Editing Tritone substitution (section)

==Summary==

In tonal music, a conventional [[perfect cadence]] consists of a [[dominant seventh chord]] followed by a tonic chord. For example, in the key of C major, the chord of G<sup>7</sup> is followed by a chord of C. In order to execute a tritone substitution, a common variant of this progression, one would replace the dominant seventh chord with a dominant chord that has its root a [[tritone]] away from the original:

[[File:Table of 3 kinds of perfect cadence.png|thumb|center|500px|Three kinds of perfect cadence]]

[[Franz Schubert]]'s [[String Quintet (Schubert)|String Quintet in C major]] concludes with a dramatic final cadence that uses the third of the above progressions. The conventional G<sup>7</sup> chord is replaced in bars 3 and 4 of the following example with a D{{music|flat}}<sup>7</sup> chord, with a [[diminished fifth]] (G{{music|natural}} as the [[enharmonic equivalent]] of A{{music|bb}}); a chord otherwise known as a '[[French sixth]]':[[File:Schubert C major Quintet ending.wav|thumb|Schubert C major Quintet ending]]
<score raw="1">
\header { tagline = ##f }
\layout { \context { \Staff \remove "Time_signature_engraver" } }
\new StaffGroup <<
 \new Staff \with { instrumentName = "Violin I" } \relative c' {
  c1\fz\> |
  \tuplet 3/2 { c8\!( d e } \tuplet 3/2 { f g a } \tuplet 3/2 { b c d } e16 f g a) |
  b1~\fff |
  b1 |
  c4-. r r2 |
  c,,4-. r r2 |
  \appoggiatura des8 c1*3/4\fermata\> s4\! | \bar "|."
 }
 \new Staff \with { instrumentName = "Violin II" } \relative c' {
  g1~\fz\> |
  <g e'>4\!( <c g'> <e c'> <g e'>) |
  <b g'>1~\fff |
  q1 |
  <c g'>4-. r r2 |
  c,4-. r r2 |
  \appoggiatura des8 c1*3/4\fermata\> s4\! |
 }
 \new Staff \with { instrumentName = "Viola" } \relative c {
  \clef alto
  e!1(\fz\> |
  c'4)(\! e g c) |
  f1~\fff |
  f1 |
  e4-. r r2 |
  <c, c,>4-. r r2 |
  \appoggiatura des,8 c1*3/4\fermata\> s4\! |
 }
 \new Staff \with { instrumentName = "Violoncello" } \relative c, {
  \clef bass
  <c g' e' c'>4 r r2 |
  r4 c-. c-. c-. |
  \appoggiatura es8 des1~\fff\startTrillSpan
  des1*7/8 s8\stopTrillSpan |
  \grace { c32 des } c4-. r r2 |
  c4-. r r2 |
  \appoggiatura des8 c1*3/4\fermata\> s4\! |
 }
 \new Staff \with { instrumentName = "Violoncello" } \relative c, {
  \clef bass
  c1~ |
  c4 c-. c-. c-. |
  \appoggiatura es8 des1~\fff\startTrillSpan
  des1*7/8 s8\stopTrillSpan |
  \grace { c32 des } c4-. r r2 |
  c4-. r r2 |
  \appoggiatura des8 c1*3/4\fermata\> s4\! |
 }
>>
</score>

Christopher Gibbs (2000, p.&nbsp;105) says of this ending: "within the last movement of the quintet, darker forces continue to lurk: the piece ends with a manic coda building to a dissonant [[fortissimo]] chord with a D-flat [[Trill (music)|trill]] in both [[cello]]s, and then a final tonic inflected by a D-flat [[appoggiatura]]... The effect is overwhelmingly powerful."<ref>Gibbs, C.H. (2000) ''The Life of Schubert''. Cambridge University Press.</ref>

The closing bars of the first movement of Schubert's [[Schubert's last sonatas|Piano Sonata in A major, D959]] use both a conventional perfect cadence and a cadence featuring a tritone substitution, this time in the form of an '[[Augmented sixth chord|Italian Sixth]].' Bars 345-9 end with a regular cadence in A major. Instead of repeating this pattern to conclude the movement, the bars that follow replace the E7 chord with a B{{music|b}}<sup>7</sup>.[[File:Schubert, A major sonata D959, first movement bars 345-357.wav|thumb|Schubert, A major sonata D959, first movement bars 345-357]][[File:Schubert, A major sonata D959, first movement bars 345-358.png|thumb|center|500px|Schubert, A major sonata D959, first movement bars 345-357]]

There are similarities here with the ambivalent ending of [[Richard Strauss]]'s [[tone poem]] ''[[Also sprach Zarathustra ]]''.<ref>[https://www.youtube.com/watch?v=vI6MUYJIAtM&t=1956s Strauss, R. (1896) "Also sprach Zarathustra]</ref> Here, according to [[Richard Taruskin]], "Strauss contrived an ending that seemed to die away on an oscillation between tonics on B and C, with C … getting the last word. Had B been given the last word, or were the extreme registers reversed, the ploy would not have worked. It would have been obvious that the C (though placed many octaves lower than its rival, in a register the ear is used to associating with the fundamental bass) was, in functional terms, making a descent to the tonic B as part of a "French sixth" chord... Rather than an ending in two keys, we are dealing with a registrally distorted, interrupted, yet functionally viable cadence on B."<ref>Taruskin, Richard (2005, p.53). ''The Oxford History of Western Music, Vol. 4: Music in the Early Twentieth Century''. Oxford and New York: Oxford University Press.</ref>