Tritone substitution

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C7 is transpositionally equivalent to the F#7, the leading tones resolve inversionally (E-B resolves to F-A, A#-E resolves to B-D#) Play F-C7-F, F-F#7-F, B-F#7-B, then B-C7-B (help*info) Substitute dominant in the chromatic circle.png
C7 is transpositionally equivalent to the F7, the leading tones resolve inversionally (E-B resolves to F-A, A-E resolves to B-D) Loudspeaker.svg Play F-C7-F, F-F7-F, B-F7-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 improvisation—often to create tension during a solo. Though examples of the tritone substitution, known in the classical world as an augmented sixth chord, can be found extensively in classical music since the Renaissance period, [1] they were not heard until much later in jazz by musicians such as Dizzy Gillespie and Charlie Parker in the 1940s, [2] as well as Duke Ellington, Art Tatum, Coleman Hawkins, Roy Eldridge and Benny Goodman. [3]

Contents

The tritone substitution can be performed by exchanging a dominant seventh chord for another dominant seven chord which is a tritone away from it. For example, in the key of C major one can use D7 instead of G7. (D is a tritone away from G).

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 G7 is followed by a chord of C. In order to execute a tritone substitution, 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:

Three kinds of perfect cadence Table of 3 kinds of perfect cadence.png
Three kinds of perfect cadence

Franz Schubert's String Quintet in C major concludes with a dramatic final cadence that uses the third of the above progressions. The conventional G7 chord is replaced in bars 3 and 4 of the following example with a D7 chord, with a diminished fifth (G as the enharmonic equivalent of A Doubleflat.svg ); a chord otherwise known as a 'French sixth':

Schubert C major Quintet ending
Schubert, Quintet in C, final bars Schubert C major Quintet ending.png
Schubert, Quintet in C, final bars

Christopher Gibbs (2000, p. 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 in both cellos, and then a final tonic inflected by a D-flat appoggiatura... The effect is overwhelmingly powerful." [4]

The closing bars of the first movement of Schubert's 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 '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 Bb7.

Schubert, A major sonata D959, first movement bars 345-357
Schubert, A major sonata D959, first movement bars 345-357 Schubert, A major sonata D959, first movement bars 345-358.png
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. 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." [5]

Analysis

Jazz

F# may substitute for C because they both have E and B/A# and pay due to voice leading considerations. Play (help*info) Tritone substitution.png
F may substitute for C because they both have E and B/A and pay due to voice leading considerations. Loudspeaker.svg Play  

A tritone substitution is the substitution of one dominant seventh chord (possibly altered or extended) with another that is three whole steps (a tritone) from the original chord. In other words, tritone substitution involves replacing V7 with II7 [6] (which could also be called V7/V, subV7, [6] or V7/V [6] ). For example, D7 is the tritone substitution for G7.

In standard jazz harmony, tritone substitution works because the two chords share two pitches: namely, the third and seventh, albeit reversed. [7] In a G7 chord, the third is B and the seventh is F; whereas, in its tritone substitution, D7, the third is F and the seventh is C (enharmonically B). Notice that the interval between the third and seventh of a dominant seventh chord is itself a tritone.

C followed quickly by the tritone it contains (E-B), its inversion (B-F), and then G Play (help*info)
. Tritone substitution common tones.png
C followed quickly by the tritone it contains (E-B), its inversion (B-F), and then G Loudspeaker.svg 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 to the tonic triad." [6] Patricia Julien says it involves replacing "harmonic root movement of a fifth with stepwise root movements (e.g., G7–C becomes D7–C) so that although stepwise root movement is involved, the relationship between the chords is functional". [8]

The tritone substitute dominant often contains the original dominant pitch (the sharp fourth, also called sharp eleventh or flat fifth, relative to the original root) due to its importance melodically and tonally, and this is one of the ways in which substitute dominants may sound and function somewhat differently than conventional dominant chords. [9] (However, sharp elevenths also occur on non-substituted dominant chords in jazz.) The substitute dominant may be used as a pivot chord in modulation. [10] 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, a distant key from F). Resolution to the original tonic is also common.

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

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. [11]

Tritone substitution and altered chord as, "nearly identical" Play (help*info)
. Tritone substitution and altered chord.png
Tritone substitution and altered chord as, "nearly identical" Loudspeaker.svg Play  .

The alt chord is a heavily altered dominant seventh chord, built on the alt scale, a scale where every scale degree except the root is flattened compared to the major scale. For example, C7alt is built from the scale C, D, E, F, G, A, B. Enharmonically, this is almost the same as the scale for G7, which is the tritone substitute of C7: G, A, B, C, D, E, F. The only difference is C, which is the sharp eleventh of the G7 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 minor scale. In the case of D7 to Cmaj7, the implied scale behind D7 would be D, E, F, G, A, B, C/D, E, F, G, A, B Doubleflat.svg , C. Because of this, the extensions of 9, 11 and 13/13 are all available, while the 11 is where it shares with the altered scale.

Classical

Classical harmonic theory would notate the substitution as an augmented sixth chord on II (the augmented sixth being enharmonic to the dominant/minor seventh). The augmented sixth chord can either be the Italian sixth It+6, which is enharmonically equivalent to a dominant seventh chord without the fifth; the German sixth Gr+6, which is enharmonically equivalent to a dominant seventh chord with the fifth; or the French sixth Fr+6, 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 chords, functioning similarly to a ii chord in a ii - V - I chord sequence. This can also be seen as a substitute for the secondary dominant of V. [12] [13]

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:

Original Play (help*info)
, tritone substitution Play
, and augmented sixth chord Play Tritone substitutions.png
Original Loudspeaker.svg Play  , tritone substitution Loudspeaker.svg Play , and augmented sixth chord Loudspeaker.svg Play

In twelve-bar blues

One of the most common usages of the tritone substitution is in the 12-bar blues. Shown below is one of the simpler forms of twelve-bar blues.

I
C7
IV
F7
I
C7
I
C7
IV
F7
IV
F7
I
C7
I
C7
V
G7
IV
F7
I
C7
I
C7

Next, here is the same 12 bars, except incorporating a tritone substitution in bar 4; that is, with G7 substituted for C7.

I
C7
IV
F7
I
C7
V
G7
IV
F7
IV
F7
I
C7
I
C7
V
G7
IV
F7
I
C7
I
C7

In a ii–V–I progression

The second common usage of the tritone substitution is in 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 Dm7–G7–CM7, substituting D7 for G7 produces the downward movement of D–D–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 to E/B).

Ii-V-I turnaround in C.png
ii–V–I turnaround in C Loudspeaker.svg Play   without a tritone substitution.
Tritone substitution ii-subV-I.png
Tritone substitution ii–II–I in C Loudspeaker.svg Play   turnaround with a tritone substitution.
Tritone substitution April in Paris mm.11-12.png
Bars 11 and 12 of "April in Paris" melody with tritone substitution in ii7–V7–i progression (ii7 not shown) making ii7II7–i. [14] Loudspeaker.svg Play  .

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 7:5 and 10:7 ratios are represented by the same interval, which is exactly half of an octave (600 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. [15]

See also

Related Research Articles

In music theory, the minor scale is three scale patterns – the natural minor scale, the harmonic minor scale, and the melodic minor scale – rather than just two as with the major scale, which also has a harmonic form but lacks a melodic form.

An altered chord is a chord that replaces one or more notes from the diatonic scale with a neighboring pitch from the chromatic scale. By the broadest definition, any chord with a non-diatonic chord tone is an altered chord. The simplest example of altered chords is the use of borrowed chords, chords borrowed from the parallel key, and the most common is the use of secondary dominants. As Alfred Blatter explains, "An altered chord occurs when one of the standard, functional chords is given another quality by the modification of one or more components of the chord."

Chord (music) Harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords in the right musical context.

Modulation (music) Change from one tonality (tonic, or tonal center) to another

In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.

Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.

A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.

In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7". An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:

In Classical music theory, a Neapolitan chord is a major chord built on the lowered (flatted) second (supertonic) scale degree. In Schenkerian analysis, it is known as a Phrygian II, since in minor scales the chord is built on the notes of the corresponding Phrygian mode.

The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on C, commonly written as Co7, has pitches C–E–G–B:

Chord substitution Technique of using a chord in place of another in a progression of chords

In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. Much of the European classical repertoire and the vast majority of blues, jazz and rock music songs are based on chord progressions. "A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing."

Jazz chords refer to chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to them, using the performer's discretion and ear. For example, if a tune is in the key of C, if there is a G chord, the chord-playing performer usually voices this chord as G7. While the notes of a G7 chord are G–B–D–F, jazz often omits the fifth of the chord—and even the root if playing in a group. However, not all jazz pianists leave out the root when they play voicings: Bud Powell, one of the best-known of the bebop pianists, and Horace Silver, whose quintet included many of jazz's biggest names from the 1950s to the 1970s, included the root note in their voicings.

In music, the axis system is a system of analysis originating in the work of Ernő Lendvai, which he developed in his analysis of the music of Béla Bartók.

In music theory, the half-diminished seventh chord is a seventh chord composed of a root note, together with a minor third, a diminished fifth, and a minor seventh. For example, the half-diminished seventh chord built on C, commonly written as Cm7(♭5), or Cø7, has pitches C–E–G–B:

Turnaround (music)

In jazz, a turnaround is a passage at the end of a section which leads to the next section. This next section is most often the repetition of the previous section or the entire piece or song.

The ii–V–I progression is a common cadential chord progression used in a wide variety of music genres, including jazz harmony. It is a succession of chords whose roots descend in fifths from the second degree (supertonic) to the fifth degree (dominant), and finally to the tonic. In a major key, the supertonic triad (ii) is minor, and in a minor key it is diminished. The dominant is, in its normal form, a major triad and commonly a dominant seventh chord. With the addition of chord alterations, substitutions, and extensions, limitless variations exist on this simple formula.

Jazz improvisation

Jazz improvisation is the spontaneous invention of melodic solo lines or accompaniment parts in a performance of jazz music. It is one of the defining elements of jazz. Improvisation is composing on the spot, when a singer or instrumentalist invents melodies and lines over a chord progression played by rhythm section instruments and accompanied by drums. Although blues, rock, and other genres use improvisation, it is done over relatively simple chord progressions which often remain in one key.

Irregular resolution

In music, an irregular resolution is resolution by a dominant seventh chord or diminished seventh chord to a chord other than the tonic. Regarding the dominant seventh, there are many irregular resolutions including to a chord with which it has tones in common or if the parts move only a whole or half step. Consecutive fifths and octaves, augmented intervals, and false relations should still be avoided. Voice leading may cause the seventh to ascend, to be prolonged into the next chord, or to be unresolved.

In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".

In music theory, the dominant seventh flat five chord is a seventh chord composed of a root note, together with a major third, a diminished fifth, and a minor seventh above the root. For example, the dominant seventh flat five chord built on C, commonly written as C75, is composed of the pitches C–E–G–B:

Seventh (chord)

In music, the seventh factor of a chord is the note or pitch seven scale degrees above the root or tonal center. When the seventh is the bass note, or lowest note, of the expressed chord, the chord is in third inversion Play .

References

  1. Kennedy, Andrews (1950). The Oxford Harmony. London: Oxford University Press. pp. 45–46.
  2. 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
  3. Owens, Thomas (1996). Bebop . Oxford University Press. p.  5.
  4. Gibbs, C.H. (2000) The Life of Schubert. Cambridge University Press.
  5. 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.
  6. 1 2 3 4 Sarath, Edward (2009). Music Theory Through Improvisation: A New Approach to Musicianship Training, p.177. ISBN   0-415-80453-1.
  7. Freeman, Daniel E. (2009). The Art of Solo Bass, p.17. ISBN   0-7866-0653-3.
  8. Julien, Patricia (2001). Jazz Education Journal, Volume 34, p.ix–xi.
  9. Ligon, Bert (2001). Jazz Theory Resources, p.128. ISBN   0-634-03861-3.
  10. Bahha and Rollins (2005). Jazzology, p.103. ISBN   0-634-08678-2.
  11. 1 2 Coker, Jerry (1997). Elements of the Jazz Language for the Developing Improvisor, p.81. ISBN   1-57623-875-X.
  12. Satyendra, Ramon. "Analyzing the Unity within Contrast: Chick Corea's Starlight", p.55. Cited in Stein.
  13. Stein, Deborah (2005). Engaging Music: Essays in Music Analysis. New York: Oxford University Press. ISBN   0-19-517010-5.
  14. 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.
  15. "Lesser Septimal Tritone".

Bibliography