Editing Augmented sixth chord (section)

==Function==
===Standard function===
From the [[Baroque music|Baroque]] to the [[Romantic music|Romantic periods]], augmented sixth chords had the same [[Diatonic function#Diatonic functions of notes and chords|harmonic function]]: as a [[chromatic]]ally altered [[predominant chord]] (typically, an alteration of [[supertonic|ii{{su|b=3|p=4}}]], [[subdominant|IV{{su|b=5|p=6}}]], [[submediant|vi<sup>7</sup>]] or their [[Parallel key|parallel]] equivalents in the minor mode) leading to a dominant chord. This movement to the dominant is heightened by the [[semitone|semitonal]] resolution to {{music|scale|5}} from above and below (from {{music|flat}}{{music|scale|6}} and {{music|sharp}}{{music|scale|4}});<ref>{{cite book |last1=Kostka |first1=Stefan |first2=Dorothy |last2=Payne |year=1995 |title=Tonal Harmony |edition=3rd |place=New York, NY |publisher=McGraw Hill |page=384 |ISBN=0070358745 }}</ref> essentially, these two notes act as [[leading-tone]]s.

During the Baroque and early Classical periods, for instruments tuned to [[meantone]] systems rather than [[well temperament]]s, the augmented sixth note ({{sup|{{music|#}}}}6) produced an excellent approximation to a [[harmonic seventh]]. The match is particularly close in [[quarter comma meantone]], where {{sup|{{music|#}}}}6 is only 3&nbsp;[[cents (music)|cents]] flat from H{{sub|7}}. This made a major triad with an added {{sup|{{music|#}}}}6 a fully consonant / harmonic chord (harmonics&nbsp;4, 5, 6, 7); as opposed to a modern [[12 tone equal temperament|equal tempered]] [[dominant seventh chord]] (M add{{sup|{{music|b}}}}7) which misses being harmonic with the minor&nbsp;7th pitch 31&nbsp;cents sharp – a dissonance.

This characteristic has led many analysts<ref name=Piston419>{{cite book | last1 = Piston | first1 = Walter | author1-link = Walter Piston | first2 = Mark | last2 = de Voto | year = 1987 | title = Harmony | edition = 5 | location = New York, NY | publisher = [[W. W. Norton & Company, Inc.]] | isbn = 0-393-95480-3 | page = 419 | ref = CITEREFPiston419 }}</ref> to compare the voice leading of augmented sixth chords to the [[secondary dominant]] V of V because of the presence of {{music|sharp}}{{music|scale|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, {{music|flat}}{{music|scale|6}} and {{music|sharp}}{{music|scale|4}}, rather than just {{music|sharp}}{{music|scale|4}}.

In most occasions, the augmented-sixth chords precede either the dominant, or the [[tonic (music)|tonic]] in [[second inversion]].{{sfn|Rimsky-Korsakov|1924|p=121}} The augmented sixths can be treated as chromatically altered [[Passing chord|passing chords]].{{sfn|Rimsky-Korsakov|1924|p=121}}

===Other functions===
{{Image frame|content=<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c' {
                \clef treble \key c \major \time 4/4
                <f b f'>1^\markup { "Italian" } <g c e>
                <g b f'>^\markup { "French" } <g c e>
                \voiceOne <b f'>^\markup { "German" } <c e>
                }
            \new Voice \relative c'' {
                \clef treble \key c \major \time 4/4
                s1 s s s 
                \voiceTwo aes2 g g1
                }
            >>
        \new Staff <<
            \relative c {
                \clef bass \key c \major \time 4/4
                des1 c \bar "||"
                des c \bar "||"
                des c \bar "||"
                }
            >>
    >> }
</score>|width=445|caption=Augmented sixths as dominants in C major, according to Tchaikovsky. Notice the early resolution of an inner voice to avoid [[parallel fifths]] in the last example.<ref name="Tchaik"/>}}

In the late Romantic period and other musical traditions, 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 (music)|dominant]] as a [[Dominant seventh chord|dominant seventh]]), its function could be reinterpreted mid-phrase. This heightens both [[chromaticism]] by making possible the [[tonicization]] of [[Distant key|remotely related keys]], and possible [[Consonance and dissonance|dissonances]] with the juxtaposition of remotely related keys.

The French sixth sees a lot of non-functional use in much Russian music of the late-Romantic period. Due to its construction of two tritones separated by a major third, it has transpositional invariance and is often used to create tonal ambiguity in highly chromatic music of the 19th century. This use actually began in Germany with its use by [[Richard Wagner|Wagner]] and [[Anton Bruckner|Bruckner]] (eg. the prelude from ''[[Tristan und Isolde|Tristan und Ysolde]]'' and Bruckner's [[Symphony No. 3 (Bruckner)|third symphony]]), but is most notable in Russian works such as [[Nikolai Rimsky-Korsakov|Rimsky-Korsakov's]] ''[[Scheherazade (Rimsky-Korsakov)|Scheherezade]]''<ref>{{Citation |title=Ears Wide Open Online {{!}} Deconstructing Rimsky-Korsakov's Scheherazade |url=https://www.youtube.com/watch?v=vRlnhaLEWMc |access-date=2023-08-19 |language=en}}</ref> and [[Alexander Scriabin|Scriabin's]] ''[[Prometheus: The Poem of Fire]]''. The chord is separated by only a single note from the half-diminished chord, or the "Tristan chord," as well as the German sixth or dominant seventh. Tonal ambiguity is created by the French sixth as it is symmetrical about a tritone, for example, the notes of a French sixth chord built on G are the same as the notes as the chord built on C sharp, up to enharmonic equivalence. Due to this tonal ambiguity, the French sixth is often used in lieu of the triad and carries with it an unresolved and uneasy sound.

Scriabin also began to add chord extensions to the French sixth, for example, he added a sixth and a ninth to create his 'mystic chord' which is found in his aforementioned ''Prometheus'' tone poem. The chord is usually combined with the [[Octatonic scale|octatonic]], or diminished, scale, as the scale contains two distinct French sixths and thus has similar symmetric properties. This combination can be found ubiquitously in much of Rimsky and Scriabin's music, as well as in some 20th century French works such as [[Claude Debussy|Debussy's]] ''[[Nocturnes (Debussy)|Nuages]]''<ref>{{Cite book |last=Forte |first=Allen |title=Debussy and the Octatonic |year=1991}}</ref> and [[Maurice Ravel|Ravel's]] ''[[Gaspard de la nuit|Scarbo]]''.<ref>{{Cite web |last=Ravel |first=Maurice |date=1908 |title=Gaspard de la nuit: III. Scarbo, piano score |url=https://imslp.hk/files/imglnks/euimg/2/22/IMSLP813748-PMLP2576-Gaspard_de_la_nuit_-_III._Scarbo.pdf |website=IMSLP}}</ref>

[[Tchaikovsky]] considered the augmented sixth chords to be [[altered dominant|altered dominant chord]]s.<ref>Roberts, Peter Deane (1993). ''Modernism in Russian Piano Music: Skriabin, Prokofiev, and Their Russian Contemporaries'', p.136. {{ISBN|0-253-34992-3}}.</ref> He described the augmented sixth chords to be [[Inverted chord|inversions]] of the [[diminished triad]] and of dominant and [[Diminished seventh chord|diminished seventh chords]] with a lowered second degree ({{music|flat}}{{music|scale|2}}), 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 2nd degree, but on the altered 6th degree in major and on the natural 6th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6th degree is nothing else than a [[Modulation (music)|modulatory]] degression into the key of the dominant".<ref name="Tchaik">{{cite book|last=Tschaikovsky|first=Peter|title=Guide to the Practica Study of Harmony|year=1900|publisher=P. Jurgenson|location=Leipzig|pages=106, 108|url=http://imslp.org/wiki/Guide_to_the_Practical_Study_of_Harmony_%28Tchaikovsky,_Pyotr%29|edition=English translation|editor=Translated from the German version by Emil Krall and James Liebling|chapter=XXVII}}</ref>

The example below shows the last nine measures from [[Franz Schubert|Schubert]]'s [[Piano Sonata in A major, D 959 (Schubert)|Piano Sonata in A major, D. 959]]. In m. 352, an Italian sixth chord built on scale degree {{music|flat}}{{music|scale|2}} functions as a [[tritone substitution|substitute]] for the dominant. 

{{block indent|<score sound="1" override_midi="SchubertAug6.mid">
    {
      #(set-global-staff-size 18)
      \new PianoStaff <<
        \new Staff <<
            \set Score.currentBarNumber = #349
            \bar ""
            \new Voice \relative c' {
                \clef bass \key a \major \time 4/4
                \once \stemUp a4 r \clef treble \omit TupletNumber \tuplet 3/2 { a8 cis e } \tuplet 3/2 { a cis e }
                a8 r \ottava #1 <cis e a> \ottava #0 r r2\fermata
                r2 \tuplet 3/2 { bes,,8 d f } \tuplet 3/2 { bes d f }
                bes8 r \ottava #1 <d gis! d'> \ottava #0 r r2\fermata \break
                r2 \tuplet 3/2 { a,,8 cis e } \tuplet 3/2 { a cis e }
                \tuplet 3/2 { a cis e } \tuplet 3/2 { cis a e } \tuplet 3/2 { a_\markup { \italic "dimin." } e cis } \tuplet 3/2 { a e cis }
                R1
                r2 <a cis e a>4 r 
                <a cis e a>1
                }
            \new Voice \relative c {
                \clef bass \key a \major \time 4/4
                \once \stemDown <cis e>4\pp
                }
            >>
        \new Staff <<
            \relative c, {
                \clef bass \key a \major \time 4/4
                \omit TupletNumber \tuplet 3/2 { a8 \sustainOn cis e } \tuplet 3/2 { a cis e } r2
                \clef treble r4 <a' cis e a>8 r r2\fermata
                \clef bass \tuplet 3/2 { bes,,,8 d f } \tuplet 3/2 { bes d f } r2
                \clef treble r4 <bes' d gis!>8 r r2\fermata
                \clef bass \tuplet 3/2 { a,,,8 cis e } \tuplet 3/2 { a cis e } r2
                R1
                \tuplet 3/2 { a8 cis e } \tuplet 3/2 { cis a e } \tuplet 3/2 { a e cis } \tuplet 3/2 { a e cis }
                a4 r <a' cis e> r 
                <a cis e>1 \bar "|."
                }
            >>
    >> }
</score>}}