View source for Augmented sixth chord

{{Short description|Chord that contains the interval of an augmented sixth}}

{{Image frame|content=<score sound="1" override_midi="Scott Joplin - Bink's Waltz, mm.95-100 German sixth MIDI.mid">

    {
      #(set-global-staff-size 16)
      \new PianoStaff <<
        \new Staff <<
            \relative c'' {
                \set Score.currentBarNumber = #95
                \bar ""
                \clef treble \key es \major \time 3/4
                \override DynamicLineSpanner.staff-padding = #3
                <es g es'>2.\f
                <c f aes c>4^\markup { \raise #4 \bold "rit." } <aes c f aes> <a es' fis a>
                <bes es g bes>2(^\markup { \raise #4 \bold "a tempo" } <c es g c>4)
                <aes d aes'>4 <f aes f'>4. <bes bes'>8
                <es, g es'>2.~\mf
                <es g es'>4
                }
            >>
        \new Staff <<
            \override Staff.SustainPedalLineSpanner.staff-padding = #6.3
            \relative c, {
                \clef bass \key es \major \time 3/4
                <c c'>4\sustainOn_\markup { \lower #9.2 \concat { \translate #'(-4.8 . 0) { "E" \flat ":  vi" \hspace #9 "ii" \raise #1 \small "6" \hspace #4.5 "Ger" \raise #1 \small "+6" \hspace #0.5 "I" \raise #1 \small "6/4" \hspace #6.5 "V" \raise #1 \small "7" \hspace #9 "I" } } }
                    <g'' c es> <g c es>
                <aes,, aes'>\sustainOff\sustainOn <c c'> <ces ces'>\sustainOff
                <bes bes'>\sustainOn <g'' bes es> <g bes es>
                <bes,, bes'>\sustainOff\sustainOn <aes'' bes d> <aes bes d>
                <es, es'>\sustainOff bes' g
                es
                }
            >>
    >> }
</score>|width=520|caption=A German sixth chord on the last beat of m. 96 in [[Scott Joplin]]'s "Binks' Waltz" (1905).<ref name="B&S">Benward, Bruce and Saker, Marilyn (2009<!--1977-->). ''Music in Theory and Practice'', Vol. II, p.105. Eighth edition. McGraw Hill. {{ISBN|9780073101880}}.</ref>}}

In [[music theory]], an '''augmented sixth chord''' contains the [[interval (music)|interval]] of an [[augmented sixth]], usually above its [[bass note|bass tone]]. This [[chord (music)|chord]] has its origins in the [[Renaissance music|Renaissance]],{{sfn|Andrews|1950|pp=45–46}} was further developed in the [[Baroque music|Baroque]], and became a distinctive part of the musical style of the [[Classical period (music)|Classical]] and [[Romantic period (music)|Romantic]] periods.{{sfn|Andrews|1950|pp=46–52}}

Conventionally used with a [[predominant chord|predominant]] [[diatonic function|function]] ([[resolution (music)|resolving]] to the [[dominant (music)|dominant]]), the three most common types of augmented sixth chords are usually called the ''Italian sixth'', the ''French sixth'', and the ''German sixth''.

==Augmented sixth interval==
{{Main|Augmented sixth}}
{{Image frame|content=<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \minor \time 4/4
                fis1 g
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \minor \time 4/4
                aes1 g \bar "||"
                }
            >>
    >> }
</score>|width=300|caption=The interval of the [[augmented sixth]] normally resolves outwards by semitone to an octave.}}

The augmented sixth interval is typically between the sixth [[scale degree|degree]] of the [[Major and minor|minor scale]], {{music|flat}}{{music|scale|6}}, and the raised fourth degree, {{music|sharp}}{{music|scale|4}}. With standard [[voice leading]], the chord is followed directly or indirectly by some form of the [[dominant chord]], in which both {{music|flat}}{{music|scale|6}} and {{music|sharp}}{{music|scale|4}} have resolved to the fifth scale degree, {{music|scale|5}}. This tendency to resolve outwards to {{music|scale|5}} is why the interval is spelled as an augmented sixth, rather than [[enharmonic]]ally as a [[minor seventh]] ({{music|flat}}{{music|scale|6}} and {{music|flat}}{{music|scale|5}}). 

Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by [[borrowed chord|borrowing]] {{music|flat}}{{music|scale|6}} of the [[parallel minor]] scale.<ref name="Aldwell478483">{{Cite book
 | last1 = Aldwell
 | first1 = Edward
 | author1-link = Edward Aldwell
 | last2 = Schachter
 | first2 = Carl
 | author2-link = Carl Schachter
 | year = 1989
 | title = Harmony and Voice Leading
 | edition = 2
 | location = San Diego, Toronto
 | publisher = [[Harcourt Brace Jovanovich]]
 | isbn = 0-15-531519-6
 | oclc = 19029983
 | pages = 478–483
}}</ref>

==Types==
There are three main types of augmented sixth chords, commonly known as the ''Italian sixth'', the ''French sixth'', and the ''German sixth''. 

{{block indent|<score sound="1">
    {
      \override Score.TimeSignature #'stencil = ##f
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                \textLengthOn
                <c fis>1^\markup { "Italian" }
                <d fis>^\markup { "French" }
                <es fis>^\markup { "German" }
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1 \bar "||"
                <aes c> \bar "||"
                <aes c> \bar "||"
                }
            >>
    >> }
</score>}}
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.<ref name="Aldwell478483"/><ref>{{Cite book | last = Gauldin | first = Robert | year = 1997
 | title = Harmonic Practice in Tonal Music | edition = 1 | location = New York | publisher = [[W.W. Norton]] | isbn = 0-393-97074-4
 | oclc = 34966355 | pages = 422–438}}</ref><ref>{{Cite book | last = Christ | first = William | year = 1973
 | title = Materials and Structure of Music | edition = 2 | volume = 2 | location = Englewood Cliffs, NJ | publisher = [[Prentice Hall]] | isbn = 0-13-560342-0 | oclc = 257117 | pages = 141–171}} Offers a detailed explanation of augmented sixth chords as well as [[Neapolitan sixth]] chords.</ref> According to Kostka and Payne, the other two terms are similar to the ''Italian sixth'', which, "has no historical authenticity-[being] simply a convenient and traditional label."<ref>Kostka & Payne (1995), p.385.</ref>

===Italian sixth===
{{Image frame|content=<score sound="1" override_midi="BeethovenOp78.mid">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \tempo "Allegro vivace"
                \clef treble \key fis \major \time 2/4
                \override DynamicLineSpanner.staff-padding = #2.8
                <fis bis>4.(\f <eis cis'>8)
                <eis gis> r r <fis ais>\p
                <dis b'!>8.( <cis ais'>16) <b gis'>8-. <ais fis'>-.
                <gis eis'>4 r
                }
            >>
        \new Staff <<
            \relative c {
                \clef bass \key fis \major \time 2/4
                <d fis>4.( <cis gis'>8)
                <b! cis> r r ais
                gis8.( ais16) b8-. bis-.
                cis4 r
                }
            >>
    >> }
</score>|width=420|caption=The second movement of [[Beethoven]]'s [[Piano Sonata No. 24 (Beethoven)|Piano Sonata in F{{music|sharp}} major, Op. 78]], begins with an Italian sixth chord.}}
The Italian sixth (It<sup>+6</sup> or It<sup>6</sup> or {{music|sharp}}iv<sup>6</sup>) is derived from iv<sup>6</sup> with an altered fourth [[Scale-degree|scale degree]], {{music|sharp}}{{music|scale|4}}. This is the only augmented sixth chord comprising just three distinct notes; in [[Four-part harmony|four-part writing]], the tonic pitch is [[Voicing (music)#Doubling|doubled]]<!--wouldn't it be because it's the best voice leading strategy?-->.
{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                <c fis>1 <d g>
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1_\markup { \concat { "It" \raise #1 \small "+6" \hspace #4.3 "V" } } 
                <g b> \bar "||"
                }
            >>
    >> }
</score>}}

The Italian sixth is enharmonically equivalent to an incomplete [[dominant seventh]].{{sfn|Rimsky-Korsakov|1924|p=121}} {{music|b}}VI7={{music|#}}V7: A{{music|b}}, C, (E{{music|b}},) G{{music|b}}.

===French sixth===
[[File:French sixth chord in Schubert's Am Feirabend.png|thumb|350px|A French sixth chord in Schubert's ''[[Die schöne Müllerin]]'', #5: "Am Feierabend"<ref>[[Allen Forte|Forte, Allen]], ''Tonal Harmony'', third edition (S.l.: Holt, Rinehart, and Wilson, 1979): p.355. {{ISBN|0-03-020756-8}}. Original with all uppercase Roman numerals.</ref> {{audio|French sixth chord in Schubert's Am Feirabend.mid|Play}}]]

The French sixth (Fr<sup>+6</sup> or Fr{{su|b=3|p=4}}) is similar to the Italian, but with an additional tone, {{music|scale|2}}. 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]]),<ref>Blatter, Alfred (2007). ''Revisiting Music Theory: a Guide to the Practice'', p.144. {{ISBN|978-0-415-97440-0}}. "One may note that the French sixth contains the elements of a whole tone scale commonly associated with French impressionistic composers."</ref> though they also make frequent appearances in Russian music.

{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                <d fis>1 <d g>
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #3.7 "V" } } 
                <g b> \bar "||"
                }
            >>
    >> }
</score>}}

This chord has the same notes as a [[dominant seventh flat five]] chord and is in fact the [[second inversion]] of II<sup>7{{Music|b}}5</sup>.

===German sixth===
The German sixth (Ger<sup>+6</sup> or Ger{{su|p=6|b=5}}) is also like the Italian, but with an added tone, {{music|flat}}{{music|scale|3}}.

{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                <es fis>1 <d g>
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1_\markup { \concat { \translate #'(-2 . 0) { "Ger" \raise #1 \small "+6" \hspace #4.5 "V" } } }
                <g b> \bar "||"
                }
            >>
    >> }
</score>}}

In Classical music, however, it appears in much the same places as the other variants, though perhaps less often because of the [[counterpoint|contrapuntal]] difficulties outlined below. It appears frequently in the works of Beethoven,{{efn|Notable examples include the themes of the slow movements (both in variation form) of the opp. 57 ("Appassionata") and 109 piano sonatas.}} and in [[ragtime music]].<ref name="B&S" /> The German sixth chord is [[enharmonically equivalent]] to a [[dominant seventh chord]] though it functions differently.

==== Avoiding parallel fifths ====
It is more difficult to avoid [[parallel fifths]] when resolving a German sixth chord to the dominant chord. These parallel fifths, referred to as ''[[Consecutive fifths#Mozart fifths|Mozart fifths]]'', were occasionally accepted by [[Common practice period|common practice]] composers. There are two ways they can be avoided:

{{ordered list
|The {{music|flat}}{{music|scale|3}} can move to either {{music|scale|1}} or {{music|scale|2}}, thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between {{music|flat}}6 and {{music|flat}}{{music|scale|3}}.<ref>{{Cite book
 | last1 = Benjamin
 | first1 = Thomas
 | last2 = Horvit
 | first2 = Michael
 | last3 = Nelson
 | first3 = Robert
 | year = 2008
 | title = Techniques and Materials of Music: From the Common Practice Period Through the Twentieth Century
 | edition = seventh
 | location = Belmont, CA
 | publisher = Thomson Schirmer
 | isbn = 978-0-495-18977-0
 | oclc = 145143714
 | page = 165
}} Beethoven frequently moves from one form of the chord to another in such a way, sometimes passing through all three.</ref>

{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c' {
                \clef treble \key c \major \time 4/4
                \voiceOne fis1 g
                }
            \new Voice \relative c' {
                \clef treble \key c \major \time 4/4
                \voiceTwo es2 d2~ d1
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1
                <g b> \bar "||"
                }
            >>
    >> }
</score>}}

|The chord can resolve to a [[Second inversion|{{music|64 chord}} chord]], functionally either as a [[Cadential six-four|cadential {{music|64 chord}}]] intensification of V, or as the second [[Inversion (music)#Inverted chords|inversion of I]]. The cadential {{music|64 chord}}, in turn, resolves to a [[root-position]] V. This [[chord progression|progression]] ensures that, in its voice leading, each pair of voices moves either by [[contrapuntal motion|oblique motion or contrary motion]] and avoids parallel motion altogether. In minor modes, both {{music|scale|1}} and {{music|flat}}{{music|scale|3}} do not move during the resolution of the German sixth to the cadential {{music|64 chord}}. 

{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c' {
                \clef treble \key c \minor \time 4/4
                \voiceOne fis1 g
                }
            \new Voice \relative c' {
                \clef treble \key c \minor \time 4/4
                \voiceTwo es1 es2 d2
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \clef bass \key c \minor \time 4/4
                \voiceOne c1 c2 b
                }
            \new Voice \relative c' {
                \clef bass \key c \minor \time 4/4
                \voiceTwo aes1 g \bar "||"
                }
            >>
    >> }
</score>}}

In major modes, {{music|flat}}3 can be enharmonically respelled as {{music|sharp}}{{music|scale|2}}, allowing it to resolve upwards to {{music|natural}}{{music|scale|3}}. This may be called a doubly-augmented sixth, although in reality it is the fourth that is doubly augmented.<ref name=carl/>{{Rp|99}}

{{block indent|<score sound="1">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c' {
                \clef treble \key c \major \time 4/4
                \voiceOne fis1 g
                }
            \new Voice \relative c' {
                \clef treble \key c \major \time 4/4
                \voiceTwo dis1 e2 d
                }
            >>
        \new Staff <<
            \new Voice \relative c' {
                \clef bass \key c \major \time 4/4
                \voiceOne c1 c2 b
                }
            \new Voice \relative c' {
                \clef bass \key c \major \time 4/4
                \voiceTwo aes1 g \bar "||"
                }
            >>
    >> }
</score>}}}}

===Other types===
Other variants of augmented sixth chords can be found in the repertoire, and are sometimes given whimsical geographical names. For example: 4–{{music|flat}}6–7–{{music|sharp}}2; (F–A{{music|flat}}–B–D{{music|sharp}}) is called by one source an ''Australian sixth'', and 1- 2 - {{music|#}}4 - {{music|#}}6 (C - D - F{{music|#}} - A{{music|#}} ) sometimes called the ''Japanese sixth, Blackadder, or Ikisugi chord.''<ref>{{Cite book
 | last = Burnard
 | first = Alex
 | year = 1950
 | title = Harmony and Composition: For the Student and the Potential Composer
 | location = Melbourne
 | publisher = [[Allans Music]] (Australia)
 | oclc = 220305086
 | pages = 94–95
}}</ref><ref>{{Cite web|date=2019-11-15|title=Blackadder Chord (en)|url=https://soundquest.jp/quest/chord/chord-mv8/blackadder-chord-en/|access-date=2021-04-06|website=SoundQuest|language=ja}}</ref> Such anomalies usually have alternative interpretations.

==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>}}

==Inversions==
Augmented sixth chords are occasionally used with a different chord member in the [[Bass note|bass]]. Since there is no consensus among theorists that they are in [[root position]] in their normal form, the word "[[Inverted chord|inversion]]" isn't necessarily accurate, but is found in some textbooks, nonetheless.{{Citation needed|date=November 2018}} Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

[[Jean-Jacques Rousseau|Rousseau]] held that the chord could not be inverted.<ref>{{cite book|last=Rousseau|first=Jean Jaques|title=Dictionnaire de Musique|year=1826 |publisher=Paris Emler Fréres |url=https://archive.org/details/dictionnairedem01rous}}</ref> Seventeenth century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources.<ref>Ellis, Mark (2010). ''A Chord in Time: The Evolution of the Augmented Sixth from Monteverdi to Mahler'', pp. 92–94. Farnham: Ashgate. {{ISBN|978-0-7546-6385-0}}.</ref> 

The excerpt below is from [[Johann Sebastian Bach|J.S. 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{{music|sharp}}–E{{music|flat}}); these two voices resolve inward to an octave.

{{block indent|<score sound="1" override_midi="Excerpt from Bach's Mass in B Minor.mid">
    { 
  #(set-global-staff-size 16)
  \set Score.proportionalNotationDuration = #(ly:make-moment 1/8)
<< \new StaffGroup <<
        \new Staff <<
            \set Staff.midiInstrument = #"voice oohs"
            \relative c' {
                \clef treble \key g \major \time 3/2
                fis1 f2 e1 \breathe es2 d2^( c4 b) c2 b1.\fermata \bar "|."
                }
            \addlyrics { pul -- tus est, se -- pul -- tus est. }
            >>
        \new Staff <<
            \set Staff.midiInstrument = #"voice oohs"
            \clef treble \key g \major \time 3/2
            \new Voice \relative c' {
                c2  b1~ b2 \breathe c bes a1 a2 g1.\fermata
                }
            \addlyrics { _ sus __ et, se -- pul -- tus est.  }
            >>
        \new Staff <<
            \set Staff.midiInstrument = #"voice oohs"
            \clef "treble_8" \key g \major \time 3/2
            \new Voice \relative c {
                fis1^( gis2~ gis) a \breathe g! g1 fis2 d1.\fermata
                }
            \addlyrics { pul -- tus, se -- pul -- tus est. }
            >>
        \new Staff <<
            \set Staff.midiInstrument = #"voice oohs"
            \clef bass \key g \major \time 3/2
            \new Voice \relative c {
                dis2( d) d cis \breathe c cis d1 d2 g,1.\fermata
                }
            \addlyrics { pul -- tus est et se -- pul -- tus est. }            >>
    >>
    { \new PianoStaff <<
         \new Staff <<
            \set Staff.midiInstrument = #"piano"
            \clef treble \key g \major \time 3/2
            \new Voice \relative c' {
                R1. R1. R1. R1.\fermata
                } >>
         \new Staff <<
            \set Staff.midiInstrument = #"piano"
            \clef bass \key g \major \time 3/2
            \new Voice \relative c, {
                <dis dis'>4-.( <dis dis'>-. <d d'>-. <d d'>-. <d d'>-. <d d'>-.)
                <cis cis'>-.( <cis cis'>-. <c c'>-. <c c'>-. <cis cis'>-. <cis cis'>-.)
                <d d'>-.( <d d'>-. <d, d'>-. <d d'>-.^\ppp <d d'>-. <d d'>-.)
                <g g'>1.\fermata
                } >>
            >>}
>> }
</score>}}

== Related chords ==
In music theory, the double-diminished triad is an archaic concept and term referring to a [[triad (music)|triad]], or three note chord, which, already being minor, has its [[root (chord)|root]] raised a semitone, making it "doubly diminished". However, this may be used as the derivation of the augmented sixth chord.<ref>Ernst Friedrich Richter (1912). ''Manual of Harmony'', p.94. Theodore Baker.</ref> For example, F–A{{music|b}}–C is a minor triad, so F{{music|#}}–A{{music|b}}–C is a doubly diminished triad. This is enharmonically equivalent to G{{music|b}}–A{{music|b}}–C, an incomplete [[Dominant seventh chord|dominant seventh]] A{{music|flat}}{{music|7 chord}}, missing its [[Fifth (chord)|fifth]]<!--in D{{music|b}}-->), which is a [[tritone substitution|tritone substitute]] that [[Resolution (music)|resolves]] to G. Its [[Inverted chord|inversion]], A{{music|b}}–C–F{{music|#}}, is the Italian sixth chord<!--a predominant in C--> that resolves to G.

Classical harmonic theory would notate the [[Tritone substitution|tritone substitute]] as an augmented sixth chord on {{music|flat}}2. The augmented sixth chord can either be (i) an It<sup>+6</sup> [[enharmonically equivalent]] to a dominant seventh chord (with a missing [[Fifth (chord)|fifth]]); (ii) a Ger<sup>+6</sup> equivalent to a dominant seventh chord with (with a fifth); or (iii) a Fr<sup>+6</sup> equivalent to the [[Lydian dominant]] (with a missing fifth), all of which serve in a classical context as a substitute for the [[secondary dominant]] of V.<ref>Satyendra, Ramon. "Analyzing the Unity within Contrast: Chick Corea's ''Starlight''", p.55. Cited in Stein.</ref><ref>Stein, Deborah (2005). ''Engaging Music: Essays in Music Analysis''. New York: Oxford University Press. {{ISBN|0-19-517010-5}}.</ref>

{{block indent|<score sound="1">
{
    \relative c' {
        \time 4/4
        <des f aes ces>1^\markup { "Tritone sub" } 
        <c e g c> \bar "||"
        <des f b>^\markup { "(i) Italian" } 
        <c e c'> \bar "||"
        <des f aes b>^\markup { "(ii) German" } 
        <c e g c> \bar "||"
        <des f g b>^\markup { "(iii) French" } 
        <c e g c> \bar "||"
    }
}
</score>}}

All variants of augmented sixth chords are closely related to the [[applied dominant]] V<sup>7</sup> of {{music|flat}}II. Both Italian and German variants are enharmonically identical to dominant seventh chords. For example, in the key of C, the German sixth chord could be reinterpreted as the applied dominant of D{{music|flat}}.

{{block indent|<score sound="1">
    {
      \override Score.TimeSignature #'stencil = ##f
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                <es ges>1
                <c fis>
                <es fis>
                }
            >>
        \new Staff <<
            \relative c' {
                \clef bass \key c \major \time 4/4
                <aes c>1_\markup { \center-align { \concat { "V" \raise #1 \small "7" "/♭II" } } } \bar "||"
                <aes c>1_\markup { \concat { "It" \raise #1 \small "+6" } } \bar "||"
                <aes c>1_\markup { \concat { "Ger" \raise #1 \small "+6" } } \bar "||"
                }
            >>
    >> }
</score>}}

[[Simon Sechter]] explains the chord of the French sixth chord as being a chromatically altered version of a [[seventh chord]] on the second [[Degree (music)|degree]] of the scale, {{music|scale|2}}. The German sixth is explained as a chromatically altered [[ninth chord]] on the same [[Root (chord)|root]] but with the root omitted.<ref name="Sechter">{{cite book|last=Sechter|first=Simon|title=Die Grundsätze der musicalischen Komposition|year=1853|publisher=Breitkopf und Härtel|location=Leipzig|language=German}}</ref>

{{block indent|<score sound="1">
    {
      \override Score.TimeSignature #'stencil = ##f
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \key c \major \time 4/4
                \textLengthOn
                <fis c'>1^\markup { "French" } 
                <fis c' es>^\markup { "German" } 
                }
            >>
        \new Staff <<
            \relative c {
                \clef bass \key c \major \time 4/4
                <d aes'>1 \bar "||"
                <\parenthesize d aes'>1 \bar "||"
                }
            >>
    >> }
</score>}}

The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the A{{music|flat}}, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F{{music|sharp}} – being chromatically raised – must rise.
==Relationship between the different types==
The following "curious chromatic sequence",<ref>Ouseley, Frederick. A. Gore (1868). ''A Treatise on Harmony'', pg. 138, Oxford, Clarendon Press.</ref> graphed by [[Dmitri Tymoczko]] as a four-dimensional [[tesseract]],<ref>Tymoczko, Dimitri. ''A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice'' (Oxford and New York: Oxford University Press, 2011), pg. 106. {{ISBN|978-0-19-533667-2}}.</ref> outlines the relationships between the augmented sixth chords in [[12TET]] tuning:

[[File:Schlegel wireframe 8-cell.png|right|thumb|A tesseract. The diminished seventh chords occupy points on two diagonally opposite corners.]]

* Starting with a [[diminished seventh chord]], lower any [[factor (chord)|factor]] by a [[semitone]].  The result is equivalently to a German sixth chord.
* From the German sixth chord, lower any factor by a semitone so that the result is [[anhemitonic scale|ancohemitonic]] (i.e.: possesses no half steps). The result is a French sixth chord or [[minor seventh chord]] possibly posing as a virtual augmented sixth.
* From the French sixth chord (or minor seventh chord posing as augmented sixth), there exists a factor which, when lowered by semitone, gives a result equivalent to a [[half-diminished seventh chord]] possibly posing as a virtual augmented sixth.
* From the half-diminished seventh chord as augmented sixth, there exists a factor which, when lowered by a semitone, is equivalent to a diminished seventh chord at the interval one semitone lower than the diminished seventh chord which started the [[Sequence space|sequence]].
* Three [[Phase (waves)|repetitions]] of the above complete the cycle in [[Modulo (mathematics)|modulo-12]] [[Phase space|note space]], forming a [[Necklace (combinatorics)|necklace]] of three tesseracts joined at opposite [[vertex (graph theory)|corners]] by diminished seventh chords and subsuming all 12 notes of the [[chromatic scale]].

===Minor seventh as virtual augmented sixth chord===
The [[minor seventh chord]] may also have its interval of [[Subtonic|minor seventh]] (between the root and seventh degree (i.e.: C–B{{music|flat}} in C–E{{music|flat}}–G–B{{music|flat}}) rewritten as an [[augmented sixth]] (C–E{{music|flat}}–G–A{{music|sharp}}).<ref name="Ouseley, Frederick 1868 pg. 137" /> Rearranging and transposing, this gives A{{music|flat}}–C{{music|flat}}–E{{music|flat}}–F{{music|sharp}}, a virtual [[minor chord|minor]] version of the German sixth chord.<ref>Ouseley (1868), pg. 143ff.</ref> Again like the typical +6, this enharmonic interpretation gives a resolution [[Irregular resolution|irregular]] for the minor seventh but normal for the augmented sixth, where the two voices at the enharmonic [[major second]] converge to a [[unison]] or diverge to an [[octave]].<ref name="Christ, William 1966 p. 154" />

===Half-diminished seventh as virtual augmented sixth chord===
The [[half-diminished seventh chord]] is the [[Melodic inversion|inversion]] of the German sixth chord<ref>Hanson, Howard. (1960) Harmonic Materials of Modern Music, p.356ff. New York: Appleton-Century-Crofts. LOC 58-8138.</ref> (it is its inversion as a [[Set (music)|set]], rather than as a [[Chord (music)|chord]]). Its interval of minor seventh (between root and seventh degree (i.e.: C–B{{music|flat}} in C–E{{music|flat}}–G{{music|flat}}–B{{music|flat}}) can be written as an augmented sixth (C–E{{music|flat}}–G{{music|flat}}–A{{music|sharp}}).<ref name="Ouseley, Frederick 1868 pg. 137">Ouseley, Frederick. A. Gore (1868). ''A Treatise on Harmony'', pg. 137, Oxford, Clarendon Press.</ref>  Rearranging and transposing, this gives A{{music|flat}}–C{{music|flat}}–D–F{{music|sharp}}, a virtual minor version of the French sixth chord.<ref>Chadwick, G. W. (1922). ''Harmony: A Course of Study'', pg. 138ff, Boston, B. F. Wood. {{No ISBN}}</ref>{{Quote needed|date=March 2015}}  Like the typical +6, this enharmonic interpretation gives a resolution irregular for the half-diminished seventh but normal for the augmented sixth, where the two voices at the enharmonic major second converge to a unison or diverge to an octave.<ref name="Christ, William 1966 p. 154">Christ, William (1966). ''Materials and Structure of Music'', v.2, p. 154. Englewood Cliffs: Prentice-Hall. LOC 66-14354.</ref>

==Tristan chord==
{{main|Tristan chord}}
[[Richard Wagner]]'s [[Tristan chord]], the first vertical sonority in his opera, ''[[Tristan und Isolde]]'', can be interpreted as a [[Half-diminished seventh chord|half-diminished seventh]] that transitions to a French sixth in the key of A minor (F–A–B–D{{music|sharp}}, in red below). The upper voice continues upward with a long [[appoggiatura]] (G{{music|sharp}} to A). Note that the D{{music|sharp}} resolves down to D{{music|natural}} instead of up to E:<ref>Benward, Bruce, and Marilyn Nadine Saker (2008). ''Music in Theory and Practice, vol. 2'', p.233. Boston: McGraw-Hill. {{ISBN|978-0-07-310188-0}}.</ref>

{{block indent|<score lang="lilypond" override_ogg="Wagner Tristan opening (orchestral).ogg">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \clef treble \key a \minor \time 6/8
                \voiceOne \partial8 r8 R2. gis4.->(~ gis4 \once \override NoteHead.color = #red a8 ais8-> b4~ b8) r r
                }
            \new Voice \relative c' {
                \override DynamicLineSpanner.staff-padding = #4.5
                \once \override DynamicText.X-offset = #-5
                \voiceTwo \partial8 a\pp( f'4.~\< f4 e8 \once \override NoteHead.color = #red dis2.)(\> d!4.)~\p d8 r r
                }
            >>
        \new Staff <<
            \relative c {
                \clef bass \key a \minor \time 6/8
                \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.(_\markup { \concat { "Fr" \raise #1 \small "+6" \hspace #8 "V" \raise #1 \small "7" } } <e gis>4.)~ <e gis>8 r r
                }
            >>
    >> }
</score>}}

==See also==
*[[Neapolitan chord]]
*[[Acoustic scale]]

==Notes==
{{notelist}}

==References==
{{Reflist|refs=

<ref name=carl>Carl McKinley (2011). [https://books.google.com/books?id=0SdNAwAAQBAJ&pg=PA99 ''Harmonic Relations: A Practical Textbook for the Study of Harmony'']. Eugene, Oregon: Resource Publications. {{isbn|9781610975315}}.</ref>


}}

==Further reading==
* {{Cite book | last = Andrews | first = Herbert Kennedy | year = 1950 | title = The Oxford Harmony | edition = 1st | volume = 2 | location = London | publisher = [[Oxford University Press]] | oclc = 223256512 }}
* {{cite book|last=Piston|first=Walter|title=Harmony|year=1941|publisher=W. W. Norton & Company|location=New York and London|edition=co-author Mark DeVoto 5th – 1987 }}
* {{cite book|last=Rimsky-Korsakov|first=Nikolai|year=1924|title=Practical Treatise on Harmony|orig-year=1886|publisher=A. Büttner.|location=St. Petersburg|edition=13th}}

==External links==

* [https://commons.wikimedia.org/wiki/Category:Augmented_sixths Augmented sixths] in Commons.

{{Chords}}
{{Chromaticism}}

{{DEFAULTSORT:Augmented Sixth Chord}}
[[Category:Chords]]
[[Category:Chromaticism]]