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.

Coltrane Substitution:

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.