Coltrane Pitch Diagrams: Wrapping notes around a torus
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Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#2Is this the Tonnetz, or is it different?
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#3Coincidentally, 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
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#4Is this the Tonnetz, or is it different?
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.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#5This looks like a perfect fit for a Max4Live patch. I've always been fascinated by the links between harmony and geometry.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#6This is as much about Coltrane as it is about Lateef, which makes this story even more fascinating. It's a shame that it ends so abruptly.
Lateef was successful with many things, but I enjoy his performances from the 60s best. When Lateef joined Cannonball Adderley's quintet at that time, Cannonball said that it wasn't really justified to call it a sextet now, because Lateef played so many instruments so well, that he should really count as more than one member.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#7Is this the Tonnetz, or is it different?
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 like this that isn't topologically equivalent to the Tonnetz.
If you find this sort of stuff interesting, you might also like to check out the writings of Fred Lerdahl and Dmitri Tymoczko, who come at these scale and chord topologies from a more academic perspective.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#8Earlier 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…
That sounds promising since it does disprove my earlier line of argument. That said, there is more work to be done to show equivalence.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#9This looks like a perfect fit for a Max4Live patch. I've always been fascinated by the links between harmony and geometry.
I'd love to add this into the Ornament and Crime (http://ornament-and-cri.me/) for modular synth as well, which has a Tonnetz app already.
Re: Coltrane Pitch Diagrams: Wrapping notes around a torus
#10I 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!