Augmented sixth chord

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{ #(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 } >> >> }
A German sixth chord on the last beat of m. 96 in Scott Joplin's "Binks' Waltz" (1905).[1]

In

Romantic periods.[3]

Conventionally used with a

function (resolving to the 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

{ \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 "||" } >> >> }
The interval of the augmented sixth normally resolves outwards by semitone to an octave.

The augmented sixth interval is typically between the sixth

enharmonically as a minor seventh (♭scale degree 6 and ♯scale degree 5
).

Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by

parallel minor scale.[4]

Types

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

{ \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 "||" } >> >> }

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.[4][5][6] 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."[7]

Italian sixth

{ \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 } >> >> }

The Italian sixth (It+6 or It6 or ♯iv6) is derived from iv6 with an altered fourth

scale degree, ♯scale degree 4. This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled
.

{ \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 "||" } >> >> }

The Italian sixth is enharmonically equivalent to an incomplete

dominant seventh.[8]
♭VI7=♯V7: A♭, C, (E♭,) G♭.

French sixth

A French sixth chord in Schubert's Die schöne Müllerin, #5: "Am Feierabend"[9] Playⓘ

The French sixth (Fr+6 or Fr4
3) is similar to the Italian, but with an additional tone,

Impressionist music),[10]
though they also make frequent appearances in Russian music.

{ \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 "||" } >> >> }

This chord has the same notes as a

dominant seventh flat five chord and is in fact the second inversion
of II7♭5.

German sixth

The German sixth (Ger+6 or Ger6
5) is also like the Italian, but with an added tone, ♭scale degree 3.

{ \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 "||" } >> >> }

In Classical music, however, it appears in much the same places as the other variants, though perhaps less often because of the

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 Mozart fifths, were occasionally accepted by common practice
composers. There are two ways they can be avoided:

  1. The ♭scale degree 3 can move to either scale degree 1 or scale degree 2, thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between ♭6 and ♭scale degree 3.[11]
    { \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 "||" } >> >> }

Other types

Other variants of augmented sixth chords can be found in the repertoire, and are sometimes given whimsical geographical names. For example: 4–♭6–7–♯2; (F–A♭–B–D♯) is called by one source an Australian sixth, and ♭7–1–3–♯5 (B♭–C–E–G#), sometimes called the Japanese sixth, Blackadder, or Ikisugi chord.[13][14] Such anomalies usually have alternative interpretations.

Function

Standard function

From the

chromatically altered predominant chord (typically, an alteration of ii4
3, IV6
5, vi7 or their parallel equivalents in the minor mode) leading to a dominant chord. This movement to the dominant is heightened by the semitonal resolution to scale degree 5 from above and below (from ♭scale degree 6 and ♯scale degree 4);[15] essentially, these two notes act as leading-tones
.

This characteristic has led many analysts

major mode, the chromatic voice leading is more pronounced because of the presence of two chromatically altered notes, ♭scale degree 6 and ♯scale degree 4, rather than just ♯scale degree 4
.

In most occasions, the augmented-sixth chords precede either the dominant, or the tonic in second inversion.[8] The augmented sixths can be treated as chromatically altered passing chords.[8]

Other functions

{ \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 "||" } >> >> }

In the late Romantic period and other musical traditions, especially

remotely related keys, and possible 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 Wagner and Bruckner (eg. the prelude from Tristan und Ysolde and Bruckner's third symphony), but is most notable in Russian works such as Rimsky-Korsakov's Scheherezade[18] and 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 begun 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, 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 Debussy's Nuages[19] and Ravel's Scarbo.[20]

inversions of the diminished triad and of dominant and diminished seventh chords with a lowered second degree (♭scale degree 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 modulatory degression into the key of the dominant".[17]

The example below shows the last nine measures from

Piano Sonata in A major, D. 959. In m. 352, an Italian sixth chord built on scale degree ♭scale degree 2 functions as a substitute
for the dominant.

{ #(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 "|." } >> >> }

Inversions

Augmented sixth chords are occasionally used with a different chord member in the

inversion" isn't necessarily accurate, but is found in some textbooks, nonetheless.[citation needed
] Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

Rousseau considered that the chord could not be inverted.[22] Seventeenth century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources.[23]

The excerpt below is from 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♯–E♭); these two voices resolve inward to an octave.

{ #(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 } >> >>} >> }

Related chords

In music theory, the double-diminished triad is an archaic concept and term referring to a

inversion
, A♭–C–F♯, is the Italian sixth chord that resolves to G.

Classical harmonic theory would notate the

secondary dominant of V.[25][26]

{ \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 "||" } }

All variants of augmented sixth chords are closely related to the

applied dominant
V7 of ♭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♭.

{ \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 "||" } >> >> }

Simon Sechter explains the chord of the French sixth chord as being a chromatically altered version of a seventh chord on the second degree of the scale, scale degree 2. The German sixth is explained as a chromatically altered ninth chord on the same root but with the root omitted.[27]

{ \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 "||" } >> >> }

The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the A♭, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F♯ – being chromatically raised – must rise.

Relationship between the different types

The following "curious chromatic sequence",

12TET
tuning:

A tesseract. The diminished seventh chords occupy points on two diagonally opposite corners.
  • Starting with a diminished seventh chord, lower any 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 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.
  • Three repetitions of the above complete the cycle in modulo-12 note space, forming a necklace of three tesseracts joined at opposite 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 minor seventh (between the root and seventh degree (i.e.: C–B♭ in C–E♭–G–B♭) rewritten as an augmented sixth (C–E♭–G–A♯).[30] Rearranging and transposing, this gives A♭–C♭–E♭–F♯, a virtual minor version of the German sixth chord.[31] Again like the typical +6, this enharmonic interpretation gives a 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.[32]

Half-diminished seventh as virtual augmented sixth chord

The

inversion of the German sixth chord[33] (it is its inversion as a set, rather than as a chord). Its interval of minor seventh (between root and seventh degree (i.e.: C–B♭ in C–E♭–G♭–B♭) can be written as an augmented sixth (C–E♭–G♭–A♯).[30] Rearranging and transposing, this gives A♭–C♭–D–F♯, a virtual minor version of the French sixth chord.[34][need quotation to verify] 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.[32]

Tristan chord

Main article: 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 that transitions to a French sixth in the key of A minor (F–A–B–D♯, in red below). The upper voice continues upward with a long appoggiatura (G♯ to A). Note that the D♯ resolves down to D♮ instead of up to E:[35]

{ \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 } >> >> }

See also

Notes

  1. ^ Notable examples include the themes of the slow movements (both in variation form) of the opp. 57 ("Appassionata") and 109 piano sonatas.

References

  1. ^
    ISBN 9780073101880
    .
  2. ^ Andrews 1950, pp. 45–46.
  3. ^ Andrews 1950, pp. 46–52.
  4. ^
    OCLC 19029983
    .
  5. OCLC 34966355
    .
  6. Neapolitan sixth
    chords.
  7. ^ Kostka & Payne (1995), p.385.
  8. ^ a b c Rimsky-Korsakov 1924, p. 121.
  9. ISBN 0-03-020756-8
    . Original with all uppercase Roman numerals.
  10. 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."
  11. OCLC 145143714
    . Beethoven frequently moves from one form of the chord to another in such a way, sometimes passing through all three.
  12. ISBN 9781610975315
    .
  13. OCLC 220305086
    .
  14. ^ "Blackadder Chord (en)". SoundQuest (in Japanese). 2019-11-15. Retrieved 2021-04-06.
  15. ISBN 0070358745
    .
  16. ISBN 0-393-95480-3
    .
  17. ^ a b Tschaikovsky, Peter (1900). "XXVII". In Translated from the German version by Emil Krall and James Liebling (ed.). Guide to the Practica Study of Harmony (English translation ed.). Leipzig: P. Jurgenson. pp. 106, 108.
  18. ^ Ears Wide Open Online | Deconstructing Rimsky-Korsakov's Scheherazade, retrieved 2023-08-19
  19. ^ Forte, Allen (1991). Debussy and the Octatonic.
  20. ^ Ravel, Maurice (1908). "Gaspard de la nuit: III. Scarbo, piano score" (PDF). IMSLP.
  21. ISBN 0-253-34992-3
    .
  22. ^ Rousseau, Jean Jaques (1826). Dictionnaire de Musique. Paris Emler Fréres.
  23. ISBN 978-0-7546-6385-0
    .
  24. ^ Ernst Friedrich Richter (1912). Manual of Harmony, p.94. Theodore Baker.
  25. ^ Satyendra, Ramon. "Analyzing the Unity within Contrast: Chick Corea's Starlight", p.55. Cited in Stein.
  26. ISBN 0-19-517010-5
    .
  27. ^ Sechter, Simon (1853). Die Grundsätze der musicalischen Komposition (in German). Leipzig: Breitkopf und Härtel.
  28. ^ Ouseley, Frederick. A. Gore (1868). A Treatise on Harmony, pg. 138, Oxford, Clarendon Press.
  29. ISBN 978-0-19-533667-2
    .
  30. ^ a b Ouseley, Frederick. A. Gore (1868). A Treatise on Harmony, pg. 137, Oxford, Clarendon Press.
  31. ^ Ouseley (1868), pg. 143ff.
  32. ^ a b Christ, William (1966). Materials and Structure of Music, v.2, p. 154. Englewood Cliffs: Prentice-Hall. LOC 66-14354.
  33. ^ Hanson, Howard. (1960) Harmonic Materials of Modern Music, p.356ff. New York: Appleton-Century-Crofts. LOC 58-8138.
  34. ^ Chadwick, G. W. (1922). Harmony: A Course of Study, pg. 138ff, Boston, B. F. Wood. [ISBN unspecified]
  35. ISBN 978-0-07-310188-0
    .

Further reading

External links
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