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Harmonic progression
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").[1] 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.
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."[2] 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.[2] In playing that style, Coltrane found it "easy to apply the harmonic ideas I had.... I started experimenting because I was striving for more individual development."[3] He developed his sheets of sound style while playing with Miles Davis and with pianist Thelonious Monk during this period.[4] 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.[5]
Precisely because of this equidistancy, the roots of these three chords can produce a destabilizing effect; if C, A♭ and E appear as the tonic pitches of three key areas on a larger level, the identity of the composition's tonal center can only be determined by the closure of the composition.
Looking above at the marked chords from "Have You Met Miss Jones?", B♭, G♭ and D are spaced a major third apart. On the circle of fifths it appears as an equilateral triangle:
By rotating the triangle, all of the thirds cycles can be shown. Note that there are only four unique thirds cycles. This approach can be generalized; different interval cycles will appear as different polygons on the diagram.
Musical examples
Tune Up
These are the first eight bars of the Miles Davis composition "Tune Up".[citation needed] The chord changes are relatively simple, a straightforward application of the ii–V–I progression, which is extremely common in jazz.
The chord progression is a standard ii7–V7–I progression in D major and then in C major. Assume that the time signature is 4 4 and that each ii and V chord gets four beats and the I chord gets eight beats.
Countdown
The changes below show Coltrane's substitution of chord changes over "Tune Up". The ii–V–I progression from "Tune Up" still appears but is enhanced with several transition chords that lead to a more complex harmonic progression.
In the standard Coltrane change cycle the ii–V–I is substituted with a progression of chords that cycle back to the V–I at the end. In a 4 4 piece, each chord gets two beats per change.
Coltrane developed this modified chord progression for "Countdown", which is much more complex. At its core, "Countdown" is a variation of "Tune Up",[13] but the harmonic substitutions occur rapidly and trick the listener into thinking that they are listening to a completely unrelated tune. The ii, V and I remain, but in between are other chords (highlighted in yellow and blue) from the major thirds cycle centered around each I. Preceding the first chord of each major thirds cycle is its V chord.
An earlier Coltrane piece, "Lazy Bird", also features two tonal centers a major third apart in its A section.
Giant Steps
The "Giant Steps" cycle is the culmination of Coltrane's theories applied to a completely new chord progression. Coltrane uses the cycle in descending major third tonal transpositions in the opening bars and then ascending ii–V–I progressions separated by a major third in the second section of "Giant Steps". The second section is basically the inverse of the bridge section described in "Have You Met Miss Jones" above.
This table shows which scales are used for the different chords:
Chords
Scale
Change in scale
BMaj7
B major
I
D7 → GMaj7
G major
V-I
B♭7 → E♭Maj7
E♭ major
V-I
Am7 → D7 → GMaj7
G major
ii-V-I
B♭7 → E♭Maj7
E♭ major
V-I
F♯7 → BMaj7
B major
V-I
Fm7 → B♭7 → E♭Maj7
E♭ major
ii-V-I
Am7 → D7 → GMaj7
G major
ii-V-I
C♯m7 → F♯7 → BMaj7
B major
ii-V-I
Fm7 → B♭7 → E♭Maj7
E♭ major
ii-V-I
C♯m7 → F♯7
B major
ii-V
Standard substitution
Although "Giant Steps" and "Countdown" are perhaps the most famous examples, both use slight variants of the standard Coltrane changes (the first eight bars of "Giant Steps" use a shortened version that does not return to I, and in "Countdown" the progression begins on ii7 each time). The standard substitution can be found in several Coltrane compositions and arrangements recorded around this time, including "26-2" (a reharmonization of Charlie Parker's "Confirmation"), "Satellite" (based on the standard "How High the Moon"), "Exotica" (loosely based on the harmonic form of "I Can't Get Started"), Coltrane's arrangement of "But Not for Me", and the bridge of his arrangement of "Body and Soul".[citation needed]
In "Fifth House" (based on "Hot House", i.e. "What Is This Thing Called Love?") the standard substitution is implied over an ostinato bass pattern with no chordal instrument instructed to play the chord changes. When Coltrane's improvisation superimposes this progression over the ostinato bass, it is easy to hear how he used this concept for his freer playing in later years.
↑ Porter, Lewis (January 28, 2000). John Coltrane: His Life and Music. Ann Arbor, Michigan: University of Michigan Press. p.151. ISBN978-0-472-08643-6.
1 2 Demsey, David (1996). John Coltrane plays Giant steps. Milwaukee, Wisconsin: Hal Leonard. p.145. ISBN0-7935-6345-3.
↑ Demsey, David (1991). "Chromatic Third Relations in the Music of John Coltrane". Annual Review of Jazz Studies. 5: 158. ISBN0-8108-2478-7.
↑ Ruhlmann, William. "John Coltrane". AllMusic. Retrieved 21 December 2018.
↑ Baker, David (1990). David Baker's Modern Concepts in Jazz Improvisation: A Comprehensive Method for All Musicians. Alfred Publishing. pp.92–93. ISBN0-7390-2907-X.
↑ Proctor, Gregory (1978). Nineteenth-Century Chromatic Tonality: A Study in Chromaticism, p.150. Ph.D., Diss., Princeton. Cited in Demsey (1991), p.148.
↑ Porter, Lewis (1999). John Coltrane: His Life and Music. The University of Michigan Press. p.147.
Further reading
Baker, David N. (1990). The Jazz Style of John Coltrane. Alfred Publishing. ISBN0-7692-3326-0.
Nettles, Barrie & Graf, Richard (1997). The Chord Scale Theory and Jazz Harmony. Advance Music, ISBN3-89221-056-X
Weiskopf, Walt; Ray Ricker (1991). Coltrane - A Player's Guide to His Harmony. New Albany, Indiana: Jamey Aebersold.
Yamaguchi, Masaya (2003). John Coltrane Plays Coltrane Changes. Milwaukee: Hal Leonard Corp. ISBN0-634-03864-8.
Yamaguchi, Masaya (2002). "A Creative Approach to Multi-Tonic Changes: Beyond Coltrane's Harmonic Formula", Annual Review of Jazz Studies 12. ISBN0-8108-5005-2
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