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Coltrane Pitch Diagrams: Wrapping notes around a torus

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Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#31

Post by stephencanon »

elihu wrote: post #23
stephencanon wrote: post #7

Earlier quoted context omitted.

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…

It's equivalent to a torus in equal temperament, because the pattern repeats in a predictable way when the notes alias each other. In a just intonation 3-5 lattice, it extends infinitely without repetition.

Indeed--you can still map it onto the torus but the lattice doesn't line up neatly; you get irrational spirals that cover the surface.

But, since this is in the context of Trane and Lateef, I think ET is a reasonable assumption.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#32

Post by stephencanon »

dbranes wrote: post #21

Here's a generalization that yields an infinite family of similar observations. Step 1. Take any "torus knot with n marked points": which for our purposes will mean homeomorphism classes of embeddings from a circle with n marked points, to the torus. Step 2. Draw it on paper. In the case of the Coltrane drawing, n = (5 octaves * 13 notes per octive) = 65. The author exhibited 3 non-homeomrphic embeddings of this circ…

I'm totally with you, but there are 12 notes per octave (at least in the standard western scale). =)

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#33

Post by bigiain »

andybak wrote: post #24
bigiain wrote: post #19

Earlier quoted context omitted.

You might enjoy this piece too: https://www.youtube.com/watch?v=lzkOFJMI5i8 (Steve Reich's Clapping Music...)

Skip "Clapping". It's fun but you wouldn't listen to it for anything other than intellectual interest. Other Reich though - Drumming is a wonderful midpoint between formalistic process-driven music but it still can give you goosebumps. He gets less process driven as time goes on - which I think is a good thing in many ways. For me probably the high point of his work is something like Music for 18 Musicians. Simultane…

I saw Drumming performed in the round by Synergy Percussion in Sydney a few years back - it was _beautiful!_

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#34

Post by IAmGraydon »

westoncb wrote: post #14

Anyone know a nice source for learning some basic music theory? To be more specific, something that would teach whatever would be required to understand the musical concepts in this article (for example). 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 withou…

The only thing that learning music theory will do for you in this case is make you realize that most of what you see in this article is nonsense. Certainly, none of it will help you make music. I say this as a songwriter and student of music theory for 20 years.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#35

Post by snaily »

westoncb wrote: post #14

Anyone know a nice source for learning some basic music theory? To be more specific, something that would teach whatever would be required to understand the musical concepts in this article (for example). 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 withou…

A blog post: "Music theory for [non-music] nerds": https://eev.ee/blog/2016/09/15/music-theory-for-nerds/

Previous discussion here: https://news.ycombinator.com/item?id=12528144

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#36

Post by ZenoArrow »

forapurpose wrote: post #17

Are there musicians of today, with popularity similar to Coltrane's in 1960, that study and explore the theory of music at this level? If not, why not? Was jazz, and bebop in particular, unique in this regard? 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…

> "Are there musicians of today, with popularity similar to Coltrane's in 1960, that study and explore the theory of music at this level?"

Jacob Collier springs to mind, though he's less well known than John Coltrane.

http://youtu.be/DnBr070vcNE

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#37

Post by UncleEntity »

forapurpose wrote: post #17

Are there musicians of today, with popularity similar to Coltrane's in 1960, that study and explore the theory of music at this level? If not, why not? Was jazz, and bebop in particular, unique in this regard? 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…

I heard (back in the '90s) Trey Anastasio was heavy into the music theory.

Don't know if it's true since I never got into Phish so YMMV.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#38

Post by adamsea »

IAmGraydon wrote: post #34
westoncb wrote: post #14

Anyone know a nice source for learning some basic music theory? To be more specific, something that would teach whatever would be required to understand the musical concepts in this article (for example). 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 withou…

The only thing that learning music theory will do for you in this case is make you realize that most of what you see in this article is nonsense. Certainly, none of it will help you make music. I say this as a songwriter and student of music theory for 20 years.

Damn son, talk about dropping the hammer on ‘em.

As a longtime, trained musician with a bit of theory, I’d love to get a breakdown. Would you be willing to explain what is nonsensical about the article?

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#39

Post by westoncb »

IAmGraydon wrote: post #34
westoncb wrote: post #14

Anyone know a nice source for learning some basic music theory? To be more specific, something that would teach whatever would be required to understand the musical concepts in this article (for example). 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 withou…

The only thing that learning music theory will do for you in this case is make you realize that most of what you see in this article is nonsense. Certainly, none of it will help you make music. I say this as a songwriter and student of music theory for 20 years.

My main interest is just that it seems like an interesting system—and it's cool that it can be put into correspondence with sounds.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#40

Post by adamsea »

forapurpose wrote: post #17

Are there musicians of today, with popularity similar to Coltrane's in 1960, that study and explore the theory of music at this level? If not, why not? Was jazz, and bebop in particular, unique in this regard? 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…

Names which spring to mind (though bear in mind popularity is quite a relative term when it comes to jazz). And that I’m not super-up on the current jazz scene:

Wadada Leo Smith, Vijay Iyer, Branford Marsalis, Dave Douglas, Kamasi Washington

They all have varying degrees of popularity and avant-gardness. Also, it’s not really fair to compare any of them (or any other contemporary players) to Coltrane - that was a special time for jazz. Plus music has moved on — new genres, instruments, it’s new times.

Candidates for the new John Coltrane, Id argue, would be hip hop producers:

J Dilla, Madlib, Flying Lotus (who is actually related to Alice Coltrane), DJ Premier, Pete Rock, RZA, Q-Tip, are some of the most influential producers who have strong connections to jazz. By which I mean knowledge of, musical influence from, and also using samples of jazz (though arguably that’s the least relevant part) in their work.

You could make an argument for rappers, too (Rakim, Nas, etc), as hip hop is the inheritor of the jazz tradition, but it is trickier comparing rapping - oral poetry at heart - to instrumental music.

One reason, imho, jazz had that golden age was that it was during a time in NYC when there was a critical concentration of talent and opportunities for jazz musicians to make a living playing gigs there.

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