Augmented Sixth Chords

The Neapolitan of the previous lesson descended toward the tonic from a half step above. The chords in this lesson aim not at the tonic but at the dominant, and they close in on it by half step from both sides at once.

The augmented sixth frame

The core of an augmented sixth chord is just two notes.

• ♭6 — a half step above the dominant
• ♯4 — a half step below the dominant

In C, major or minor, that is Ab and F#, bracketing the dominant G from above and below.

Count the interval between them. Six letters from A to F, ten half steps. A major 6th is nine, so this is one half step wider: an augmented 6th. The chord is named after it.

Fig. 1 is the whole of the augmented sixth chord. Two notes expand outward by a half step each and land on the octave of the dominant. The remaining chord tones are only a question of what fills the frame.

Three types — different fillings

The three varieties differ in what is added to the frame. They carry national names, but the connection to actual regions is thin; they are conventional labels.

Type	Notes (in C)	Added to the frame	Voices
Italian sixth (It6)	Ab C F#	the tonic only	3
French sixth (Fr6)	Ab C D F#	tonic and second degree	4
German sixth (Ger6)	Ab C Eb F#	tonic and ♭3	4

The Italian has only three voices, so writing it in four parts requires doubling the tonic C. The two framing notes, Ab and F#, both have fixed destinations, and doubling either guarantees parallels. C is the only note that may be doubled.

The three augmented sixths compared

▶Italian (three voices)▶French (+ second degree)▶German (+ ♭3)

Check: All share the same Ab and F# frame and land on the same dominant. The Italian, with three voices, sounds thin and leaves the tension of the frame exposed. The French adds D and floats in a way reminiscent of the whole-tone scale. The German adds Eb and acquires almost the density of a dominant seventh. In all three, the outer voices open in opposite directions at the moment of resolution.

Ab C F# → G

Check

What are the notes of the German sixth (Ger6) in A minor?

F A B D#F A C D#F A C EbF A D#

Check answer

Why it must not be written as a diminished 7th

Ab and F#. On the keyboard those are the same two keys as Ab and Gb, a diminished 7th. The sound is identical.

The spelling still may not be changed, because notation encodes the direction of resolution.

Interval	Direction of resolution
Augmented	expands outward
Diminished	contracts inward

Read Ab and F# as an augmented 6th and they open outward onto the octave G. Read Ab and Gb as a diminished 7th and they close inward toward something else. Same two keys; the spelling decides where they go.

This is the clearest payoff of the enharmonic material in Unit 0. A staff records not only how high a note is but where it is going next. Describe music by pitch class alone and that information is lost entirely.

Check

Why can a chord spelled with Ab and Gb (a diminished 7th) not be treated as an augmented sixth chord?

A diminished 7th leaves the chord without a fifthDiminished seventh chords do not existA diminished 7th contracts inward, which contradicts the outward expansion onto the octave of the dominantA diminished 7th is not dissonant

Check answer

The problem unique to the German sixth

The German sixth is Ab C Eb F#. Counted in half steps alone, that is identical to Ab7 (Ab C Eb Gb). Having the density of a dominant seventh makes it the richest sounding and the most used of the three.

That richness creates a problem: moving directly to the dominant produces parallel fifths.

The bass Ab and the alto Eb are a perfect 5th apart. When both descend to G and D, they are a perfect 5th apart again. Two voices moving the same direction through consecutive perfect 5ths is exactly the parallel fifths of Unit 5. The Italian has no Eb and the French has D in its place, so the problem is specific to the German.

The remedy is to insert the second-inversion tonic chord between them.

In Fig. 4 the Eb does not move across the two chords. Parallel fifths require both voices to move, so one staying put prevents them. The bass falls a half step from Ab to G, the soprano’s F# rises a half step to G, the frame resolves, and the i64 then releases into V.

The cadential 6-4 is doing the same job here as before. Unit 4’s treatment of the second-inversion tonic as an ornament of the dominant returns from a different angle.

Two routes out of a German sixth

▶Direct (parallel fifths)▶Through the second inversion

Check: The first goes straight to the dominant. It passes as sound, but the fifths moving in parallel in the inner voices make it something classical harmony avoids. The second passes through the second-inversion tonic. The Eb is handed on unchanged and the music then releases into the dominant. The longer path to the landing makes the eventual resolution register more strongly.

Ger6 → V → i

How the three chromatic chords relate

Reordering what Unit 8 has covered so far by relationship to the dominant makes the structure visible.

Chord	How it engages the dominant
Secondary dominant (V7/V)	treats the dominant as a temporary tonic and approaches its leading tone from a half step below
Neapolitan (N6)	descends toward the tonic from a half step above, by way of the dominant
Augmented sixth	brackets the dominant by half step from above and below, converging from both sides

All three exploit the pull of the half step. Chromatic harmony is, in essence, the technique of manufacturing leading-tone half steps in places other than the leading tone.

▶ Play Ab7 in the chord finder and listen It is the same sonority as the German sixth. The spelling differs, though - Ab C Eb Gb against the augmented sixth's Ab C Eb F#, differing in how the fourth note is written. Confirm with both ear and eye that identical sound with different spelling means a different destination Chord Finder →

One sonority being readable two ways was a problem here. Exploiting that deliberately turns it into a different technique — modulation, which is the subject of the next lesson.