April | 2015 | Bill Plake Music

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!

The longer I teach the Alexander Technique to musicians, the more frequently one particular issue arises: the lack of clarity between cause and effect where practice and technique are concerned. Below is a brilliant description of this potential obstacle to progress:

The players/teachers do what they do; they tell the student what they think they do; the students think they heard what the teachers said about what they think they do; the students then try to do what they think the teachers said about what they think they do.

-Denis Wick, Retired Principle Trombonist, London Symphony Orchestra

Let’s look at this quote in detail.

“The players/teachers do what they do;” Yes, they do. For better or for worse. Truth be told, there are a number of very fine musicians who play well despite what they do. In other words, their misdirected efforts or sub-optimal overall coordination are obstacles that they’ve overcome well enough to let their skills shine through.

“they tell the student what they think they do;” This is often where the confusion begins. It’s a matter of causality versus coincidence. Just because something happens while getting a specific result doesn’t meant that it was the cause of the result. For example, if you do this “thing with your tongue” every time you take a breath to play a wind instrument or sing, it doesn’t mean that “thing” you do is helping you produce an optimal breath. As a matter of fact, it might be even interfering with your breathing.

“the students think they heard what the teachers said about what they do;” So maybe you try to describe this “thing you do with your tongue” to your students, but because of their sensory perceptions/experiences, and how they take in your words, they completely misapprehend what you’ve explained to them. (In essence, they’ve misapprehended your misapprehension.)

“the students then try to do what they think the teachers said about what they think they do.” And the confusion continues. Because the students now “know” what to do, they try to carry it out, no matter how far it is from the original understanding/intention of the teacher, nor no matter how far it is out of accordance with their human design and/or with acoustics.

So now, this “thing with your tongue” that your teacher taught you not only doesn’t help you with your breathing, but also, it’s not even what your teacher thinks it is in the first place.

And this is how a good deal of misinformation is passed on from teacher to student. Some of these students themselves becoming teachers to further perpetuate misconceptions.

So how do you counter this tendency?

1. Question things. Try to understand the cause and effect relationships between specific efforts and results. Doing something a certain way just because a master musician says to do it that way may not necessarily guarantee success. Become a respectful, but healthy skeptic (like some of my favorite students). Same thing if you’re on the teaching side of things. Question why, and understand why, you do the things you do as you play (especially before you tell your students to do likewise).

2. Study the science. The more you understand your design (more specifically your musculoskeletal anatomy and physiology), the easier it is to filter out (or at least re-frame) counterproductive advice. Same with understanding acoustics. If something is acoustically impossible or flies in the face of anatomical reality, you can simply discard it. Aim, as scientists do, to understand the “mechanism” of how and why something works they way it does. (This also applies to the point above about “questioning things”.)

3. Improve your sensory perception. This is where the Alexander Technique comes in handy. You’re often not doing with yourself exactly what you think you’re doing. Part of the study and application of the Alexander Technique is bridging this perceptual gap between what you think you’re doing, and what you’re actually doing.

4. Be wary of words. There can be so much flexibility in the meaning of even the most carefully chosen words. What you read, or are told, may not at all reflect the intention and understanding of whomever read or spoke them. When it comes to teaching and learning highly skilled activities, words without a direct and clear kinesthetic experience can often be misleading for both teacher and student.

So whether you are learning, are teaching, or doing both, staying cognizant of these potential communication gaps between teacher and student can significantly improve results.