A concept introduced by Joseph Schillinger and Nicolas Slonimsky, the idea of multiple tonics derived from equal division of the octave appealed to John Coltrane, who proceeded to compose the groundbreaking tune "Giant Steps". The composition features a series of dominant chords and ii-V-I turnarounds resolving to three tonalities built on the B augmented triad (the three-tonic system):

B D7 | G B♭7 | E♭ | Am7 D7 |

G B♭7 | E♭ F♯7 | B | Fm7 B♭7|

E♭ | Am7 D7 | G | C♯m7 F♯7 |

B | Fm7 B♭7 | E♭ | C♯m7 F♯7 || (B)

This concept was very innovative for the jazz world, to the point that Tommy Flanagan was unable to properly improvise on the original "Giant Steps" recording. Developing this technique further, Coltrane started utilizing the three-tonic system (and later, the four-tonic system as well, which is based on tonics derived from a diminished seventh chord) as a reharmonization tool, which has ultimately become known as "Coltrane changes".^[1] In this example from "Countdown" (which is really a "Coltrane changes" version of "Tune Up", the well-known jazz standard composed by Miles Davis), the long ii-V-I in the key of D major is laced with V-I progressions that resolve to the three tonics of the D augmented triad:

original (Tune Up): Em7 | A7 | D | D |

reharmonized (Countdown): Em7 F7 | B♭ D♭7 | G♭ A7 | D |

This kind of reharmonization mostly requires alteration of the original melody because of the frequent modulations and therefore, becomes "reharmonization of the changes" rather than the classic concept of re-harmonizing the melody.

References

1. ↑ Farah Jasmine Griffin and Salim Washington (2008). Clawing at the Limits of Cool. Thomas Dunne Books. p. 242. ISBN 0-312-32785-4. http://books.google.com/books?id=QC2A5AYGFXkC. Retrieved Jul. 16, 2009.