Back in the late 90s I came across this drawing in Lateef’s book and studied it closely. I found that it actually describes not a flat disk but a torus (aka donut) with a string winding around it. There are versions of the torus for all the symmetrical intervals (semitone, whole tone, minor third, major third). What changes from one interval to the next is the angle of the string.<p>I diagrammed each of the intervals and shared my work with Lateef. We had a warm conversation.<p>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.
An artist friend of mine, Howard Penner, made a cleaned-up version of this diagram in Illustrator, for an unpublished paper that another musician friend wrote about it. [1]<p>I can't find these papers by Hafez Modirzadeh [2] online, but there are some other papers with references to them:<p>"Spiraling Chinese Cyclic Theory and Modal Jazz Practice Across Millenia", Journal for Music In China. (II:2). 2000<p>Book Review for In The Course of Performance: Studies in the World of Musical Improvisation. Journal of the Society for Ethnomusicology. (XLIV:1). 2000<p>"Spiraling Cyclic Theory and Modal Jazz Practice: The 60-Tone Case of John Coltrane and Ching Fang", SEM Conference Paper (Nov. 20), Austin. 1999<p>[1] <a href="http://imgur.com/gallery/oJKln" rel="nofollow">http://imgur.com/gallery/oJKln</a><p>[2] <a href="http://radiodecibel.nl/index.php?page=artist&id=Hafez%20Modirzadeh" rel="nofollow">http://radiodecibel.nl/index.php?page=artist&id=Hafez%20Modi...</a>
Much more interesting (IMHO) is the Giant Steps animation by Michal Levi:<p><a href="https://www.youtube.com/watch?v=rh6WTAHKYTc" rel="nofollow">https://www.youtube.com/watch?v=rh6WTAHKYTc</a><p>It perfectly shows the structure of the music. The later music video One (set to music of Jason Lindner) is also beautiful:<p><a href="https://www.youtube.com/watch?v=qypqwcrO3YE" rel="nofollow">https://www.youtube.com/watch?v=qypqwcrO3YE</a>
So... What's the deal with the diagram then? The article explains nothing. Some vague ramblings about the geometry of Einstein's quantum theory (?) and no discussion of Coltrane's drawing at all.
The article opens with the claim that "Albert Einstein and John Coltrane had quite a lot in common" but then hardly addresses that further.<p>Did Einstein have any musical talent/interests?