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…
Perhaps Harmonic Experience by W.A. Mathieu.
This seems pretty much like exactly what I was looking for—thanks!
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). =)
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?
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 not so down on it as an intellectual lark as that poster.
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:
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). =)
Doesn't the spiral array model discard enharmonic equivalence?
I think there's a way around this if you imagine concentric shells with harmonic rotation, but I'd have to go and look up one of my old notebooks from a few years ago. I stopped writing/playing music regularly after a massive construction project in my neighborhood :-/
Oh no! Start again! Been stuck doing covers/arrangements for a few years myself...
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…
Yes, there are a plethora of extremely talented musicians, of every genre who take music theory extremely seriously in order to reach top competitive level.
If you look at any live performance of a pop star, most likely their band will include drummer, guitarists, keyboard player, sound engineers at the top of their game. They might even be playing jazz on the side :)
Check out this pretty much random video of two great young guitarist getting pretty deep in applying theory
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.
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 that kind of thing, you probably like prose writing like this as well. You certainly don't need to analyze all mathematical relations and artifacts to improvise masterfully. In my experience, the more time a player focuses on this type of thing, the less energy they put into actually having something to express. Or perhaps it has something to do with a fear that they will find they have nothing to say, so they avoid that challenge by making technique and mathematical-theoretical relationships the focus of their practice. The only composer I can think of who managed to be obsessed with the math of things while actually using them to create a unique language through which he expessed ideas,style, and narrative was Messaien. (in his modes studies and bird calls) I do understand why many jazz musicians reached for spirituality and really complex mathematical relationships in modes of improvisation:it's because they were not granted the legitamacy and respect they deserve (and craved, many of them, like Monk, for example) from so-called arbiters of "high culture". If what they were doing could be serious and difficult and inscrutable except with hours and hours of thinky labor, they felt it might elevate them.Of course this was totally not needed and what they (monk especially) were creating had a laguage and history of its own that was in many ways more innovative and culturally relevant than that what they sought to be included with. Of course that's easy to say now.It must have been frustrating, like for Ornette.
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