I diagrammed each of the intervals and shared my work with Lateef. We had a warm conversation.
He mentioned to me that “Coltrane was always drawing things like this.” This particular drawing was something Coltrane did between set breaks at a gig they did together. Coltrane gave it to Lateef at that gig.
He did a particular live solo that left a deep impression. The whole thing was integrated. There was a simple little motif that he built on, playing it over and over again, elaborating on bits, remembering the variations, repeating them, adding little elaborations to the elaborations. Eventually, it became like a labyrinth with the original motif in the center.
Thanks for pointing out the "two circles" way of factoring a torus. I hadn't thought of that.
I see semitones going around the main circle - but how are they connected back to themselves the other way ?
I can't find these papers by Hafez Modirzadeh  online, but there are some other papers with references to them:
"Spiraling Chinese Cyclic Theory and Modal Jazz Practice Across Millenia", Journal for Music In China. (II:2). 2000
Book Review for In The Course of Performance: Studies in the World of Musical Improvisation. Journal of the Society for Ethnomusicology. (XLIV:1). 2000
"Spiraling Cyclic Theory and Modal Jazz Practice: The 60-Tone Case of John Coltrane and Ching Fang", SEM Conference Paper (Nov. 20), Austin. 1999
What you're seeing is a spiral at an angle orthogonal to the angle of view. Imagine a spiral curling around the Z-axis, and a viewer looking straight down Z. The arms of the spiral aren't visible because they are occluded.
It perfectly shows the structure of the music. The later music video One (set to music of Jason Lindner) is also beautiful:
I have a mild case of synesthesia and this is one of the closest things I have seen/heard (:) ) that comes close-ish to capturing how I see/feel when I experience great music.
Of course, I was not surprised to see the creator of the video list a similar motivation in his caption for the upload.
     
C D E F# Ab Bn? C D E F# An? Bb C D E Gb Ab Bb C D E F# G# Bb C D E F# Ab Bb C
C# Eb F G A B C# Eb F G A B Dn Eb F G A B C# Dn F G A B C# En? F G A B
n = (natural sign)
? = its hard to read the scribbles.
..I've got a better description here https://music.stackexchange.com/a/33787
Curious though if you have a take on the boxed numbers over the C's. Perhaps calling out how the original tonic position changes in relation to everything else as you move around the circle?
EDIT: Just saw your other comment interpreting it as a spiral, which effectively answers my question.
I think the importance of there being five tonal regions is that this enables the multiples of 12 to line up at 60. These numbers are significant because they connect back to the Babylonian sexagesimal ("base 60") system used in both music theory and trigonometry.
Did Einstein have any musical talent/interests?
Talks about musical talents, but also some other things where you might see similarities if you read it, then stories about Coltrane.
Also feynmann liked percussions a lot and maybe music in general.
What I find in learning music alone, is that it's highly relative, there's no real absolute, so the space of combination is huge, yet very regular in principles; what's not to like for a scientist.
Quoting article above:
Music is an abstract medium — the printed note requires
interpretation and execution. Like the written line of
code, there is often much more than meets the eye.
I've been studying theory for a while now, and it's become obvious we know a lot less about music than we think we do.
In a way I agree with you, the more you dig the less you know. But at the same time, I have this feeling that .. I do know music. I know because when I'm on it, the few times it happened, it wasn't a theory, but more like a sense of spaces. A sense that fills you in a way that is impossible not to notice. Things are simple, borderline automatic, a very thin closed loop of sensation and action. A bit like an ODE ;) If you're tuned, you can now "see" that space  path, lines and curves and glide on them through the movement inertia.
It's not a static space, it's more like a slightly viscous fluid that also responds to your changes of momentum. If you decide not to glide smoothly anymore, you're welcome to do so, but the ground, the space will now change shape, so you have to know how to stay tuned and react to that. Then you can keep on gliding and it will feel musical.
My most used word when speaking about music is sensitivity.
 seeing in the abstract geometrical sense, a notion of direction, distance, scale, that we use to move, but can be used to organize any kind of sensory inputs I believe.
E.g. scales could be thought of buildings. One can hardly make one without inflecting it in some way that reflects values. To the point where evading this inevitability invokes meta-communication.
When improvising over changes, it is easy to get lost in a compositional idea and lose one's place in the form. Maintaining a simple "relational data structure" like this circle is way way to maintain one's balance a place in the overall form and structure. Jazz musicians work to internalize this in practice, so that in performance, they can be free and expressive while still within the form. And then...there is Dolphy.!!
Once you tune your ear into it, it's absolutely everywhere.
I have a copy but I'm way too stupid/musically uneducated to grok it. Back when I started with music at the age of 12 I thought it was "cool" to be autodidact and not know theory and I have regretted it ever since, because try as I might learning it now, it doesn't really stick. You need those 8-10 hours of practice a day I suppose, and they're hard to come by in your adult life.
it seems in other drawings which appear to also be by Coltrane they are drawn as you suggest, A + Ab/Bb preserving the symmetry
Thanks for pointing that out!
Not exactly thinking of a visualiser but it would be interesting to see how one could actually do that