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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

#51

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 bit late to the game, but I've really enjoyed reading Musimatchics by Gareth Loy, it explains music theory from a mathematical and historical perspective: https://mitpress.mit.edu/books/musimathics

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#52

Earlier quoted context omitted.

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.

I agree with you on this as a lifelong musician and improvisor. It isn't the math of grammar we think about when conversing to convey meaning and style. We think about what we want to say and how we want to say it. We listen and build something together just like we do in conversation. There is a kind of obsession among some jazz players with spirituality though, it is true. If you are the sort of person who likes th…

> most of what you see in this article is nonsense

How as a creative person are you okay with saying blank statements like that? Sure if you just want to only talk about John Coltrane's drawing out of his time and only focus on today, possibly.

As someone who has several years of Music Theory and a grandfather that retired as a NYC Jazz Musician I absolutely know many people that worked this way. Heck we had 20 years of the "Mozart Effect" (Was bogus since day one that believed passively listening to Mozart made children and lab rats smarter). BUT music is mathematical and some people have certainly taken this bogus Mozart thing and found out the math behind music. For decades the musical music was captivated with math in the 20th century. This wasn't some spiritual journey in music it was a mathematical puzzle they were trying to work out.

The best example of Music based on Math was Iannis Xenakis, who composed from 1940s into the 1990s. Now he is certainly a required taste and I would say listening to his music live MIGHT make it more palatable but he was using computers in the 1960s to help his compositions. He wasn't Thelonious Monk who just played everything in the hardest keys to prove how great he was on piano but just wrote music from the love he had for mathematics and engineering. Classical music or "European Classical Music" was more into Math and as the high brow crowd was into his stuff it certainly was inside the head of John Coltrane, Miles and Ornette Coleman.

https://en.wikipedia.org/wiki/Iannis_Xenakis

https://www.youtube.com/watch?v=n2O8bMlEijg

Stravinky's Septet from 1952 can also show how this serial technique composition had huge influence on Jazz in the late 50s and early 60s. Especially when you listen to Miles Davis and Bill Evans "Sketches of Spain." You see that thousands of musicians were exploring and thinking about the "Math of Grammar."

https://www.youtube.com/watch?v=ijSmRoPzMaY

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#53
post #52

Earlier quoted context omitted.

I agree with you on this as a lifelong musician and improvisor. It isn't the math of grammar we think about when conversing to convey meaning and style. We think about what we want to say and how we want to say it. We listen and build something together just like we do in conversation. There is a kind of obsession among some jazz players with spirituality though, it is true. If you are the sort of person who likes th…

> most of what you see in this article is nonsense How as a creative person are you okay with saying blank statements like that? Sure if you just want to only talk about John Coltrane's drawing out of his time and only focus on today, possibly. As someone who has several years of Music Theory and a grandfather that retired as a NYC Jazz Musician I absolutely know many people that worked this way. Heck we had 20 years…

Well, it's difficult to discuss this math/music issue in a just a comment-length mini-essay and manage to get at what I'm trying to convey. I didn't write the "nonsense" comment myself, but i do hear the legit and justified frustration in it. Sketches of Spain- beautiful. Xenakis though. Man, every time I have had to perform one of his pieces, I'm thinking I should be paid double or they should just hook a digital sound making device up to his score so they don't have to pay anyone to practice that stuff! I guess some people enjoy it? He is the perfect example of what I was trying to get at. Does he have ideas? I guess so...? Do i need to practice them? Um, only if I get paid double/triple for the gig. Know what I mean? It isn't that I'm saying that musicians don't ever practice this way or compose using these devices. Tons of jazz musicians sit around with Slonimsky, mathing their way to a technique in improv that is truly justified by labor. People do it. It is a bit ridiculous. There is a pianist here in NYC who does this- she's a fantastic pianist and composer without Slonimsky and the like. She has compositional ideas and stylistic ones. I will say she is a cold player, but she's battling it out in a tough shark tank, so I get that she feels she has to join the arms race. I'm just saying that the musicians/composers I admire most focus on the human communication, style, and content aspect of improv and the aspect of music that comments upon culture and also inspires cultural change and reflection. Nuance. in As a young musician, I was forced to practice this thinky-mathy way for various professors. With age comes the perspective and mercy I hope to show my students and colleagues when I don't spend our valuable practice and rehearsal time on retrograde-inversions and the set of combinatorial relationships in a given collection, i.e. things that don't sound like much (except to a music theorist who studied serialism and 12-tone) but are justified by practice room labor. I'm definitely not trying to claim that there aren't musicians that go down this path-- there certainly are! Famous ones, even! For me though, it's is a flag waving frantically that loudly signals a lack of artistic content, usually. But not always, as I said. This is only my opinion, however. I voiced it because there aren't enough musicians/teachers/composers who voice this pushback against the macho-mathy in jazz. There is this fallacy that anyone who can't play all mathy w the Slonimsky snippets weaving in and out of their improv should not be listened to when they say, "hey! why are we practicing this stuff??? I'm not a computer! I'm an artist-human!" I'm just saying some of us don't feel bullied (not saying you are doing that-you were just raising a legit point) and we feel perfectly fine calling out this approach for its mad dash to cover up for a severe lack of artistic content and a fear that one is vulnerable to being unseated from the throne.

I'd say jazz is really suffering from a lack of artistic content right now, and I believe it's a direct result of years of this kind of prove-your-mathy-badassery-technical-arms-race among jazz musicians. This is what happens when an "island is sinking"- people start pushing others off the sinking island so there is room for themselves. Jazz (and classical) is kinda sinking. Hopefully we can heal from this and get away from analogue versions of computer music (Xenakis) and back to humanity soon. It's funny, the defense against the sinking is causing it to sink faster by being less human, less relevant. Ironic.

But I sure didn't say that people don't get all up into the math of interrelationships in music theory. They do- I would hate for a non-musician to think they had to do that though to understand music. Absolutely not!In fact, I'm just saying that isn't what music is about for me, as a composer-musician. (I want to encourage people to love music, not to feel bullied by the 'difficulty" of its theory)

also: you said, "...He wasn't Thelonious Monk who just played everything in the hardest keys to prove how great he was on piano..."

What? I don't think that's what Monk was doing at all! Monk developed a sonic language all his own. I don't think any keys were hard for him... nor are they for any professional musician. Monk thought in sound texture and color. They are just different sounds. Sometimes you need a freshness or a timbre that a special key provides. Enough jazz music is written in B-flat if you know what I mean.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#54
post #45

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…

This is only going to be useful in a partial way, and more likely to be helpful if you play guitar, but Richard Lloyd (formerly of the band Television) explains the "circle of fourths and fifths" here: https://youtu.be/mNmEq-cP9Oo https://youtu.be/9lSifKZ80H4

I took a lesson from Richard Lloyd once. In that format, he goes much deeper into the Circle of Fifths. He finds as much spiritual meaning in it as Coltrane did in the symmetries found in the drawings of the original article.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#55
post #28

I'm excited to see others on the journey of connecting music theory and math. I feel like taking equal-temperament for granted obscures a lot of the simplest connections. Just intonation has a treasure trove of interesting implications (and challenges), and the math is elementary school stuff [0]. [0] https://music.stackexchange.com/a/33787

Just intonation leads to giving up on key changes, though. And it gives up the flexibility of the piano and fretted instruments - if you want to play well in a different key, you have to re-tune the piano!

The dominance of equal temperament can probably be traced directly to the rise of the piano in importance.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#56
post #38

Earlier quoted context omitted.

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?

I think what the grandparent is getting at is that music is a culturally-mediated perceptual phenomenon, and so the geometric interpretations here are an artifact of the model rather than of how our minds organize pitch into some musical Gestalt. I both agree with that (I love Coltrane, but as the article accidentally implies, this is about as meaningful as numerology) and find the artifacts to be pretty cool, so I’m…

[deleted]

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#57
post #52

Earlier quoted context omitted.

I agree with you on this as a lifelong musician and improvisor. It isn't the math of grammar we think about when conversing to convey meaning and style. We think about what we want to say and how we want to say it. We listen and build something together just like we do in conversation. There is a kind of obsession among some jazz players with spirituality though, it is true. If you are the sort of person who likes th…

> most of what you see in this article is nonsense How as a creative person are you okay with saying blank statements like that? Sure if you just want to only talk about John Coltrane's drawing out of his time and only focus on today, possibly. As someone who has several years of Music Theory and a grandfather that retired as a NYC Jazz Musician I absolutely know many people that worked this way. Heck we had 20 years…

You also rightly said, "For decades the musical music was captivated with math in the 20th century. This wasn't some spiritual journey in music it was a mathematical puzzle they were trying to work out."

Yeah, you are right, for some. But actually, for some others, it was a serious spiritual journey. Like for George Crumb! (way into numerology- used it in Ancient Voices, Black Angels and other pieces- yeikes!- but some people dig this-- remember though, some people also dig a good seance or a good horoscope you know?)

https://music7703lsu.wordpress.com/2017/03/12/liturgical-num...

https://www.youtube.com/watch?v=11o8nHk-l_o

Also- look into Webern's beliefs about numbers. He was really driven/controlled by this superstition. There is certainly a tradition of just this kind of spirituality that is alive in jazz today. Sun Ra was all about this spirituality without the math stuff. https://www.youtube.com/watch?v=djBKQNVj5Cc

Anyhow, computers had a lot to do with this math obsession in 20th century music composition.

And Ornette? Was he about math at all? I may not know about this. For me, having played a lot of his music, I'd say that his music is a music-of-the-people, and much more about folk music than jazz, although he's of course a great jazz musician. One of the greatest, and maybe because of this fact. He had confidence in the simplicity of his ideas. He didn't seem out to prove anything to anyone. Harmelodics has absolutely nothing to do with mathematical relationships or theory. It's all about each bringing what they think to a melody. (in very short, here) But if he was about math, I just don't know it. Please tell me, so I can look into it.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#58
post #40

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 spe…

Totally agree with you. Excellent answer. Vijay most of all with the theory/math. I sat through a lecture he gave on ragas in jazz once, and it was essentially a math class about ragas.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#59

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…

Most jazz musicians today under the age of 45, went to music school. Brad Mehldau went to the New School. (someone mentioned Brad) The jazz faculty at the New School, when he went there at least, was ramming theory down every student (most music school does this as one of the main requirements of graduation). The piano/comp/theory teachers then (Gary Dial and Armen Donelian?) were all about the theory, especially for pianists, who kind of have to have the structure nailed down in their heads in order to accompany others at least.

But nearly every musician you will hear on a recording or at a concert these days went to music school. Music school has to employ all of its academic faculty, so as a result, they have to require several years of varying kinds of theory, counterpoint, jazz theory, etc. I could go into why the music schools feel that they have to overload every musician with all kinds of required theory classes, but you'd likely be bored. Let's just say it makes everyone feel comfortable with how legit pro they are.

So to answer the question, no, jazz is not unique. Bebop is not unique in this way. All musicians who go to a serious top-10 conservatory must waste a boatload of time taking all sorts of theory classes. Some programs are better than others. The conservatory I went to put musicians through a brutally boring and in-depth multi-year course of theory and analysis.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#60
post #52

Earlier quoted context omitted.

> most of what you see in this article is nonsense How as a creative person are you okay with saying blank statements like that? Sure if you just want to only talk about John Coltrane's drawing out of his time and only focus on today, possibly. As someone who has several years of Music Theory and a grandfather that retired as a NYC Jazz Musician I absolutely know many people that worked this way. Heck we had 20 years…

Well, it's difficult to discuss this math/music issue in a just a comment-length mini-essay and manage to get at what I'm trying to convey. I didn't write the "nonsense" comment myself, but i do hear the legit and justified frustration in it. Sketches of Spain- beautiful. Xenakis though. Man, every time I have had to perform one of his pieces, I'm thinking I should be paid double or they should just hook a digital so…

I realised a while back that music theory is like modular synthesis.

You can keep collecting modules - ideas about theory - forever. But only one person in a hundred, at most, knows how to make them work together to produce something audiences are going to want to hear more than once.

Coltrane may have been one of those people. But if he was, it was because he was Coltrane.

Most people who play with these ideas aren't. And acquiring more ideas and theories won't change that for them.

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