Coltrane Changes - The Major Thirds Cycle

The 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:

Precisely because of this equidistancy, the roots of these three chords can produce a destabilizing effect; if C, A-flat, 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. —Demsey (1991)

Looking above at the marked chords from "Have You Met Miss Jones?", B♭-G♭-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.