Editing Augmented sixth chord (section)

===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>}}}}