3.6: Augmented Sixth Sonorities

32.1 Introduction

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

Example 32–1. Ludwig van Beethoven, String Quartet No 2 (Op. 18, No. 2), III. Scherzo. Allegro, mm 1–8.

\[\hat5\]

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 32–2.

a. M6–P8

b. A6–P8

c. A6–P8 with inner voice

\[\hat5\]

\[\hat1\]

\[\hat6\]

Example 32–3.

\[\hat6\]

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.)

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Exercise 32–1a:

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

\[\hat4\]

Answer

G must be replaced with G#.

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Exercise 32–1b:

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

\[\hat4\]

Answer

E must be replaced with E#

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Exercise 32–1c:

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

\[\hat4\]

Answer

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

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Exercise 32–1d:

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

\[\hat4\]

Answer

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

\[\hat4\]

\[\hat6\]

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.

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Exercise 32–2a:

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)6—indicates an augmented sixth sonority.

Answer

augmented sixth sonority

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Exercise 32–2b:

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?

Answer

applied chord

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Exercise 32–2c:

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?

Answer

applied chord

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Exercise 32–2d:

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)6—indicates an augmented sixth sonority.

Answer

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.

\[\hat6\]

32.4 Italian augmented sixths

\[\hat4\]

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

Example 32–4.

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:

Example 32–5. Felix Mendelssohn, Lieder ohne Worte (Op. 30), 4. Agitato e con fuoco, mm. 52–60.

\[\hat4\]

Now consider the following example:

Example 32–6. Wolfgang Amadeus Mozart, Piano Sonata No.12 in F major (K.332), I. Allegro, mm. 116–126.

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.

\[\hat1\]

Example 32–7.

\[\hat1\]

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

Example 32–8. Johann Sebastian Bach, “Ich hab mein Sach Gott heimgestellt” (BWV 351), mm. 1–2.

\[\hat6\]

Activity 32-3

Activity 32–3

Create Italian augmented sixths and resolve them in various keys.

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Exercise 32–3a:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this Italian sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

---

Exercise 32–3b:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this Italian sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

---

Exercise 32–3c:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this Italian sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

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Exercise 32–3d:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this Italian sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

(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:

Example 32–9. Louise Farrenc, 20 Etudes de moyenne Difficulté pour Piano (Op. 42), No. 17, mm. 1–8.

\[\hat5\]

Activity 32-4

Activity 32–4

Exercise 32–4:

Question

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

Maria Agata Szymanowska, 6 Marches for Piano, No. 5 in Bb major, Trio, mm. 1–8.

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.

Answer

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?

Answer

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

Maria Agata Szymanowska, 6 Marches for Piano, No. 5 in Bb major, Trio, mm. 1–8.

32.5 French augmented sixths

\[\hat2\]

Example 32–10.

\[\hat4\]

\[\hat2\]

Observe the voice leading in the following example:

Example 32–11. Ludwig van Beethoven, Piano Sonata No. 8 [“Pathétique”] (Op. 13), III. Rondo. Allegro, mm. 44–47.

\[\hat6\]

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

Example 32–12. Ludwig van Beethoven, Piano Sonata No. 4 (Op. 7), II. Largo con gran espressione, mm. 72–74.

\[\hat4\]

\[\hat6\]

Activity 32-5

Activity 32–5

Create French augmented sixths and resolve them in various keys.

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Exercise 32–5a:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this French sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

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Exercise 32–5b:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this French sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

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Exercise 32–5c:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this French sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

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

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Exercise 32–5d:

Question

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

Hint

\[\hat6\]

Answer

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

Follow-up question

Resolve this French sixth to a dominant triad using proper voice-leading.

Hint

\[\hat5\]

Answer

(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

\[\hat1\]

\[\hat3\]

Example 32–13.

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):

Example 32–14.

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:

Example 32–15. Ludwig van Beethoven, Piano Sonata No. 8 [“Pathétique”] (Op. 13), III. Rondo. Allegro, mm. 1–8.

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:

Example 32–16. Maria Agata Szymanowska, 6 Minuets, No. 2 in G minor, Trio, mm. 1–16.

\[\hat6\]

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

Example 32–17. Wolfgang Amadeus Mozart, Piano Sonata No. 6 in D major (K.284), I. Allegro, mm. 11–19.

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.

\[\hat6\]

Activity 32-6

Activity 32–6

Create German augmented sixths and resolve them in various keys.

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Exercise 32–6a:

Question

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

Hint

\[\hat6\]

Answer

(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

\[\hat5\]

Answer

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

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Exercise 32–6b:

Question

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

Hint

\[\hat6\]

Answer

(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

\[\hat5\]

Answer

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

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Exercise 32–6c:

Question

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

Hint

\[\hat6\]

Answer

(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

\[\hat5\]

Answer

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

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Exercise 32–6d:

Question

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

Hint

\[\hat6\]

Answer

(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

\[\hat5\]

Answer

(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:

Example 32–18. Maria Theresia von Paradis, 12 Lieder auf ihrer Reise in Musik gesetzt, 9. “Vaterlandslied,” mm. 15–23.

\[\hat5\]

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

Example 32–19. Franz Schubert, Schwanengesang (D.957), 12. “Am Meer,” mm. 1–3.

\[\hat3\]

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

Example 32–20. Hugo Wolf, Mörike-Lieder (IHW 22), 24. “In der Frühe,” mm. 1–2.

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:

Example 32–21. Felix Mendelssohn, Lieder ohne Worte (Op. 102), 3. Presto, mm. 9–17.

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:

Example 32–22. Ludwig van Beethoven, Piano Sonata No. 21 [“Waldstein”] (Op. 53), I. Allegro con brio, mm. 18–23.

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:

Example 32–23. Sophia Maria Westenholz, 12 Deutsche Lieder (Op. 4), 3. “Das Glücke der Liebe,” mm. 1–9.

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. Franz Schubert, Piano Sonata No. 16 (D.845), I. Moderato, mm. 21–27.

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:

Example 32–25.

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 Gb—resolves 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.

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Exercise 32–7a:

Question

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

Answer

C# should be replaced with Db.

Follow-up question

To which key does this dominant seventh belong?

Hint

\[\hat5\]

Answer

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

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Exercise 32–7b:

Question

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

Answer

A# should be replaced with Bb.

Follow-up question

To which key does this dominant seventh belong?

Hint

\[\hat5\]

Answer

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

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Exercise 32–7c:

Question

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

Answer

B§ should be replaced with Cb.

Follow-up question

To which key does this dominant seventh belong?

Hint

\[\hat5\]

Answer

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

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Exercise 32–7d:

Question

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

Answer

G# should be replaced with Ab.

Follow-up question

To which key does this dominant seventh belong?

Hint

\[\hat5\]

Answer

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

32.8 Summary

\[\hat6\]

\[\hat6\]

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.