m. 60: b $\hat6$ and # $\hat4$ move to $\hat5$ while the tritone formed by $\hat1$ and # $\hat4$ resolves outward to a minor sixth. The harmonic effect, though brief, is striking and emphasizes the arrival of the dominant in a way that a diatonic chord cannot.

Now consider the following example:

Here, the Italian sixth appears directly after a root-position tonic. The inner-voice D in the tonic remains stationary while the outer voices expand to form the augmented sixth, Bb–G#. All three voices move as expected to the V chord at the beginning of m. 123.

Italian sixth chords in textures with four or more voices always double the third above the bass (scale degree $\hat1$). Note that the inner voices move in contrary motion to one another, and also in contrary motion to their registral companions:

As you can see in Example 32–7, the doubled scale degree $\hat1$ moves to both the leading tone and to scale degree $\hat2$ in the ensuing V chord. Scale degrees # $\hat4$ and b $\hat6$ are never doubled since doing so would lead to parallel octaves as a result of their strong tendency to resolve to $\hat5$.

The following excerpt shows an Italian sixth in four voices (note that, despite the key signature, this passage begins in G minor):

On the second beat of the first full measure, we find an Italian sixth: b $\hat6$ in the bass, $\hat1$ in the soprano and tenor, and # $\hat4$ as a chromatic lower neighbor to the D from the preceding i chord. Again, all four voices resolve as expected to the pitches of the V chord.

Activity 32-3

Activity 32–3

Create Italian augmented sixths and resolve them in various keys.

### Question

Write a four-voiced Italian augmented sixth sonority in D minor.

Hint

In a minor key, an Italian augmented sixth will have $\hat6$ in the bass with # $\hat4$ and two $\hat1$s in the upper voices.

(Answers may vary, provided Bb is in the bass and G# and two Ds appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s and the two $\hat1$s will move to the leading tone and $\hat2$.

(Answers may vary, provided Bb and G# both move to A and the two Ds move to C# and E.)

### Question

Write a four-voiced Italian augmented sixth sonority in B minor.

Hint

In a minor key, an Italian augmented sixth will have $\hat6$ in the bass with # $\hat4$ and two $\hat1$s in the upper voices.

(Answers may vary, provided G is in the bass and E# and two Bs appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s and the two $\hat1$s will move to the leading tone and $\hat2$.

(Answers may vary, provided G and E# both move to F# and the two Bs move to A# and C#.)

### Question

Write a four-voiced Italian augmented sixth sonority in Eb major.

Hint

In a major key, an Italian augmented sixth will have b $\hat6$ in the bass with # $\hat4$ and two $\hat1$s in the upper voices.

(Answers may vary, provided Cb is in the bass and A§ and two Ebs appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s and the two $\hat1$s will move to the leading tone and $\hat2$.

(Answers may vary, provided Cb and A§ both move to Bb and the two Ebs move to D and F.)

### Question

Write a four-voiced Italian augmented sixth sonority in E major.

Hint

In a major key, an Italian augmented sixth will have b $\hat6$ in the bass with # $\hat4$ and two $\hat1$s in the upper voices.

(Answers may vary, provided C§ is in the bass and A# and two Es appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s and the two $\hat1$s will move to the leading tone and $\hat2$.

(Answers may vary, provided C§ and A# both move to B and the two Es move to D# and F#.)

Now consider the following example:

In this excerpt, an Italian sixth appears at the end of m. 7, just after a tonicized subdominant chord. Notice the similarity between the iv6 and the It6. The two chords are nearly identical, the only difference being that the root of the iv6 is (D) replaced by a chromatic passing tone (D#). In this case, the Italian sixth does not progress directly to a V chord. Instead, it moves to another strong dominant function chord: a cadential 6/4. The resolution of the augmented interval, however, remains the same—F and D# each move a half-step in contrary motion to octave $\hat5$s.

Activity 32-4

Activity 32–4

### Question

The following excerpt includes four chords with chromatic pitches labeled A, B, C, and D:

Which of these four chords is an Italian augmented sixth?

Hint

Since this excerpt is in a major key, an augmented sixth chord will require at least two different accidentals.

Chord D is an Italian augmented sixth. (Chords A and B are both V7/V and chord C is a V7/IV.)

### Follow-up question

Does the Italian sixth move directly to V? Or is there some intervening sonority?

Hint

Does m. 7 begin with a root-position dominant?

This Italian sixth moves to a cadential 6/4 on the downbeat of m. 7 before the music progresses to V7.

# 32.5 French augmented sixths

The Italian sixth is relatively thin in texture, containing only three unique pitch classes. The French sixth, by contrast, adds an augmented fourth above the bass (scale degree $\hat2$) and produces significantly more dissonance among the voices. It is sometimes referred to as an augmented 4/3 chord, though this is not to imply that it is a seventh chord in second inversion. Example 32–10 illustrates:

We can see the voice-leading already familiar to us from the Italian sixth: # $\hat4$ and b $\hat6$ resolve outward by semitone to $\hat5$, and the third above the bass (scale degree 1) steps down to the leading tone. Instead of doubling $\hat1$, as in the Italian sixth, we’ve added a fourth voice: B ( $\hat2$). Since scale degree $\hat2$ is also the fifth of the dominant chord, it is commonly held when the French sixth resolves to V.

The incorporation of $\hat2$ into the French sixth leads to yet another tritone, this time with the bass. The presence of two tritones ( $\hat1$# $\hat4$ and b $\hat6$ $\hat2$) gives the French sixth its characteristically piercing sound. The added dissonance adds an even greater urgency to the sonority, further activating its tendency to resolve to V.

Observe the voice leading in the following example:

In the second half of m. 46 we find a clear example of a French augmented sixth. As you can see, the outer voices come about as chromatic passing tones: b $\hat6$ (Cb) steps down to $\hat5$ (Bb) and # $\hat4$ (A§) steps up to $\hat5$. Scale degree $\hat1$ is held over from the preceding IV6 chord while $\hat2$, completing the two-tritone make-up of the French sixth, is introduced in anticipation of the V chord.

Example 32–12 shows another instance of a French augmented sixth:

Here, the dissonant augmented sixth is introduced gradually. An applied viio6/V chord follows an auxiliary passing 6/4 chord in m. 73, introducing the temporary leading tone F# (# $\hat4$). (Were the F left natural, the harmony would have followed the common IV–(I6/4)–IV6 progression.) The bass then steps down chromatically to Ab, forming an augmented sixth with # $\hat4$. The tonic pitch is sustained throughout, and in the highest voice we find $\hat2$, completing the French sixth sonority. In this case, the augmented sixth sonority does not resolve directly to the dominant. Instead it introduces a cadential 6/4 chord like we saw in Example 32–9.

Note:The doubling of b $\hat6$ in Example 32–12 appears to lead to parallel octaves as the French sixth moves to the cadential 6/4. This is the result of doubling the bass line at the octave. True parallel octaves occur between two independent voices. These octaves simply arise from doubling, which is used here to create a thicker texture.

Activity 32-5

Activity 32–5

Create French augmented sixths and resolve them in various keys.

### Question

Write a four-voiced French augmented sixth sonority in E minor.

Hint

In a minor key, a French augmented sixth will have $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat2$ in the upper voices.

(Answers may vary, provided C is in the bass and F#, E, and A# appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ moves to the leading tone and $\hat2$ is sustained.

(Answers may vary, provided C moves to B, E moves to D#, A# moves to B, and F is sustained.)

### Question

Write a four-voiced French augmented sixth sonority in G minor.

Hint

In a minor key, a French augmented sixth will have $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat2$ in the upper voices.

(Answers may vary, provided Eb is in the bass and A, G, and C# appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ moves to the leading tone and $\hat2$ is sustained.

(Answers may vary, provided Eb moves to D, G moves to F#, C# moves to D, and A is sustained.)

### Question

Write a four-voiced French augmented sixth sonority in A major.

Hint

In a major key, a French augmented sixth will have b $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat2$ in the upper voices.

(Answers may vary, provided F§ is in the bass and B, A, and D# appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ moves to the leading tone and $\hat2$ is sustained.

(Answers may vary, provided F§ moves to E, A moves to G#, D# moves to E, and B is sustained.)

### Question

Write a four-voiced French augmented sixth sonority in E minor.

Hint

In a major key, a French augmented sixth will have b $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat2$ in the upper voices.

(Answers may vary, provided Fb is in the bass and Bb, Ab, and D§ appear in the upper voices.)

### Follow-up question

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ moves to the leading tone and $\hat2$ is sustained.

(Answers may vary, provided Fb moves to Eb, Ab moves to G, D§ moves to Eb, and Bb is sustained.)

# 32.6 German augmented sixths

German augmented sixth sonorities consist of the same augmented sixth filled in with a major third (scale degree $\hat1$) and a perfect fifth (b $\hat3$ in major, $\hat3$ in minor). They are sometimes referred to as augmented 6/5 chords. German sixths are the most commonly used variety.

Because b $\hat3$ forms a perfect fifth above b $\hat6$, the resolution of the German sixth can lead to parallel fifths:

Example 32–13 shows the parallel fifths that arise when moving from a German sixth directly to V. Composers generally avoid this by including an intervening cadential 6/4 chord before the V. The 6/4 is shown in Example 32–14 where the perfect fifth in the left hand (F and C) is mediated obliquely by a minor sixth (E and C) before arriving at the perfect fifth of the V chord (E and B):

You might have noticed that the first chord in Example 32–14 sounds like a familiar diatonic harmony: the German sixth is enharmonically equivalent to a dominant seventh chord. If the D# in Example 32–13 were respelled as Eb, the chord (F, A, C, and Eb) could be interpreted as V7 in the key of Bb. Composers often take advantage of that enharmonic equivalence as a modulatory device. We will return to that idea momentarily.

The following excerpt provides a clear example of the German augmented sixth:

In m. 6, the presence of F# makes a German augmented sixth out of what would otherwise be heard as a VI chord. As expected, the resolution of the augmented sixth is delayed by a cadential 6/4 chord, offsetting the parallel fifths from Ab and Eb to G and D.

The following example shows another German augmented sixth resolving in the same manner, this time in a major key:

In this minuet, a German sixth appears after a IV6 at the end of m. 12. Because this passage is in Bb major, the chord requires three accidentals: Gb ( $\hat6$), E§ (# $\hat4$), and Db (b $\hat3$). (The tones forming the augmented interval are both doubled.) Once again, the chord moves first to a cadential 6/4 before progressing to a root position dominant chord, though here, with the change of register in the right hand, the intervening chord is less essential.

The examples above illustrate the most common treatment of the German sixth, but there are others. The following example shows an alternative:

In this excerpt from a Mozart sonata the German sixth resolves directly to V in m. 17. The parallel fifths are concealed since F§ does not move directly to E. Instead, E appears in an upper voice, coming out of D in the alto.

As we’ve seen, there are a variety of ways to approach an augmented sixth sonority. Augmented sixths are often prepared by a subdominant chord in first inversion (IV6; iv6 in minor), as seen in Example 32–1, Example 32–11, Example 32–16, and Example 32–17. This approach is widely used since the bass note ( $\hat6$) is already in place. In these cases, # $\hat4$ arises as a chromatic passing tone, making the augmented sixth a chromatic elaboration of subdominant harmony. The submediant (VI) is another common approach (Example 32–5), as is the tonic triad—either in root position (Example 32–6 and Example 32–8) or in first inversion (Example 32–15).

Activity 32-6

Activity 32–6

Create German augmented sixths and resolve them in various keys.

### Question

Write a four-voiced German augmented sixth sonority in G major.

Hint

In a major key, a German augmented sixth will have b $\hat6$ in the bass with # $\hat4$, $\hat1$, and b $\hat3$ in the upper voices.

(Answers may vary, provided Eb is in the bass and Bb, G, and C# appear in the upper voices.)

### Follow-up question

Resolve this German sixth to a cadential 6/4 chord using proper voice-leading.

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ and b $\hat3$ are sustained.

(Answers may vary, provided Eb moves to D, C# moves to D, Bb moves to B§, and G is sustained.)

### Question

Write a four-voiced German augmented sixth sonority in Bb major.

Hint

In a major key, a German augmented sixth will have b $\hat6$ in the bass with # $\hat4$, $\hat1$, and b $\hat3$ in the upper voices.

(Answers may vary, provided Gb is in the bass and Db, Bb, and E§ appear in the upper voices.)

### Follow-up question

Resolve this German sixth to a cadential 6/4 chord using proper voice-leading.

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ and b $\hat3$ are sustained.

(Answers may vary, provided Gb moves to F, E§ moves to F, Db moves to D§, and Bb is sustained.)

### Question

Write a four-voiced German augmented sixth sonority in F# minor.

Hint

In a minor key, a German augmented sixth will have $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat3$ in the upper voices.

(Answers may vary, provided D is in the bass and A, F#, and B# appear in the upper voices.)

### Follow-up question

Resolve this German sixth to a cadential 6/4 chord using proper voice-leading.

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ and $\hat3$ are sustained.

(Answers may vary, provided D moves to C#, B# moves to C#, and A and F# are sustained.)

### Question

Write a four-voiced German augmented sixth sonority in F minor.

Hint

In a minor key, a German augmented sixth will have $\hat6$ in the bass with # $\hat4$, $\hat1$, and $\hat3$ in the upper voices.

(Answers may vary, provided Db is in the bass and Ab, F, and B§ appear in the upper voices.)

### Follow-up question

Resolve this German sixth to a cadential 6/4 chord using proper voice-leading.

Hint

Remember, the voices forming the augmented sixth will expand outward to octave $\hat5$s, while $\hat1$ and $\hat3$ are sustained.

(Answers may vary, provided Db moves to C, B§ moves to C, and Ab and F are sustained.)

# 32.7 Other uses of augmented sixth sonorities

So far, the augmented sixth sonorities we have examined have been relatively straightforward. In each case the augmented sixth functioned as a chromatic pre-dominant, adding dramatic tension to a cadential phrase. Augmented sixth sonorities can function in other ways as well. We will now look at how they can be used to prolong harmonies, and how they can act as agents of modulation.

Consider the following example:

The phrase shown in Example 32–18 ends with an extended prolongation of dominant harmony in E minor. The dominant is tonicized in mm. 18–19, first with a V6/5/V and then with a viio7/V. In mm. 20–21, the G# moves to an upper voice and $\hat5$ in the bass is decorated with a chromatic upper neighbor Bb. With scale degrees $\hat1$ and $\hat2$ in the inner voices, these chromatic pitches form a French augmented sixth. The sonority resolves as expected in m. 22 and the music moves on to the next phrase. In this context, the augmented sixth adds chromatic flavor to an otherwise routine dominant prolongation.

You may encounter other types of auxiliary sonorities that contain an augmented sixth, as in the opening measures of the following example:

Like the augmented sixths in Example 32–18, the sonority that opens this piece expands a functional reference harmony. In this case, however, a I chord is prolonged: Ab, D#, and F# are neighbors to members of the tonic triad while C is sustained in the bass. Ab and F#—the pitches forming the augmented sixth—both resolve normatively to G, the fifth of the tonic. The result resembles a German augmented sixth—b $\hat3$ appears here as # $\hat2$ (D#), underscoring the neighbor function—but the chord does not perform its usual pre-dominant role. Auxiliary sonorities of this sort are generally referred to as common-tone augmented sixth chords.

Example 32–20 contains another common-tone augmented sixth:

In this song, the chord on the second half of beat two prolongs the initial tonic harmony. Bb, E, and G# are neighbors to members of the initial tonic while D is sustained in the bass. Just as before, the augmented sixth resolves outward to an octave on the fifth of the tonic triad. Here, the result resembles a French augmented sixth, but like Example 32–19, the function is prolongational, not pre-dominant.

Augmented sixths are also used to facilitate modulations. Consider the following excerpt and its modulation from A minor to E minor, the minor dominant:

In mm. 11–12 we find a typical progression with a German sixth resolving to the dominant. The same progression is heard in m. 16, transposed down by a perfect fourth to the key of E minor. The unique sound of an augmented sixth resolving is still fresh in our ears from m. 12. Because the German sixth in m. 16 is so closely associated with the dominant, it invites us to retroactively reinterpret the tonic triad in m. 15 as a pivot chord, where i = iv. The augmented sixth, in other words, provides a clear signal of the modulation half a bar before the new dominant by drawing a connection with a progression previously heard in a different key.

A similar scenario may be observed in the following example:

After two full bars of vi in mm. 20–21, the “tenor” voice steps up to a chromatic passing tone (A#). That chromatic alteration transforms the chord into an Italian sixth, leading us to retroactively reinterpret the preceding vi6 as iv6 in E minor. Again, the uniquely recognizable effect of the augmented sixth signals the modulation before the appearance of the new dominant. Similar examples may be cited of augmented sixths being used to modulate back to the tonic.

Note: Augmented sixth chords can also precede applied dominant chords, as in the following example:

In such cases, the various scale degrees that make up the chord in question are the same as usual, but are derived from the tonicized key, not the home key.

As mentioned above, the German sixth is particularly useful in modulations because of it enharmonic equivalence with a dominant seventh chord. The following excerpt takes advantage of that very property:

Example 32–24 begins with an expansion of dominant harmony in Bb major: V is prolonged with a series of cadential 6/4 chords. The third time through, however, Eb is respelled as D#. The change in notation, producing an augmented sixth sonority over F, paves the way to a cadential 6/4 chord in A minor and the new tonic in m. 26. In other words, V7 in Bb major, spelled with Eb, is enharmonically reinterpreted as a German sixth in A minor, spelled with D#. The effect is startling—particularly after the prolongation of V in mm. 21–23—and calls attention to the modulation and cadence in A minor.

The following example clarifies this kind of enharmonic reinterpretation:

In the first part of Example 32–25 we see a German sixth resolving in the usual way to a cadential 6/4. In the second part, the same chord—with the F# respelled as Gbresolves as a dominant seventh in an entirely different key. When a German sixth is enharmonically reinterpreted for the sake of a modulation, the new key will be a half-step away from the original key. In other words, a German sixth in C may also resolve as a dominant seventh in Db (the key of the Neapolitan). This type of modulation can also occur in the opposite direction: what is heard initially as a dominant seventh in Db might end up resolving as a German sixth in C.

Activity 32-7

Activity 32–7

German augmented sixth sonorities are enharmonically equivalent to dominant seventh chords. For each of the following exercises, respell the German sixth as a dominant seventh and identify the key to which it belongs.

### Question

Respell one of the pitches in the following German augmented sixth to create a dominant seventh chord:

C# should be replaced with Db.

### Follow-up question

To which key does this dominant seventh belong?

Hint

If Eb is $\hat5$, what is $\hat1$?

A German sixth in G major is enharmonically equivalent to V7 of Ab.

### Question

Respell one of the pitches in the following German augmented sixth to create a dominant seventh chord:

A# should be replaced with Bb.

### Follow-up question

To which key does this dominant seventh belong?

Hint

If C is $\hat5$, what is $\hat1$?

A German sixth in E minor is enharmonically equivalent to V7 of F.

### Question

Respell one of the pitches in the following German augmented sixth to create a dominant seventh chord:

B§ should be replaced with Cb.

### Follow-up question

To which key does this dominant seventh belong?

Hint

If Db is $\hat5$, what is $\hat1$?

A German sixth in F major is enharmonically equivalent to V7 of Gb.

### Question

Respell one of the pitches in the following German augmented sixth to create a dominant seventh chord:

G# should be replaced with Ab.

### Follow-up question

To which key does this dominant seventh belong?

Hint

If Bb is $\hat5$, what is $\hat1$?

A German sixth in D minor is enharmonically equivalent to V7 of Eb.

# 32.8 Summary

Augmented sixth sonorities feature a dissonant, augmented interval between b $\hat6$ ( $\hat6$ in minor) and # $\hat4$. Those scale degrees act as dual leading tones that expand outward, wedge-like, and resolve by semitone to $\hat5$. In doing so, augmented sixths function as chromatic pre-dominant chords and thus fall into the same category as the Neapolitan which also involves chromatic alterations (see Chapter 31). The presence of # $\hat4$ links them to secondary dominant harmonies, but they should not be understood as tonicizing V. Because of their unique, striking quality, they are often used to signal important structural cadences.

The interval formed by b $\hat6$ and # $\hat4$ is the defining trait of these sonorities, but they usually occur with one of three combinations of other notes. The Italian augmented sixth includes a major third above the bass (scale degree $\hat1$, routinely doubled), while the French sixth includes a major third and augmented fourth above the bass (scale degrees $\hat1$ and $\hat2$). The German sixth, the most common of the three varieties, includes a major third and perfect fifth above the bass (scale degrees $\hat1$ and b $\hat3$, $\hat3$ in minor) and has the richest texture.

Augmented sixths can also be useful in prolongations and modulations. Because they are closely tied to V, they can be used to efficiently mark the new dominant of a modulatory destination. Furthermore, the enharmonic equivalence between a German sixth and a dominant seventh chord make the German sixth a handy means of modulating to a distantly-related key, the tonic of which is a half-step away.