[mrbrowning]

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.

[soundwave106]

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).

[adamsea]

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.