A Survey of Music Theory for the College Classroom: Chromatic Harmony 2 and 20th Century Music

Augmented Sixth Chords and Enharmonic Modulation

Overview

Augmented sixth chords are another class of chromatic chords that are used by composers to enrich harmonic textures and propel motion toward the dominant and tonic chords. Two of these chords, the German augmented sixth (Ger+6) and the Italian augmented sixth (It+6) are enharmonically spelled Mm7 chords, while the French augmented sixth chord (Fr+6) is an entirely new structure and sound type in our studies. The reasons for the names of these chords lay in the distant past, and no geographic meaning should be attached to them.

Augmented sixth chords have a strong predominant function, replacing either the subdominant or supertonic harmonies in motion toward the dominant chord, and are typically preceded in progressions by supertonic, subdominant, and submediant chords. Augmented sixth chords can also be used as dominant substitutes that progress directly to the tonic chord, and more rarely will be used to tonicize something other than the dominant or tonic chords in a key. We will explore each of these prospects in turn.

By far the most typical use of an augmented sixth chord is as a predominant function. The augmented sixth arises because the tonicized note is approached simultaneously by notes a half step above and half step below. When inverted, this o3 becomes an +6, and the resolution is outward to the octave. When progressing to the V chord, this characteristic interval consists of the \(\hat{6}\) and \(\hat{4}\).

augmented sixth to dominant scale degree

To these two altered scale degrees the It+6 adds the tonic scale degree, the Ger+6 adds the tonic and \(\hat{3 }\), and the Fr+6 adds the tonic and supertonic scale degrees. Keep in mind that the \(\hat{3 }\) and \(\hat{6}\) are already present in minor keys.

augmented sixth chords

Part-Writing Augmented Sixth Chords

The part-writing guidelines for augmented sixth chords are not difficult. All predominant augmented sixth chords resolve directly to the V or to a I64 – V, and the\(\hat{6}\) scale degree is usually found in the bass. The interval of the +6 should resolve outward to the octave, with the other chord tones exhibiting smooth voice leading. When writing It+6 chords in SATB textures, the tonic note is to be doubled. Please note the interesting exception to the use of parallel fifths that arises when the Ger+6 progresses to V.

When an augmented sixth chord resolves directly to a V7, the top note of the +6 resolves to the 7th of the V7, as shown in the last example.

part writing augmented sixth chords

Occasionally the \(\hat{4}\) is in the bass rather than the \(\hat{6}\). This inverts the +6 to a o3, and the usual resolution is for this interval to collapse inward to the unison or octave. Note again the parallel fifths that occur when the Ger+6 progresses directly to V.

augmented sixth chords with raised four in bass

Atypical It+6, Ger+6, and Fr+6 Chords

Augmented sixth chords occasionally substitute for dominant harmonies and progress directly to the tonic chord. Augmented sixth chords more rarely progress to a scale degree other than the tonic or dominant. We will adopt the analysis practices of the secondary dominant and leading tone chords when analyzing these uses of the +6 chord, for example It+6/I(i), Ger+6/I(i), Fr+6/I(i), It+6/IV, Ger+6/ii, Fr+6/VI, and so forth. Note that some theorists prefer using scale degrees for these occurrences of +6 chords rather than roman numerals, for example It+6/\(\hat{1}\), Ger+6/\(\hat{1}\), Fr+6/\(\hat{1}\). As with secondary functions, only scale degrees that can serve a tonic function can be tonicized with an augmented sixth chord.

Spelling +6 chords that progress to something other than the dominant can be a little trickier than usual. The following procedure can be applied to any instance in which the +6 tonicizes a scale degree other than the dominant.

  • Find X, the note (scale degree) to be tonicized.
  • Go down a P5 and act as if X is the dominant in the key a P5 below X.
  • Build the +6 chord to X in that key using the same technique we learned when building pre-dominant +6 chords.
    • Semitone above/semitone below tonicized note + tonic scale degree in key = It+6
    • Semitone above/semitone below tonicized note + tonic scale degree in key + scale degree \(\hat{3}\) = Ger+6
    • Semitone above/semitone below tonicized note + tonic scale degree in key + scale degree \(\hat{2}\) = Fr+6

In the following example, the tonic scale degree in C/c is being tonicized. Go down a P5 from C to F and build the +6 chord as if it were progressing to the dominant in the key of F/f.

augmented sixth chords to the tonic

Some theorists conceive of augmented sixth chords as altered chords, which is useful when analyzing or constructing the most common occurrences of these chords. When progressing to the dominant chord or scale degree, the following is seen:

  • The It+6 can be considered as a IV built on the \(\hat{4}\) and with a \(\hat{6}\) (the \(\hat{6}\) is already present in minor mode).
  • The Ger+6 can be considered as a IV7 built on the \(\hat{4}\) and with a \(\hat{6}\) and \(\hat{3}\) (the \(\hat{6}\) and \(\hat{3}\) are already present in minor mode).
  • The Fr+6 that can be considered as a II7 with a with a \(\hat{4}\) and \(\hat{6}\)(the \(\hat{6}\) is already present in minor mode).

Likewise, when progressing to a tonic triad or scale degree, the following is seen:

  • The It+6/I (i) can be considered as a VII with a \(\hat{2}\).
  • The Ger+6/I (i) can be considered as a VII7 with a \(\hat{2}\) and \(\hat{6}\).
  • The Fr+6/I (i) can be considered as a V7 with a \(\hat{2}\).

Enharmonic Modulation

Enharmonic equivalence references the point that there are more than two spellings for any given note. Obvious examples are the notes C and D, but less common ones such as E and F are to be found. Similarly, we can take advantage of enharmonic spellings to reinterpret chords in different keys. Enharmonic modulation takes advantage of the fact that o7 and Mm7 (Dom7) chords can be resolved in diverse ways. Each o7 chord can resolve in four different ways, and each Mm7 chord can resolve in two different ways. 

Fully Diminished Seventh Chords

We will begin by studying o7 chords. Because o7 chords are comprised only of m3 intervals, they are “aurally inversionless.” The B in the following chord is the leading tone to C. It is therefore a viio7 in C/c.

enharmonic modulation example

Even when the chord is inverted on paper, the aural result is that of stacked m3 intervals. In the following example, note that the A to B is an +2, which is enharmonic with a m3.

enharmonic modulation example 2

Because of this quality, each chord member can serve as the leading tone to the pitch a semitone above it. This means that it is as valid to hear the Bo7 chord resolve to the keys of A/a, G, or E/e or their enharmonic equivalents as it is to the key of C/c. Composers take advantage of this aural ambiguity to effect modulation to foreign keys.

The D in this chord is the leading tone to E and is now a viio42 in E/e. If you play the chord at the piano, it still looks like you are playing the notes B, D, F and A. This is the essence and power of enharmonic modulation.

enharmonic modulation example 3

The F in this chord is now the leading to G, so it is now a viio43 in G. We would need to enharmonically spell the chord to take it to F major or f minor (E G B D), which is enharmonic to G.

enharmonic modulation example 4

The A cannot be the leading tone to B♭♭ because B♭♭is not a “real” key. We must enharmonically spell the A as a G, which now serves as the leading tone to A. It is now a viio65 in A/a.

enharmonic modulation example 5

Keep in mind that any of the examples above can also serve as secondary leading tone functions. The tonicized notes can in themselves be the dominant, subdominant, and so forth of a new key.

Dominant Seventh Chords

The enharmonic usage of the Mm7 is simpler than those for the o7. The Ger+6 chord is merely a Mm7 spelled enharmonically. In the following example, a garden variety C7 serves as the dominant function to F. This F could be the tonic of a key, or it could be the target of a secondary function in another key. 

enharmonic modulation example 6

In the next example, the m7 between the root and the seventh has been respelled as an +6. It is now a Ger+6 that leads to the note B, which is the dominant of E/e. While it is possible for the Ger+6 to progress to something other than the dominant V chord in the new key, this is an uncommon usage in enharmonic modulation.

enharmonic modulation example 7

As with the o7 chord, these enharmonically spelled Mm7 chords can help smooth over modulations to foreign keys. Whether o7 or Mm7/Ger+6 chords are used, they may be spelled in the old key or in the new key. Because these are a type of common chord modulation, the method of identifying them with brackets, key names, and Roman numerals is the same.

enharmonic modulation example 8

When analyzing enharmonic modulation, it is important to ascertain the key to which the piece is moving. Try to find dominant functions – cadential six-four chords are especially helpful – and then back up a chord to locate the exact point of modulation.

The following example illustrates how enharmonic reinterpretation can be used to effect enharmonic modulation to distant keys. In each case the sonority is first used in its typical function – as a o7 and Dom7 in the respective keys – and then as a o7 and Ger+6 in the new keys. 

enharmonic modulation progression

Neapolitan Chords in Enharmonic Modulations

Neapolitan chords can also be spelled enharmonically to effect modulation to remote keys. In the next example, the Neapolitan chord is spelled enharmonically to produce a modulation up a semitone. The N6 chord may be spelled in the old key, enharmonically in the new key, or with elements of both as in the next example.

Neapolitan chord in enharmonic modulation

Modal Borrowing in Enharmonic Modulations

Modal borrowing can be used to create colorful modulations, and sometimes enharmonic reinterpretation can be used in conjunction with this. The next example is from the second movement of Beethoven’s Piano Sonata Op. 13 No. 8. After a PAC in the tonic key of A major in measure 36 (note that measure numbers appear at the end of the measure in this example), Beethoven changes mode to a♭ minor in measure 37. By measure 44 we find a PAC in E major. Beethoven leverages aminor, the parallel minor of the tonic key of A major, to effect modulation to E major, which is the enharmonically spelled submediant key (F major) of a minor. Amajor and F♭ major stand in a chromatic mediant relationship.

A♭ – a♭ (mm. 37-41) -- F♭/E (mm. 41-45)

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