John Coltrane illustrates the mathematics of jazz

taylorbuley

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!

rectang

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.

cloudfudge

As someone who's really into music theory, I am always annoyed by what I perceive as a patronizing faux exaltation of it supposedly being mathematically based. It's not math; it's cyclical patterns. Yes, it can all be represented mathematically, and it is surprising to some people how something with feeling can map to these interesting cycles of discrete values in unexpectedly regular ways, and there are very interesting mathematical ratios involved, but that doesn't make it math. I don't think we need to pat John Coltrane on the head and talk about how he's actually kind of smart because he's doing math .

moogly

Odd to mention Einstein and not Slonimsky, whose work he studied a lot and built upon.

evanb

I don't remember much about music theory but I know enough about symmetry to know that there's a mistake in the diagram at 9 o'clock.

mellosouls

Original article should be the link (2017 btw): https://www.openculture.com/2017/04/the-tone-circle-john-col...