Coltrane Pitch Diagrams



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In the mid 90s I was browsing in the bookstore at Berklee College of Music in Boston. I was looking for Slonimsky’s Thesaurus of Scales and Melodic Patterns, a book of algorithmically-generated scales which had a following among jazz musicians, most notably John Coltrane.

Near it on the shelves I came across a similar but more peculiar book, Repository of Scales and Melodic Patterns, by Yusef Lateef.

As a frontispiece he had included two surprising images.

What were these? A small note at the bottom of the acknowledgements said:

Geometric Drawings: By John Coltrane, 1960. Gifts to Yusef from John.

Over time I became fascinated by the Coltrane drawings and set about decoding them using a protractor, compass and tracing paper.

First I made a clean schematic of Coltrane’s marked-up diagram.

In thinking about it I realized it could be simplified from two rings to one without losing any of the intrinsic relationships.

Of course, from a musician’s perspective this had the surprising result of converting from a whole-tone scale in Coltrane’s original to a chromatic scale in my single-ring version. Then I realized there could be a three-ring version as well, with the intervals on each ring describing diminished triads.

This new three-ring version was visually strange and beautiful, and had a feature that wasn’t evident in either the one-ring or two ring versions: a winding pattern.

Pick a section starting with C and walk to the next C, one semitone at a time. The first four notes of the series would be C, C#, D, Eb. In the one and two ring versions D and Eb are adjacent, but in the three-ring version Eb is on the far ring.

That got me to thinking of the series as a winding banner.

And from there a 3D pattern, not a flat one.

I made a clean final version of this sketch.

From there it was natural to go on to versions with four, five and six rings.

When I had finished my six-ring version, I was sorry that I couldn’t go any further, because each set of rings shows a symmetric interval, and there are no symmetric intervals larger than this.

My drawings were complete, so I made a little title page for the collection.


Not long after I went to a Yusef Lateef concert. It was at Lincoln Center in New York City. He was a stellar player and the show was unforgettable.

After the performance I made my way to the crowd of people chatting by the stage door with the musicians, introduced myself, and asked him to sign my copy of his book.

We talked about the Coltrane diagrams. I showed him a version of my work. He told me that Coltrane had been drawing the original diagrams between sets on a gig they did together, and had given them to him. Lateef said this wasn’t the first time. “He was always doing that,” Lateef said.

That was probably during a period when Coltrane was studying Slonimsky and thinking about generative patterns for melodies. The year was 1960. He was growing from the modernist formalisms of bebop harmony — all bright lines and strict causality — to the ecstatic spirituality of free jazz. The connection between his post-bop and free jazz was numerology, a belief that divine or mystical phenomena can arise from quantitative thinking.

1960 was arguably his peak year. He founded his landmark band with McCoy Tyner and Elvin Jones and recorded his signature hit, “My Favorite Things.” Whatever the diagrams meant to him, they were connected with his best art.


Lateef was warm and generous with his time. I promised to send my own schematics, and later that year I did, along with a cover letter.