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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

#61

Post by brooklyn_ashey »

TheOtherHobbes wrote: post #60
brooklyn_ashey wrote: post #53

Earlier quoted context omitted.

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'…

exactly. well said.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#62

Post by soundwave106 »

mrbrowning wrote: post #44
adamsea wrote: 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…

The author of the original post seemed to miss that Coltrane was drawing a "circle of fourths" (all the notes you see that are squared in the diagram are part of this) with a +1 / -1 half step radiating from them. I'm not entirely sure what John Coltrane was trying to do here, but the circle of fourths is well established theory. From my perspective, the transformations the author did were strange to me. They made neat letter patterns but I'm not sure they made musical ones.

From my personal perspective (and all music is to some degree personal opinion), I'm not a fan of trying to orient too much "numerology" to our 12 note equal tempered system (12TET). The 12 note equal tempered system really doesn't pattern all that well to what humans typically find as "consonant": whole integer ratio harmony. EG: One can say the most pleasing ratios follow as such - 2:1 (C:C - octave), 3:2 (C:G, fifths), 4:3 (C:F, fourths), 5:4 (C:E, maj. thirds). That has a certain "math as beauty" look to it when you look at the ratios, but the letter sequence is not as pretty. So if one is trying to find "numerology sense" in music harmony, I personally I think one should use frequencies or frequency ratios instead.

My personal impression about too many 20th century music theories, is that too often theories overfocused on 12TET note relationships, and led to some music that in general is difficult to get into (atonal, 12 tone, serial, etc.). These "have their uses" (some of the theories have found great success as scoring techniques for, say, horror films), and some people do seem to genuinely enjoy it. But the theories that I see that were more successful in the public eye (and in my mind as well) are "less is more" type theories (eg modal jazz or minimalism).

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#63

Post by zengid »

beat wrote: post #55
zengid wrote: 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.

I don't know about you but I don't own a piano. I do have several computers though, and they all have a soundcard. Dynamic tuning is a problem that can be solved by software!

I'm fine with equal temperament dominating, but it shouldn't be taken for granted as the only system for selecting an intonation. When I went to school for music the only time we talked about intonation was in music history. I'd like to change that.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#64

Post by baldfat »

brooklyn_ashey wrote: post #53
baldfat wrote: 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…

> "Thelonious Monk who just played everything in the hardest keys to prove how great he was on piano..."

Can't find where I read that. I believe it was a Miles Davis biography I read years ago. I know many Jazz greats thought the same of Monk. When you listen to "Monk meets John Coltrain" you can just see the two of them just making the hardest possible way to resolve what each other was doing. It is almost like they played musical dare for the last 9 months and finally gotten to a place where we got that album.

As a saxophonist I really enjoyed playing to his work, but my keyboard friends would get so worked up. Just look at 'round midnight. The key signature and the accidentals make it almost unreadable. Plus sure we can play in any key but certain one's are easier than others and it seem like it was always the key that couldn't make it harder if one tried. It was always known if you shown any weakness in playing keys that everyone else would keep modulating to try and mess you up.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#65

Post by brooklyn_ashey »

baldfat wrote: post #64
brooklyn_ashey wrote: post #53

Earlier quoted context omitted.

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…

> "Thelonious Monk who just played everything in the hardest keys to prove how great he was on piano..." Can't find where I read that. I believe it was a Miles Davis biography I read years ago. I know many Jazz greats thought the same of Monk. When you listen to "Monk meets John Coltrain" you can just see the two of them just making the hardest possible way to resolve what each other was doing. It is almost like they…

One-upping is definitely a solo strategy that has a long history, and the tradition continues today. I just don't see Monk's key choice as some kind of proof of his skill. He wrote tunes that often sat awkwardly and offered a lot of space, like "We See" or "Coming on The Hudson" or even "Blue Monk" of all pieces. I feel those as offering freedom of direction and color- offering lots of rhythmic, motivic, and harmonic interpretational options. I guess that's why I love playing Monk tunes. And also his unique accent in the way he played- accent-inflection that was so of himself and so personal. It was confident and simple. I'm personally not a fan of the one-upsman approach to soloing, but it definitely exists.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#66

Post by baldfat »

brooklyn_ashey wrote: post #65
baldfat wrote: post #64

Earlier quoted context omitted.

> "Thelonious Monk who just played everything in the hardest keys to prove how great he was on piano..." Can't find where I read that. I believe it was a Miles Davis biography I read years ago. I know many Jazz greats thought the same of Monk. When you listen to "Monk meets John Coltrain" you can just see the two of them just making the hardest possible way to resolve what each other was doing. It is almost like they…

One-upping is definitely a solo strategy that has a long history, and the tradition continues today. I just don't see Monk's key choice as some kind of proof of his skill. He wrote tunes that often sat awkwardly and offered a lot of space, like "We See" or "Coming on The Hudson" or even "Blue Monk" of all pieces. I feel those as offering freedom of direction and color- offering lots of rhythmic, motivic, and harmonic…

Thank I never get to geek out on Jazz anymore. I moved to a different city and never got to crack into the scene that is here.

To me Monk = craziest and most intellectually stimulating harmonies of all time. No one has ever played his music and fooled you into thinking it was by Thelonious.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#67

Post by adamsea »

brooklyn_ashey wrote: post #58
adamsea wrote: post #40

Earlier quoted context omitted.

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.

That must have been awesome! I was lucky enough to see Vijay & Wadada in Chicago last year. Indian music is crazy/complex/awesome - I learned a tiny bit about it when learning about Olivier Messiaen's "Quartet for the End of Time."

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#68

Post by adamsea »

soundwave106 wrote: post #62
mrbrowning wrote: post #44

Earlier quoted context omitted.

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…

The author of the original post seemed to miss that Coltrane was drawing a "circle of fourths" (all the notes you see that are squared in the diagram are part of this) with a +1 / -1 half step radiating from them. I'm not entirely sure what John Coltrane was trying to do here, but the circle of fourths is well established theory. From my perspective, the transformations the author did were strange to me. They made ne…

Thank you both for the thoughtful answers :). I think what you both said makes a lot of sense.

The one thing I'll throw in is that graphic notation (which I don't know a lot about) is an area where something like the OP can also have relevance - a way of visually expressing musical ideas (including, perhaps, some ideological content meant to inform attitude of the musician). It's also a blurry place between "functional" music notation and art.

I hadn't looked closely at the actual notation in the article - sounds like it may have lacked some rigor.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#69

Post by wyclif »

beat wrote: post #54
wyclif wrote: post #45

Earlier quoted context omitted.

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.

You are lucky. He's an idiosyncratic and eccentric, but unique and brilliant guitar teacher. Also one of the most influential guitarists ever. He has issues too, but I think his unique approach overcomes his mental health history and he's stabilized a lot after getting the right medication. I've heard he now conducts lessons over Skype and I should check to see if he's taking new students.

Re: Coltrane Pitch Diagrams: Wrapping notes around a torus

#70

Post by brooklyn_ashey »

adamsea wrote: post #67
brooklyn_ashey wrote: post #58

Earlier quoted context omitted.

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.

That must have been awesome! I was lucky enough to see Vijay & Wadada in Chicago last year. Indian music is crazy/complex/awesome - I learned a tiny bit about it when learning about Olivier Messiaen's "Quartet for the End of Time."

It was so boring. North and South Indian music is wonderful-I love it. But hearing Vijay break that down was mind-numbing. I like some of his music. Wadada can be great too! But I really wish we could stop justifying jazz by the labor it takes to produce/understand it. I need a break from jazz versions of Radiohead and Hendrix tunes as well. This trend is heralding the content crisis I'm afraid.
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