If you’ve studied jazz improvisation for any length of time, you no doubt soon learned about the most essential chord progression: ii-V7-I.

This harmonic movement is the foundational building block of many standard songs from the American Songbook, and of many standard jazz compositions, as well.

Once you learn it in all keys, you gain greater understanding and control over what you do as you play over chord changes: clearer melodic statements, immediate understanding of chord/scale families/key centers, stronger sense of bar form, deeper understanding of harmonic movement/relationships, etc.

It’s as if this previously overwhelming world of chords somehow became smaller and more manageable, as you recognize, hear and respond to the various ii-V7 components (and their substitutions) that you encounter as you improvise.

You’ll spend a lot of time working with this cyclical, diatonic chord progression, using it as a template through which to practice patterns, chord substitutions and licks.

But there is another chord progression, which is also cyclical (but not  diatonic) that can be immensely helpful to your development as a linear improviser: the Coltrane Matrix.

The Coltrane Matrix (also known as the “Coltrane Changes” and the “Coltrane Cycle”) is a staple of the modern jazz language. The harmonic centerpiece of John Coltrane’s jazz classic, Giant Steps, the matrix itself is a tonal cycle in which the octave is divided into three equal parts (descending major thirds).

In the key of C major for example, it would be: C-Ab-E-C. This is converted into a harmonic cycle by beginning each modulation with a dominant 7th chord moving to its tonic:

As you can see, there are three tonal centers in this cycle (C, Ab and E) that, by virtue of its symmetrical nature, return to the starting tonality (C major).

John Coltrane also used this matrix as a harmonic foundation on some of his other pieces (e.g., Countdown, which is a re-harmonization of Miles Davis’ Tune up) as well as using it as a chord substitution on many standard songs (e.g. But Not For Me).

And Thelonious Monk’s masterpiece, Brilliant Corners, has lots of elements of this harmonic form within its borders.

Yet besides these pieces I’ve mentioned and a few others, there probably aren’t that many compositions in the jazz lexicon that employ this harmonic sequence.

So why, you might ask, is it such an important chord progression?

Well, besides the fact that everytime you play through it you’re covering three different keys, it offers a challenge in connecting these radically shifting keys (hence the name, Giant Steps) in a smooth, voice-leading, melodic manner. Even simply using the chord tones by themselves, you can find some compelling, cogent sounding voice-led jazz language melodies:

I spent lots of time improvising and working out simple melodic patterns that connect both the major to dominant chords (e.g., C maj7 to Eb7) , and the dominant chords to their major chords (e.g., Eb7 to Ab maj7).

Once I became proficient in easily and smoothly connecting these tonalities, I started looking for less obvious ways to connect them. This is when the deeper value of studying these changes came to my consciousness.

Because I spent so much time practicing over this matrix, its angular sound became deeply imprinted in my ear. So much so, that as I began to explore some of these “less obvious” ways of playing through the changes, I found (to my surprise and delight)  that I could easily  hear these new explorations in relation to the original chords.

This opened up my playing not only over the Coltrane Matrix, but also, over ii-V type chord progressions, as well.

I began to explore further, and realized that many common tonalities are shared between these symmetrically related chords:

In the above example, I’m using triad pairs, specifically: major/augmented.

Each major triad is formed from the fifth degree of the scale (e.g., G major triad over Cmaj7 chord), and each augmented triad is formed from the 9th of the dominant, and by raising the 11th (e.g., F augmented triad over Eb7). You’ll notice that, because of the symmetrically related tonalities of the matrix, the augmented triad is actually the same  for each dominant chord (with two different enharmonic spellings). The strength of this melodic movement doesn’t lie in its voice leading, but in its structural sequence.

Because I could now both understand  and hear  this relationship, it gave me lots of new possibilities as I explored playing over standard songs. It both simplified harmonic substitutions (by finding common tonalities over dominant chords), and extended the possibilities.

As I started to explore further, I found some strange, but beautiful melodic combinations:

This is a variation on the Cry Me A River jazz cliché. Not only do I start on the raised 11th of major (F#), but I also resolve up  to the raised 11th of major (instead of resolving down to the 3rd) as I move from dominant to tonic, creating a haunting sounding Lydian colored tonality.

As you can see, these kind of explorations can both strengthen and challenge your ear, as well as your concept of harmonic relationships. Working through the matrix this way can help you develop and establish a very personal  sounding harmonic vocabulary, no matter the chord changes (or lack of chord changes!)

I still practice over this harmonic sequence regularly, continuing to cultivate my ear, my harmonic intellect/curiosity and my melodic language. Each time I work on it, I either have a “what would this sound like?” moment, or a “wow, that sounded wonderful!” moment as I stumble upon some new discovery (or both!)

If you spend lots of time working through the Coltrane Matrix, ii-V7-I will seem like a walk in the park. You’ll play with a new kind of freedom, fluency and imagination.

If you’d like something to spark your imagination and challenge your ears, consider my eBook, The Coltrane Matrix: 40 Unique Melodic Ideas in All 12 Keys, which documents some of my explorations and discoveries. Each of the 40 melodies is explained in brief, clear detail (and as the title suggests, is put into all 12 keys).

And yes, you can certainly use the Coltrane Matrix directly as a substitution for ii-V cycles (the way Cotrane did on the above mentioned But Not For Me) to add tension and interest to your solo. There’s a whole world of possibilities waiting for you discover them. Have fun on your journey!