User:Blehfu/Sandbox/Augmented sixth chord



An augmented sixth chord contains the interval of an augmented sixth above its "root." 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.

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.

Standard harmonic function
From the Baroque to the Romantic period, augmented sixth chords have had the same harmonic function: As an chromatically altered predominant chord (typically, an alteration of ii$_3^4$, IV$_5^6$, vi7 or their 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.

During the Romantic period, the augmented sixth harmony increased in ambiguity as composers explored other functional possibilities outside of its role as a predominant. See.

Variants
There are several variants of the augmented sixth chord, each named after a European nationality though irrelevant to their respective origin and function. Theorists have struggled for centuries to explain the origins of these chords, define their roots, and fit them into conventional harmonic theory.

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

Examples

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

French sixth
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. This chord is called "French" because its notes are all contained within the same whole tone scale, lending a sonority common to French music in the 19th century.

Examples

 * Richard Wagner's famous 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 appoggiatura in the upper voice. Note that the D♯ resolves downwards to D♮ instead of E:

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. 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.

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 a 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.

Examples

 * A German sixth can be found in the high passage heard twice in the "Passepied" from Debussy's Suite Bergamasque.
 * A German sixth chord from Michael Haydn's Requiem in C minor, first movement:

Other variants
Other variants of augmented sixth chords are sometimes found in the repertoire, and are sometimes given whimsical geographical names. For example, a chord comprising 4, ♭6, 7, and ♯2 is called by one source an Australian sixth. Such anomalies usually have alternative interpretations.

"Inverted" 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.

Examples

 * Tchaikovsky's, Symphony no. 5 (op. 64, I), Allegro con anima (bars 3–4).
 * The following excerpt shows an augmented sixth chord in inversion used by Bach. 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:

"Roots" of augmented sixth chords
Theorists vary in their treatment of the roots of augmented sixth chords.

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 spellings with different functions (i.e., both predominant as a German sixth and dominant and 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.

Enharmonic equivalency of the French sixth
The French sixth has two characteristics in common with the diminished seventh chord: 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 could be reinterpreted as 2, ♯4, ♯5, ♯7, i.e., the French sixth of the ♯IV key area.
 * 1) Both chords are constructed of two superimposed tritones; in the French sixth, between ♭6-2 and 1-♯4. 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.

Dominant functions
All variants of augmented sixth chords are closely related to the applied dominant V7 of ♭II; both Italian and German variants are enharmonically identical. For example, in the key of C, the German sixth chord, A♭–C-E♭-F♯, could be reinterpreted as A♭-C-E♭–G♭, the applied dominant of D♭.

French sixth sonority as dominant
In jazz, the French sixth sonority functions as a dominant instead of a predominant chord; utilizing the enharmonically equivalent property of the French sixth is a common technique is referred to as tritone substitution.

The French sixth sonority, for example A♭, C, D, F♯ in the key of C, is interpreted as a specific variation of a dominant seventh chord in the following keys: This chord is called the Lydian dominant (A♭7♯11, D7♯11).
 * V7 of D♭ with ♯4; A♭ as the root: A♭, C, D, G♭; or
 * V7 of G with ♯4; D as the root: D, F♯, G♯, C.

Augmented sixths built on scale degrees other than ♭6
Occasionally the lowest note of the augmented sixth interval is on a different scale degree. Most often, this is the result of a temporary tonicization, and the resulting augmented sixth chord is borrowed from the key of the secondary dominant which follows it. However, there are examples in the literature of these chords appearing without such a context. Schubert used it in some of his last compositions in dramatic final cadences.

Examples

 * An Italian sixth chord built on scale degree ♭2 in Schubert's piano sonata D. 959, preceded by a ♭II chord in root position (B♭-D-F♮). Instead of functioning as a predominant, here, both the ♭II and the Italian sixth chord serve in a sort of "neighbour motion," or "plagal cadence" (usually I-IV-I) in the coda. I-♭II-(It+6)-I: