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I just recently started playing out of Yusef Lateef’s book and was wondering about the Coltrane diagrams at the front of the book myself. Did Yusef ever respond? I was planning on cleaning them up myself, glad to see someone has already given a lot of thought to it!
The Coltrane originals were probably part of his estate, and I would guess have been donated to the university where he taught.
I just recently started playing out of Yusef Lateef’s book and was wondering about the Coltrane diagrams at the front of the book myself. Did Yusef ever respond? I was planning on cleaning them up myself, glad to see someone has already given a lot of thought to it!
I never heard from him. The Coltrane originals were probably part of his estate, and I would guess have been donated to the university where he taught.
The ideal would be something directed towards readers with some mathematical background (but not a PhD), conversational, and focused on concepts and maybe historical development rather than just stating facts without context.
It's conjectural on my part, but if you apply D-weighting to the resulting pitch cylinders you can conceptualize musical space as an aesthetically pleasing spherical shape: https://en.wikipedia.org/wiki/A-weighting
If you further consider the nature of stereo hearing, head-related transfer functions, and sympathetic resonance, then you could go a bit nuts in the visualization department: https://en.wikipedia.org/wiki/Head-related_transfer_function
This has actually been operationalized: https://en.wikipedia.org/wiki/Spiral_array_model It's conjectural on my part, but if you apply D-weighting to the resulting pitch cylinders you can conceptualize musical space as an aesthetically pleasing spherical shape: https://en.wikipedia.org/wiki/A-weighting If you further consider the nature of stereo hearing, head-related transfer functions, and sympathetic resonance, th…
It's a serious question; I don't know. I can't think of any current musicians but that's not conclusive. Also, I'm not sure exactly how popular John Coltrane was in 1960; certainly jazz was orders of magnitude more popular than it is now.
Earlier quoted context omitted.
I haven't thought about it in depth, but my guess is that it is not, because a lattice is not isomorphic with a cylinder or torus. Figuring out the relationship in detail would be a good project.
The Tonnetz is a torus, unwrapped onto the plane. On the first Wikipedia image ( https://en.wikipedia.org/wiki/Tonnetz ) you can see the circles of major- and minor-thirds on the 60˚ lines, whole-tone and semi-tone scales along 30˚ and vertical lines, and the circle of fifths on the horizontals. Different presentations skew it in different ways, to emphasize different features, but it's very hard to make a diagram li…
Coincidentally, i just stumbled upon this today: https://m.youtube.com/watch?v=xUHQ2ybTejU Basically a musical palindrome: https://en.m.wikipedia.org/wiki/Crab_canon
https://www.youtube.com/watch?v=lzkOFJMI5i8
(Steve Reich's Clapping Music...)
This has actually been operationalized: https://en.wikipedia.org/wiki/Spiral_array_model It's conjectural on my part, but if you apply D-weighting to the resulting pitch cylinders you can conceptualize musical space as an aesthetically pleasing spherical shape: https://en.wikipedia.org/wiki/A-weighting If you further consider the nature of stereo hearing, head-related transfer functions, and sympathetic resonance, th…
You could see the Coltrane diagrams as viewing a spiral head-on, so that the spiral nature of the structure is hidden by occlusion.
This would solve the problem of the arbitrary nature of representing only five octaves.