Editing Tritone substitution

{{Short description|Music theory concept}}
[[File:Substitute dominant in the chromatic circle.png|thumb|C7 is transpositionally equivalent to the F{{music|#}}7, the leading tones resolve inversionally (E-B{{music|b}} resolves to F-A, A{{music|#}}-E resolves to B-D{{music|#}}) {{audio|Tritone substitution I-V-I.mid|Play F-C7-F, F-F{{music|#}}7-F, B-F{{music|#}}7-B, then B-C7-B}}]]

The '''tritone substitution''' is a common [[chord substitution]] found in both [[jazz]] and [[classical music]]. Where jazz is concerned, it was the precursor to more complex substitution patterns like [[Coltrane changes]]. Tritone substitutions are sometimes used in [[musical improvisation|improvisation]]—often to create tension during a [[Solo (music)|solo]]. Though examples of the tritone substitution, known in the [[Western classical music|classical]] world as an [[augmented sixth chord]], can be found extensively in classical music since the [[Renaissance music|Renaissance]] period,<ref>{{cite book|last1=Kennedy|first1=Andrews|title=The Oxford Harmony|date=1950|publisher=Oxford University Press|location=London|pages=45–46}}</ref> they were not heard outside of classical music until they were brought into jazz by musicians such as [[Dizzy Gillespie]] and [[Charlie Parker]] in the 1940s,<ref>Everett, Walter (Autumn, 2004). "A Royal Scam: The Abstruse and Ironic Bop-Rock Harmony of Steely Dan", ''Music Theory Spectrum'', Vol. 26, No. 2, pp. 201-235</ref> as well as [[Duke Ellington]], [[Art Tatum]], [[Coleman Hawkins]], [[Roy Eldridge]] and [[Benny Goodman]].<ref>{{cite book|last=Owens |first=Thomas |title=Bebop |url=https://archive.org/details/bebopmusicitspla00owen_905 |url-access=limited |date=1996 |publisher=Oxford University Press|page=[https://archive.org/details/bebopmusicitspla00owen_905/page/n21 5]|isbn=978-0-19-510651-0 }}</ref>

The tritone substitution can be performed by exchanging a [[dominant seventh chord]] for another dominant seventh chord which is a [[tritone]] away from it. For example, in the key of C major one can use D{{music|b}}<sup>7</sup> instead of G<sup>7</sup> (D{{music|b}} is a tritone away from G, and G is the dominant of C).

==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>

==Analysis==

===Jazz / Pop===

[[File:Tritone substitution.png|thumb|right|F{{music|#}}<sup>7</sup> may substitute for C<sup>7</sup> because they both have E{{music|natural}} and B{{music|flat}}/A{{music|sharp}} and fulfill the [[voice leading]] considerations. {{audio|Tritone substitution.mid|Play}}]]

A tritone substitution is the substitution of one [[dominant seventh chord]] (possibly altered or extended) with another that is three [[whole step]]s (a [[tritone]]) from the original chord. In other words, tritone substitution involves replacing V<sup>7</sup> with {{music|b}}II<sup>7</sup><ref name="Sarath"/> (which could also be called {{music|b}}V<sup>7</sup>/V, subV<sup>7</sup>,<ref name="Sarath"/> or V<sup>7</sup>/{{music|b}}V<ref name="Sarath"/>). For example, D{{music|flat}}<sup>7</sup> is the tritone substitution for G<sup>7</sup>.

In standard [[jazz harmony]], tritone substitution works because the two chords share two pitches that themselves are a tritone apart: namely, the [[third (chord)|third]] and the [[seventh (chord)|seventh]] of the chord, albeit reversed.<ref>Freeman, Daniel E. (2009). ''The Art of Solo Bass'', p.17. {{ISBN|0-7866-0653-3}}.</ref> In a G<sup>7</sup> chord, the third is B and the seventh is F; in its tritone substitution, D{{music|flat}}<sup>7</sup>, the third is F and the seventh is C{{music|flat}} ([[enharmonic]]ally B{{music|natural}}).

[[File:Tritone substitution common tones.png|thumb|right|C<sup>7</sup> followed quickly by the tritone it contains (E-B{{music|flat}}), its inversion (B{{music|flat}}-F{{music|flat}}), and then G{{music|flat}}<sup>7</sup> {{Audio|Tritone substitution common tones.ogg|Play}}.]]

Edward Sarath calls tritone substitutions a "non-diatonic practice that is indirectly related to applied chord functions... yield[ing] an alternative melodic pathway in the [[Bass (sound)|bass]] to the [[tonic (music)|tonic]] triad."<ref name="Sarath">Sarath, Edward (2009). ''Music Theory Through Improvisation: A New Approach to Musicianship Training'', p.177. {{ISBN|0-415-80453-1}}.</ref> Patricia Julien says it involves replacing "harmonic root movement of a fifth with [[steps and skips|stepwise]] root movements (e.g., G<sup>7</sup>–C becomes D{{music|b}}<sup>7</sup>–C) so that although stepwise root movement is involved, the relationship between the chords is functional".<ref>Julien, Patricia (2001). ''Jazz Education Journal'', Volume 34, p.ix–xi.</ref>

The original dominant pitch (the sharp fourth, also called sharp eleventh or flat fifth, relative to the original root) is often added to the tritone substitute dominant, due to that note's importance melodically and tonally – this is one of the ways in which substitute dominants may sound and function somewhat differently than conventional dominant chords.<ref name="Ligon">Ligon, Bert (2001). ''Jazz Theory Resources'', p.128. {{ISBN|0-634-03861-3}}.</ref> (However, sharp elevenths can also occur on non-substituted dominant chords in jazz.) The substitute dominant may be used as a [[pivot chord]] in [[modulation (music)|modulation]].<ref>Bahha and Rollins (2005). ''Jazzology'', p.103. {{ISBN|0-634-08678-2}}.</ref> Since it is the dominant chord a tritone away, the substitute dominant may resolve down a fifth, to a tonic chord a tritone away from the previous tonic (for example, in F one may feature a ii–V on C, which with a substitute dominant resolves to G{{music|b}}, a [[distant key]] from F). Resolution from the substituted chord to the original tonic is also common.

Tritone substitutions are also closely related to the [[altered chord]] used commonly in jazz. [[Jerry Coker]] explains:

{{blockquote|Tritone substitutions and altered dominants are nearly identical... Good improvisers will liberally sprinkle their solos with both devices. A simple comparison of the notes generally used with the given chord [notation] and the notes used in tri-tone substitution or altered dominants will reveal a rather stunning contrast, and could cause the unknowledgeable analyzer to suspect errors. ... the distinction between the two [tri-tone substitution and altered dominant] is usually a moot point.<ref name="Coker 81">Coker, Jerry (1997). ''Elements of the Jazz Language for the Developing Improvisor'', p.81. {{ISBN|1-57623-875-X}}.</ref>}}

[[File:Tritone substitution and altered chord.png|thumb|right|Tritone substitution and altered dominant as "nearly identical"<ref name="Coker 81"/> {{audio|Tritone substitution and altered chord.mid|Play}}.]]

The alt chord is a heavily altered dominant seventh chord, built on the [[altered scale|alt scale]], a scale where every [[scale degree]] except the root is flattened compared to the [[major scale]]. For example, C<sup>7alt</sup> is built from the scale C, D{{music|flat}}, E{{music|flat}}, F{{music|flat}}, G{{music|flat}}, A{{music|flat}}, B{{music|flat}}. Enharmonically, this is almost the same as the scale for G{{music|flat}}<sup>7</sup>, which is the tritone substitute of C<sup>7</sup>: G{{music|flat}}, A{{music|flat}}, B{{music|flat}}, C{{music|flat}}, D{{music|flat}}, E{{music|flat}}, F{{music|flat}}. The only difference is C, which is the sharp eleventh of the G{{music|flat}}<sup>7</sup> chord. Thus, the alt chord is equivalent to the tritone substitution with a sharp–eleventh alteration.

The tritone substitution primarily implies a [[Lydian dominant scale]] or [[Lydian mode|Lydian]] [[Aeolian mode|minor scale]]. In the case of D{{music|flat}}<sup>7</sup> to C<sup>maj7</sup>, the implied scale behind D{{music|flat}}<sup>7</sup> would be D{{music|b}}, E{{music|b}}, F, G, A{{music|b}}, B{{music|b}}, C{{music|b}}/D{{music|b}}, E{{music|b}}, F, G, A{{music|b}}, B{{music|double flat}}, C{{music|b}}. Because of this, the extensions of 9, {{music|sharp}}11 and 13/{{music|flat}}13 are all available, while the {{music|sharp}}11 is where it shares with the altered scale.

===Classical===

Classical harmonic theory would notate the substitution as an [[augmented sixth chord]] on {{music|flat}}II (the augmented sixth being enharmonic to the dominant/minor seventh). The augmented sixth chord can either be the [[Augmented sixth chord#Italian sixth|Italian sixth]] It<sup>+6</sup>, which is enharmonically equivalent to a dominant seventh chord ''without'' the fifth; the [[Augmented sixth chord#German sixth|German sixth]] Gr<sup>+6</sup>, which is enharmonically equivalent to a dominant seventh chord ''with'' the fifth; or the [[Augmented sixth chord#French sixth|French sixth]] Fr<sup>+6</sup>, which is enharmonically equivalent to the Lydian dominant ''without'' the fifth but with a sharp eleven, all of which serve in a classical context as [[Predominant chord|predominant]] chords, functioning similarly to a ii chord in a [[Ii–V–I progression|ii - V - I]] chord sequence. This can also be seen 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>

Below is the original dominant-tonic progression, the same progression with the tritone substitution, and the same progression with the substitution notated as an Italian augmented sixth chord:

[[File:Tritone substitutions.png|thumb|center|400px|Original {{audio|Tritone substitutions V7-I.mid|Play}}, tritone substitution {{audio|Tritone substitutions bV7ofV-I.mid|Play|help=no}}, and augmented sixth chord {{audio|Tritone substitutions It6-I.mid|Play|help=no}}]]

===In twelve-bar blues===

One of the most common usages of the tritone substitution is in the [[twelve-bar blues|12-bar blues]]. Shown below is one of the simpler forms of twelve-bar blues.
:{| class="wikitable"
|width="30px"| I<br>C<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| V<br>G<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup>
|}
Next, here is the same 12 bars, except incorporating a tritone substitution in bar 4; that is, with G{{music|b}}<sup>7</sup> substituted for C<sup>7</sup>.
:{| class="wikitable"
|width="30px"| I<br>C<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| {{music|b}}V<br>G{{music|b}}<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| V<br>G<sup>7</sup> ||width="30px"| IV<br>F<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup> ||width="30px"| I<br>C<sup>7</sup>
|}

===In a ii–V–I progression===

The second common usage of the tritone substitution is in [[ii-V-I turnaround|ii–V–I progression]], which is extremely common in [[jazz harmony]]. This substitution is particularly suitable for jazz because it produces chromatic root movement. For example, in the progression Dm<sup>7</sup>–G<sup>7</sup>–C<sup>M7</sup>, substituting D{{music|flat}}<sup>7</sup> for G<sup>7</sup> produces the downward movement of D–D{{music|flat}}–C in the roots of the chords, typically played by the bass. This also reinforces the downward movement of the thirds and sevenths of the chords in the progression (in this case, F/C to F/C{{music|b}} to E/B).

{{multiple image
| align = center
| image1 = Ii-V-I turnaround in C.png
| width1 = 200
| alt1 = 
| caption1 = ii–V–I turnaround in C {{Audio|Ii-V-I without subV.ogg|Play}} without a tritone substitution.
| image2 = Tritone substitution ii-subV-I.png
| width2 = 200
| alt2 = 
| caption2 = Tritone substitution ii–{{music|b}}II–I in C {{Audio|Tritone substitution ii-subV-I.ogg|Play}} turnaround with a tritone substitution.
| image3 = Tritone substitution April in Paris mm.11-12.png
| width3 = 200
| alt3 = 
| caption3 = Bars 11 and 12 of "[[April in Paris (song)|April in Paris]]" melody with tritone substitution in ii<sup>7</sup>–V<sup>7</sup>–i progression (ii<sup>7</sup> not shown) making ii<sup>7</sup>–{{music|b}}II<sup>7</sup>–i.<ref>Scott DeVeaux (Autumn, 1999). "'Nice Work if You Can Get It': Thelonious Monk and Popular Song", p.180, ''Black Music Research Journal'', Vol. 19, No. 2, New Perspectives on Thelonious Monk.</ref> {{Audio|Tritone substitution April in Paris mm.11-12.mid|Play}}.
| footer = 
}}

==In other tuning systems==

The fact that a chord and its tritone substitution have the third and seventh in common is related to the fact that in [[12 equal temperament]], the [[Lesser septimal tritone|7:5]] and [[Greater septimal tritone|10:7]] ratios are represented by the same interval, which is exactly half of an octave (600 [[Cent (music)|cents]]) and is its own inversion. This is also the case in [[22 equal temperament]] and tritone substitution works similarly there. However, in [[31 equal temperament]] and other systems that distinguish between 7:5 and 10:7, tritone substitution becomes more complex. The [[harmonic seventh chord]] (approximating 4:5:6:7) contains a small tritone, so its substitution must contain a ''large'' tritone and therefore will be a different (and more dissonant) chord type.<ref name="31et">{{cite web|url=http://31et.com/interval/15/|title=Lesser Septimal Tritone}}</ref>

==See also==
*[[Axis system|Axis System]]
*[[Bird changes]]

==References==
<references/>

==Bibliography==
*DeVeaux, Scott (1997). ''The birth of bebop: A social and musical history'', p.&nbsp;104-106. Berkeley: University of California Press.
*R., Ken (2012). ''DOG EAR Tritone Substitution for Jazz Guitar'', Amazon Digital Services, Inc., ASIN: B008FRWNIW

{{DEFAULTSORT:Tritone Substitution}}
[[Category:Altered chords]]
[[Category:Chord substitution]]
[[Category:Tritones]]