Editing Augmented sixth chord (section)

==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.