The Coltrane Matrix
Coltrane Matrix: a reharmonization of chord substitutions of a basic ii-V-I with movement in major thirds creating an augmented triad. This is also know as "Coltrane Substitution," "Coltrane Changes," etc.
- Coltrane first introduced the "Coltrane Matrix" on his album Blue Train on tunes such as Moment's Notice and Lazy Bird, and later on took things further on Giant Steps.
- The B section from Have You Met Miss Jones served as inspiration for Coltrane because of the major 3rd modulation from D to Gb to Bb.
1) Here is a normal ii-V-I in C major:
| ii | V | I ||
| dmin7 | G7 | Cmaj7 ||
2) Now with the Major 3rds Cycle:
| ii V** | I* V** | I* V** | I* |
| dmin7 Eb7 | Abmaj7 B7 | Emaj7 G7 | Cmaj7 |
- This progression moves from Ab, down a major 3rd to E, then down another major 3rd to C.
- Every modulation to a new key is tonicized by a preceding V chord, indicated my the ** in the diagram.
A Visual Example
- Here is the cycle of 4ths, and as you can see, the triangle connects the tones that are a major 3rd apart.
- In this diagram, you can rotate the triangle and figure out all the possibilities for the major 3rds cycle.