John Coltrane Illustrates the Mathematics of Jazz

I notice it's a double ring, not a single circle. Two concentric chromatic rings, offset. That's not decoration: the outer ring and inner ring are the same field read at a phase offset (looks like a tritone / minor-third rotation). Fault tolerance!

The Coltrane changes are great, but on the scale of other harmonic innovations over the years inside Jazz and other traditions. They aren't analogous to Einstein.

What makes Giant Steps so amazing is the sheer speed at which those changes go past — if you slow it down, it's not that different from other Jazz tunes. It took took years of practice for Coltrane to acquire the specialized skillset for improvising over Giant Steps.

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