The Coltrane Matrix

The Coltrane Matrix (also know as “Coltrane Changes” or the “Coltrane Cycle”) are chord substitution patterns over common jazz chord progressions. John Coltrane first introduced the "Coltrane Matrix" on his album Blue Train on tunes such as Moment's Notice and Lazy Bird, and later further the chord sequence on Giant Steps. Quick fact: The B section from Have You Met Miss Jones, written by Richard Rodgers, served as inspiration for Coltrane because of the major 3rd modulation from D to Gb to Bb.

Let’s try to define what is the Coltrane Matrix. The Coltrane Matrix is a reharmonization of chord substitutions of a basic ii-V-I with movement in major thirds, which is unusual in jazz, as the movement typically follows the circle of fifths. The movement in major thirds divides the octave into thirds. For example, C, Ab, E, and back to C are all a major third apart. Let’s take a look at this in practice:

Coltrane Substitution:

1) Let’s start with 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 begins on the ii, tonicizes Ab major, then tonicizes E major, and finally tonicizes C major. Note that each of these tonicizations are a major third apart, dividing the octave into thirds.

  • Every modulation to a new key is tonicized by a preceding V chord, indicated my the **’s in the chart above. The “*” of course represents the keys being tonicized.

A Visual Example

Circle of Fifths Coltrane Matrix

  • Here is the cycle of 5ths with a triangle in the middle that connects the notes that are a major 3rd apart. You can rotate the triangle and figure out all the possibilities for the major 3rds cycle.

  • As shown by the current diagram, C, Ab, and E are all a major third apart.

So there you have it, the Coltrane Matrix in plain English. Now that you understand the theory, the next step is to start practicing. You’ll find the Coltrane changes used in many of John Coltrane’s tunes such as Giant Steps, Countdown, and many more. The real challenge is approaching these changes as a soloist. Giant Steps has almost become a right of passage for jazz musicians; navigating the changes shows you know your stuff!