Augmented sixth chord

The interval of an augmented sixth normally resolves outwards by semitone to an octave.  Play 

The 3 most common augmented sixth chords in the tonalities of C major and C minor: Italian 6th, French 6th, and German 6th.

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods. The three more common types of augmented sixth chords as usually called Italian 6th, French 6th, and German 6th.

Resolution and chord construction

The augmented sixth interval is typically between the sixth degree of the minor scale (henceforth ♭6) and the raised fourth degree (henceforth ♯4). With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both ♭6 and ♯4 have resolved to the fifth scale degree (henceforth 5). This tendency to resolve outwards to 5 is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh (♭6 and ♭5). Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by borrowing ♭6 of the parallel minor scale.

Double-diminished triad

In music theory, the double-diminished triad is an archaic concept and term referring to a triad, or three note chord, which, already being minor, has its root raised a semitone, making it doubly diminished. However, this may be used as the derivation of the augmented sixth chord.

For example, F-A♭-C is a minor triad. F♯-A♭-C is a doubly diminished triad. Note that it is enharmonically equivalent to G♭-A♭-C (incomplete dominant seventh [missing E♭] or "backdoor" dominant-seventh substitute vii^o). A♭-C-F♯ is an Italian augmented sixth chord.

Types

There are three main types of augmented sixth chords, commonly known as Italian 6th, French 6th, and German 6th. Though each is named after a European nationality, theorists disagree on their precise origins and have struggled for centuries to define their roots, and fit them into conventional harmonic theory.

Italian sixth

The Italian sixth moving to V.  Play 

The Italian sixth (It$^{+6}$ or It$^6$) is derived from iv$^6_{}$ with an altered fourth scale degree, ♯4: ♭6—1—♯4; A♭—C—F♯ in C major and C minor. This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled.

The second movement of Beethoven's piano sonata in F-sharp major, op. 78, begins with an Italian sixth chord.  Play 

The Italian 6th is enharmonically equivalent to an incomplete dominant seventh.

French sixth

The French sixth chord; the distinguishing tone is highlighted in blue.  Play 

The French sixth (Fr$^{+6}_{}$ or Fr$_3^4$) is similar to the Italian, but with an additional tone, 2: ♭6—1—2—♯4; A♭—C—D—F♯ in C major and C minor. The notes of the French sixth chord are all contained within the same whole tone scale, lending a sonority common to French music in the 19th century (especially associated with Impressionist music).

German sixth

The German sixth (Gr$^{+6}_{}$ or Ger$_5^6$) is also like the Italian, but with an added tone ♭3: ♭6—1—♭3—♯4; A♭—C—E♭—F♯ in C major and C minor. In Classical music, however, it appears in much the same places as the other variants, though perhaps less used because of the contrapuntal difficulties outlined below. It appears frequently in the works of Beethoven. The German sixth chord contains the same notes as a dominant seventh chord, though it functions differently.

It is more difficult to avoid parallel fifths when resolving a German sixth chord to the dominant, V. These parallel fifths, referred to as Mozart fifths, were occasionally accepted by common practice composers. There are two ways they can be avoided:

1. The ♭3 can move to either 1 or 2, thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between ♭6 and ♭3.
2. The chord can resolve to a "six-four" chord, functionally either as a cadential six-four intensification of V, or as the second inversion of I; the cadential six-four, in turn, resolves to a root-position V. This progression ensures that, in its voice leading, each pair of voices moves either by oblique motion or contrary motion and avoids parallel motion altogether. In minor modes, both 1 and ♭3 do not move during the resolution of the German sixth to the cadential six-four. In major modes, ♭3 can be enharmonically respelled as ♯2 if it resolves upwards to ♮3, similar in voice leading to the resolution of French sixth to the cadential six-four. This respelled chord is sometimes referred to as the English, Swiss or Alsatian sixth chord,^{[citation needed]} or as a "'doubly augmented sixth chord"', as it contains two augmented intervals. However, other sources describe it as a German sixth.

The German sixth; the distinguishing tone is highlighted in blue.  Play

The German sixth is typically followed by a I$_4^6$ chord to avoid parallel fifths.  Play

German sixth chord respelled with doubly augmented fourth (highlighted in blue) for voice-leading purposes. Also referred to as English, Swiss or Alsatian.

A German sixth chord from Michael Haydn's Requiem in C minor, first movement. ( Listen)

Other variants

Other variants of augmented sixth chords are sometimes found in the repertoire, and are sometimes given whimsical geographical names. For example: 4—♭6—7—♯2; (F—A♭—B—D♯) is called by one source an Australian sixth. Such anomalies usually have alternative interpretations.

Standard harmonic function

From the Baroque to the Romantic period, augmented sixth chords have had the same harmonic function: as a chromatically altered predominant chord (typically, an alteration of ii$_3^4$, IV$_5^6$, vi⁷ or their parallel equivalents in the minor mode) leading to a dominant chord. This movement to the dominant is heightened by the semitonal resolution of both ♭6 to 5 and ♯4 to 5; essentially, these two notes act as leading-tones. This characteristic has led many analysts to compare the voice leading of augmented sixth chords to the secondary dominant V of V because of the presence of ♯4, the leading-tone of V, in both chords. In the major mode, the chromatic voice leading is more pronounced because of the presence of two chromatically altered notes, ♭6, as well as ♯4, rather than just ♯4 in the minor mode.

Root position and inversion of augmented sixth chords

Augmented sixth chords are occasionally used with a different chord member in the bass. Since there is no consensus among theorists that they are in root position in their normal form, the word "inversion" isn't necessarily accurate, but is found in some textbooks, nonetheless. Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

Rousseau considered that the chord could not be inverted. 17th century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources.

Excerpt from Bach's Mass in B minor. At the end of the second measure, the augmented sixth is inverted to create a diminished third or tenth between the bass and the soprano (C♯—E♭); these two voices resolve inward to an octave Play 

Root positions of the augmented 6th chords in the tonality of C, according to Simon Sechter.

Simon Sechter explains the chord of the French Sixth as being a chromatically altered version of a seventh chord on the second degree of the scale. The German Sixth is explained as a chromatically altered ninth chord on the same root, but with the root omitted.

The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the A♭, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F♯ - being chromatically raised - must rise.

Extended functions

In the late Romantic period and other musical genres, especially jazz, other harmonic possibilities of augmented sixth variants and sonorities outside its function as a predominant were explored, exploiting their particular properties. An example of this is through the "reinterpretation" of the harmonic function of a chord: Since a chord could simultaneously have more than one enharmonic spelling with different functions (i.e., both predominant as a German sixth and dominant as a dominant seventh), its function could be reinterpreted mid-phrase. This heightens both chromaticism by making possible the tonicization of remote keys, and possible dissonances with the juxtaposition of remotely related keys.

Augmented sixth chords as altered dominant chords with flattened 2nd degree

See also: tritone substitution

The augmented sixth chord may be built on notes other than ♭6.

Tchaikovsky considered the augmented sixth chords as being altered dominants. He described the augmented sixth chords as inversions of the diminished triad and of dominant and diminished seventh chords with the second degree chromatically lowered, and accordingly resolving into the tonic. He notes that, "some theorists insist upon [augmented sixth chord's] resolution not into the tonic but into the dominant triad, and regard them as being erected not on the altered 2-nd degree, but on the altered 6-th degree in major and on the natural 6-th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6-th degree is nothing else than a modulatory degression into the key of the dominant".

Augmented sixths as dominants in the tonality of C, according to Tchaikovsky. Notice the preluminary resolution to avoid parallel fifths in the last example.

An Italian sixth chord built on scale degree ♭2 preceded by a ♭II chord in root position. Here the Italian sixth chord functions as a substitute for the dominant, with which it shares the third and seventh. Schubert's A major sonata, D. 959.  Play 

Classical harmonic theory would notate the "tritone substitute" as an augmented sixth chord on ♭2. The Augmented sixth chord can either be the It⁺⁶ enharmonic to a dominant 7th chord without the 5th, Gr⁺⁶, enharmonically equivalent to a dominant 7th chord with the 5th, or Fr⁺⁶ enharmonically equivalent to the Lydian dominant without the 5th, all of which serve in a classical context as a substitute for the secondary dominant of V.

Original dominant 7th-tonic progression  Play , tritone substitution (♭V⁷/V-I)  Play , augmented sixth chord (It⁶-I)  Play .

Enharmonicity to other chords

Enharmonic equivalency of the French sixth

The French sixth has two characteristics in common with the diminished seventh chord:

1. Both chords are constructed of two superimposed tritones; in the French sixth, between ♭6—2 (A♭—D) and 1—♯4 (C—F♯). Thus, both have inversional symmetry;
2. Both are enharmonically equivalent at the tritone; i.e., both chords transposed up or down a tritone will result in the same pitches as the original.

As with the diminished seventh chord, the latter property allows the chord to be used in modulating to very remote keys. For instance: ♭6—1—2—♯4; (A♭—C—D—F♯ in C), could be interpreted identically in F♯ if reordered and respelled as D—F♯—G♯—B♯, i.e., the French sixth of the ♯IV key area, displaced an interval of a tritone relative to the tonic key, I.

Dominant functions

German sixth, A♭-C-D♯-F♯, and equivalent dominant seventh, A♭-C-E♭-G♭  Play

Irregular resolution through augmented sixth equivalence  Play .

All variants of augmented sixth chords are closely related to the applied dominant V⁷ of ♭II; both Italian and German variants are enharmonically identical to dominant seventh chords. For example, in the key of C (I), the German sixth chord, A♭—C—E♭—F♯, could be reinterpreted as A♭—C—E♭—G♭, the applied dominant of D♭ (V/D♭).

Function

In most occasions, the augmented 6th cords precede either the dominant, or the tonic in second inversion.

The augmented sixths can be treated as chromatically altered passing chords.

Tristan chord

Main article: Tristan chord

Richard Wagner's Tristan chord (indicated below with Tr) from the opening of his opera, Tristan und Isolde, can be interpreted as a French sixth in the key of A minor (F-A-B-D♯) with an upwardly resolving long appoggiatura in the upper voice (G♯ to A). Note that the D♯ resolves downwards to D♮ instead of E:

See also

• Acoustic scale

Books

• Rimsky-Korsakov, Nikolai (1886). Practical Treatise on Harmony (13th - 1924 ed.). St. Petersburg: A. Büttner.