Coltrane changes

Coltrane changes (Coltrane Matrix or cycle, also known as chromatic third relations and multi-tonic changes) are a harmonic progression variation using substitute chords over common jazz chord progressions. These substitution patterns were first demonstrated by jazz musician John Coltrane on the albums Bags & Trane (on the track "Three Little Words") and Cannonball Adderley Quintet in Chicago (on "Limehouse Blues"). Coltrane continued his explorations on the 1960 album Giant Steps and expanded on the substitution cycle in his compositions "Giant Steps" and "Countdown", the latter of which is a reharmonized version of Eddie Vinson's "Tune Up". The Coltrane changes are a standard advanced harmonic substitution used in jazz improvisation.

Function

The changes serve as a pattern of chord substitutions for the ii–V–I progression (supertonic–dominant–tonic) and are noted for the tonally unusual root movement by major thirds (either up or down by a major third interval), creating an augmented triad. Root movement by thirds is unusual in jazz, as the norm is circle of fifths root movement, such as ii-V-I.

Influences

David Demsey, saxophonist and coordinator of jazz studies at William Paterson University, cites a number of influences leading to Coltrane's development of these changes. After Coltrane's death it was proposed that his "preoccupation with...chromatic third-relations" was inspired by religion or spirituality, with three equal key areas having numerological significance representing a "magic triangle", or, "the trinity, God, or unity." Demsey shows that though this meaning was of some importance, third relationships were much more "earthly", or rather historical, in origin. Mention should be made of his interests in Indian ragas during the early 1960s, the Trimurti of Vishnu, Brahma and Shiva may well have been an inherent reference in his chromatic third relations, tritone substitutes, and so on. He developed his sheets of sound style while playing with Miles Davis and with pianist Thelonious Monk during this period. In terms of the origin of this “sheets of sound” technique, saxophonist Odean Pope considers pianist Hasaan Ibn Ali a major influence on Coltrane and his development of this signature style.

Coltrane studied harmony with Dennis Sandole and at the Granoff School of Music in Philadelphia. He explored contemporary techniques and theory. He also studied the Thesaurus of Scales and Melodic Patterns by Nicolas Slonimsky (1947).

A series of similar-sounding chord changes occurs in "Ondine", the first movement of Maurice Ravel's 1908 piano suite Gaspard de la nuit. thumb|Ravel, Ondine from 'Gaspard de la Nuit', bar 67 thumb|center|600px|Ravel, Ondine from 'Gaspard de la Nuit', bar 67Other early appearances include the verse to the standard "Till the Clouds Roll By" (1917) by Jerome Kern. The bridge of the Richard Rodgers song and jazz standard "Have You Met Miss Jones?" (1937) predated Tadd Dameron's "Lady Bird", after which Coltrane named his "Lazy Bird", by incorporating modulation by major third(s). (highlighted yellow below) "Giant Steps" and "Countdown" may both have taken the inspiration for their augmented tonal cycles from "Have You Met Miss Jones?".

:{|style="text-align:center"

|+"Have You Met Miss Jones?" B section chord progression (bridge):

| | || style="background:#ff9;"| B^Maj7 || | || | || | Am⁷ || | D⁷ || | || style="background:#ff9;"| G^Maj7 || | || | || | Em⁷ || | A⁷ || | || style="background:#ff9;"| D^Maj7 || | || | || | Am⁷ || | D⁷ || | || style="background:#ff9;"| G^Maj7 || | || | || | Gm⁷ || | C⁷ || |

|}

Coltrane substitution

thumb|225px|ii–V⁷–I progression in C lasting only two measures .

The Coltrane substitution, Coltrane changes, or Countdown formula, is as follows. Start with a ii–V–I turnaround lasting four measures:

:{|style="text-align:center"

| | || | ii⁷ || | || | V⁷ || | || | I || | || | I || |

|-

| | || | Dm⁷ || | || | G⁷ || | || | C || | || | C || |

|}

with the dominant chord (V⁷) preceding the tonic (I).

One substitutes two chords for each of the first three:

:{|style="text-align:center"

| | || | ii⁷ || | || | || | || | || | || | || | || | || | || | V⁷ || | || | I

|-

| | || | Dm⁷ || | || | E⁷ || | || | A || | || | B⁷ || | || | E || | || | G⁷ || | || | C || | || |

|-

| | || | || | ╲╱<br />m2 || | || | ╲╱<br />P4 || | || | ╲╱<br />m3 || | || | ╲╱<br />P4 || | || | ╲╱<br />m3 || | || | ╲╱<br />P4

|}

Notice a dominant seventh chord preceding and thus tonicizing a major chord on C and also E and A, both a major third from C.

:{|style="text-align:center"

| style="background:#f99;"| V⁷ || | || style="background:#f99;"| I || style="background:#9f9;"| V⁷ || | || style="background:#9f9;"| I || style="background:#f9f;"| V⁷ || | || style="background:#f9f;"| I

|-

| | E⁷ || | || | A || | B⁷ || | || | E || | G⁷ || | || | C

|}

thumb|350px|Four-measure ii–V–I progression in C with Coltrane substitution .

This also may begin on C, as on "Giant Steps", giving:

:{|style="text-align:center"

| | || | C || | || | E⁷ || | || | A || | || | B⁷ || | || | E || | || | G⁷ || | || | C || | || |

|-

| | || | || | ╲╱<br />m3 || | || | ╲╱<br />P4 || | || | ╲╱<br />m3 || | || | ╲╱<br />P4 || | || | ╲╱<br />m3 || | || | ╲╱<br />P4

|}

Major thirds cycle

The harmonic use of the chromatic third relation originated in the Romantic era and may occur on any structural level, for example in chord progressions or through key changes. The standard Western chromatic scale has twelve equidistant semitones. When arranged according to the circle of fifths, it looks like this:

::Image:Fifths.png