The Coltrane Changes (or Coltrane Matrix) are a substitute harmonic progression popularized by the jazz musician on his album Giant Steps, specifically in his compositions "Giant Steps" and "Countdown", the latter which is a reharmonized version of Miles Davis's "Tune Up."
The changes serve as a pattern for the ii-V-I progression (supertonic-dominant-tonic) and are noted for the tonally unusual root movement by major thirds (as opposed to the usual minor or major seconds, thus the "giant steps").
David Demsey, professor and saxophonist, cites a number of influences leading toward's Coltrane's development of these changes. Miles Davis, who mentored Coltrane in many ways, was in the late 1950s moving toward the style of Kind of Blue. 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." He also played with pianist Thelonius Monk during this period, whose unusual harmonic and rhythmic innovations contributed greatly to Coltrane's musical development.
Coltrane studied harmony at the Granoff School of Music in Philadephia, exploring contemporary techniques and theory. He also spent much time studying the Thesaurus of Scale and Melodic Patterns by Nicolas Slonimsky (1947), which additionally served as practice material.
It is also speculated that the bridge of the Rodgers and Hart song "Have You Met Miss Jones?", the only jazz standard to incorporate a major thirds cycle (shown by the *), may have inspired Coltrane's innovation.
The standard Western chromatic scale has twelve semitones. When arranged according to the circle of fifths, it looks like this:
Looking above at the marked chords from "Have You Met Miss Jones?", D-Gb-Bb are spaced a major third apart. On the circle of fifths it appears as a 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.
"Tune Up" and "Countdown"
ii V I ii V I
| Em7 | A7 | DM7 - | Dm7 | G7 | CM7 - |
These are the first eight bars of the Miles Davis composition "Tune Up." The chord changes are relatively simple, the ii-V-I progression being extremely common in jazz.
ii * * I ii * * I
| Em7 F7 | BbM7 Db7 | GbM7 A7 | DM7 | Dm7 Eb7 | AbM7 B7 | EM7 G7 | CM7 |
Coltrane modified it into "Countdown", which appears to be much more complex. The ii and I remain, but in between are placed the other two chords from the major thirds cycle centered around each I (*). Preceding each is its V chord.
(Courtesy of Wikipedia)
The Coltrane Changes are named after the jazz sax great and refers to progressions he used featuring movement by major thirds in such songs as Giant Steps. Click below for the best in free Coltrane Changes lessons available on the web.