John Coltrane Draws a Picture Illustrating the Mathematics of Music (opens in new tab)

This Psychology Today article goes pretty deep on that front: https://www.psychologytoday.com/blog/imagine/201003/einstein...

Talks about musical talents, but also some other things where you might see similarities if you read it, then stories about Coltrane.

I think the author is alluding to Einstein and Coltrane having quite a lot in common conceptually around envisaging the universe, sacred geometry and spirituality http://upliftconnect.com/spiritual-wisdom-of-albert-einstein...

There's a quote about music and Einstein, don't know more.

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.

He played violin.

Perhaps the writer meant that while they both studied structures, they both had a personal style that was powerful and served to advance the thinking in their fields. Both were more concerned with leaving those structure to adventure toward philosophical comment through their work.

I have read that Einstein lied to improvise on violin iirc when coming up with new ideas

Einstein was a fairly talented amateur violinist as I recall.

Oh man, I'm so jealous that you got the chance to talk with Yusef Lateef. That must have been awesome to pick his brain about music. He's one of my favorite musicians (alongside Coltrane himself of course). Eastern Sounds is still one of my favorite albums. He was one of those musicians who had a unique sound but was always trying new things.

Holly cow, the torus is topologically the product of two circles S1*S1 so he must have been thinking of something cycling in two dimensions, not just one as the circle of fifhts or chord-scale theory.

Thats insanely beautiful. Thank you for sharing!!

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.

Don't understand the downvote. The first video may seem arbitrary to people not familiar with jazz theory but it's a really good representation of the structure of one of clotrane's most emblematic song. Thanks for sharing !

I still haven't figured out how to play over Giant Steps changes, although shredding through augmented scales has about a 50% success rate.

Think:color wheel. Every improvising musician (and some classical musicians as well)holds a similar diagram in their heads when practicing common chord progressions like ii-V-Is and rhythm changes, and the blues, etc... and on and on. Each note/chord in the western scale pulls against others next and opposite to it in the same way, regardless of the key one inhabits in any given moment. These relationships are dynamic; variables, in a way, pulling against one another in an interconnected system. The tonic(I, or "c" in c major, for example) has a "home" quality, the dominant (V) has a cadential quality in relation to the tonic, etc., and each chord has its role. Within this system, one can create the illusion that one is "in a key" that one is not actually fully in for the overall work-- this is like nesting methods in code. Loops are loops and the idea remains the same no matter how big or small, no matter the coding language. Chordal relations in music are the same. This diagram may be what Coltrane holds in his head as he plays patterns and repeats motives in a given solo to imply chordal relationships and "transportation" from one realm to another. These realms have anticipatory meaning we all understand unconsciously, even if we are not professional jazz musicians. (for example, we all feel the need for "do" if it is left off the end of "do re mi fa sol la ti...." in "Do, a deer".) There is nothing magical about Coltrane's diagram that I can see that is beyond what most improvisers hold in their heads as they practice patterns over chord changes. And yet, there is something wonderful about how these chords and notes create inherent meaning and character roles relative to one another-- like the color wheel. It is still cool to see the way Coltrane represented these for himself in his own mind, (in other words- how simple his ingredients- they are the same as ours, and the result!)implying how he practiced improvising, and the path those patterns may have taken.

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.!!

The pentatonic scale. [0]

Once you tune your ear into it, it's absolutely everywhere.

[0] https://en.wikipedia.org/wiki/Pentatonic_scale

I'm trying to parse out the logic, but it looks like the outer ring and inner rings are moving clockwise in whole steps, with the outer ring starting on C and the inner starting on C#. If we took the rings and straightened them out we'd have (its hard to tell some of the notes so correct me if I'm wrong):

  [1]                     [2]                     [3]                     [4]                     [5]                     [1]
   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  

Note:

  n = (natural sign)
  ? = its hard to read the scribbles.

It looks like he augments some of the intervals in the middle of the scale and diagramming how to elide from one to the other. Note that Bn could be considered distinct from B. Coltrane was familiar with the overtone series that generate what are called harmonics. Harmonics could be thought of as the sine waves that sum together to create the timbre of a pitch. If you've played guitar and you pluck the string while gently pressing the string down at the 1/2, 1/3, 1/4, 1/5 (etc) division, you'll force the string to vibrate only at the frequency that corresponds to that harmonic (ie 1/2 would force it to vibrate only at 2f where f = the lowest vibration mode of the string, sorry If I'm not conveying the physics perfectly). Anyway, the overtone-series closely approximates a major scale, but it gets tricky when you want to shift from one series to the next because the series is generated from integer ratios, and prime numbers generate similar but distinct pitches. Long story short, you can have several genus of the same note that are all mathematically distinct.

..I've got a better description here https://music.stackexchange.com/a/33787

Yeah, a little disappointed there's no explanation. They couldn't find a single musician to interview for the article?

This drawing shows a closed cycle covering five octaves. But musical pitches are not a closed cycle, they keep going down and up from there. How can you take this drawing and extend it to an arbitrarily high or low pitch? Make it a spiral.

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.

Let's imagine one note as a point on a plane, then an interval (2 notes) as a line connecting those notes. Next we have a chord (3 notes) and we get a triangle. By inverting the notes of the chord (135, 351 etc) we get a ring that representd different triangle shapes. Let's go into third dimension by adding one more note, thus a 4 chord can represent a pyramid.. you could also stay in 2D and represent a square etc.. by modulating and changing the tonal center you can move around the canvas or in space.. representing different data structures.. the horizontal movement would animate the structure as well!