The augmented sixth chord tends to be a dreaded subject in harmony courses, because it comes near the end of the textbook (e.g., Chapter 27 of Piston-DeVoto Harmony, 5th edition) but it really isn’t that complicated. There are maybe six or seven different kinds in regular use, some with geographic names: the Italian, German, and French sixths are well known, and some writers recognize Swiss or even Polish sixths. (You might wonder about the famous Neapolitan sixth, as well as the Russian sixth that I have puffed about in these pages, but these are not augmented sixth chords.). All of them have in common the interval of augmented sixth, typically in the upper voice and bass:
and differing only in what goes in the inner parts. The four shown above also have the tonic note as well as the minor sixth degree and the raised fourth degree. The black unstemmed notes show the usual resolution. The augmented sixth interval is a dissonant interval that needs to be resolved, normally by expanding to an octave, with the raised factor continuing upward, the minor degree, downward. The Italian sixth, the simplest form, might be preceded by the major subdominant in first inversion (A-C-F), so the tendency of the chromatic tones is very clear.
But (and this is an important qualification) the augmented sixth interval (A flat to F sharp) is enharmonically equivalent to a minor seventh, and this shows how the augmented sixth chord can be reinterpreted as a dominant, which makes the chord very useful for modulating between, say, C major and D-flat major — see above. (Think of those choir-room exercises, me-oh-my-oh-me going chromatically upward — or “Pianists” in Carnival of the Animals.)
The augmented sixth chord has been detected as early as the sixteenth century, but it is a rarity until the late Baroque. The chord was seldom used by Bach, though there are some striking examples (e.g., in the “Crucifixus” of the B minor Mass). But after 1750 the harmony came into its own with Viennese classicism, and Haydn, Mozart, and Beethoven made it a permanent coin of the realm. They offered many highlighted instances of what I like to call “devastating” augmented sixths, like this one from Haydn’s G minor String Quartet, op. 74 no. 3:
All of us doubtless have our favorite instances of augmented sixth chords. When a student once asked me, “What’s the earliest work of Schubert’s that has an augmented sixth chord?”, I was able to reply, “The Fantasy in G major for piano four hands, Deutsch 1.” Schubert was 13 years old then.
Until the middle of the 19th century, the most characteristic augmented sixths appear in cadences, preceding the dominant triad or the tonic six-four. With Chopin and Schumann, and even more with Wagner, the augmented sixth chord is a regular ingredient, along with much else, of advanced chromaticism. Schumann once used the augmented sixth as the very first harmony in his song “Am leuchtenden Sommermorgen” (Dichterliebe, no. 12). Walter Piston’s Harmony gives an example of particular charm: “As a dissonant chord over a dominant pedal the augmented sixth is strikingly effective.”
The augmented-sixth interval here appears inverted, as a diminished third, E sharp-G. The dominant degree in B minor, F sharp, sounds at the same time as the E sharp and the G, a cluster of three chromatic tones. Chopin seems to have liked this particular set of pitches; he used it again (pianissimo) just before the B major section of the Polonaise-fantaisie, and again in the cadenza just before the last page of the Barcarolle.
Mahler might have had Chopin’s fff in mind for the explosive beginning of the finale of his Symphony no. 1:
Shortly after this, the augmented sixth was adopted by Debussy, but that’s a story for another day. Suffice to say that the French sixth maps with the whole-tone scale; you can imagine what happened next.