John Coltrane Draws a Picture Illustrating the Mathematics of Music

Physi­cist and sax­o­phon­ist Stephon Alexan­der has argued in his many pub­lic lec­tures and his book The Jazz of Physics that Albert Ein­stein and John Coltrane had quite a lot in com­mon. Alexan­der in par­tic­u­lar draws our atten­tion to the so-called “Coltrane cir­cle,” which resem­bles what any musi­cian will rec­og­nize as the “Cir­cle of Fifths,” but incor­po­rates Coltrane’s own inno­va­tions. Coltrane gave the draw­ing to sax­o­phon­ist and pro­fes­sor Yusef Lateef in 1967, who includ­ed it in his sem­i­nal text, Repos­i­to­ry of Scales and Melod­ic Pat­terns. Where Lateef, as he writes in his auto­bi­og­ra­phy, sees Coltrane’s music as a “spir­i­tu­al jour­ney” that “embraced the con­cerns of a rich tra­di­tion of auto­phys­iopsy­chic music,” Alexan­der sees “the same geo­met­ric prin­ci­ple that moti­vat­ed Einstein’s” quan­tum the­o­ry.

Nei­ther descrip­tion seems out of place. Musi­cian and blog­ger Roel Hol­lan­der notes, “Thelo­nious Monk once said ‘All musi­cians are sub­con­scious­ly math­e­mati­cians.’ Musi­cians like John Coltrane though have been very much aware of the math­e­mat­ics of music and con­scious­ly applied it to his works.”

Coltrane was also very much aware of Einstein’s work and liked to talk about it fre­quent­ly. Musi­cian David Amram remem­bers the Giant Steps genius telling him he “was try­ing to do some­thing like that in music.”

Hol­lan­der care­ful­ly dis­sects Coltrane’s math­e­mat­ics in two the­o­ry-heavy essays, one gen­er­al­ly on Coltrane’s “Music & Geom­e­try” and one specif­i­cal­ly on his “Tone Cir­cle.” Coltrane him­self had lit­tle to say pub­licly about the inten­sive the­o­ret­i­cal work behind his most famous com­po­si­tions, prob­a­bly because he’d rather they speak for them­selves. He pre­ferred to express him­self philo­soph­i­cal­ly and mys­ti­cal­ly, draw­ing equal­ly on his fas­ci­na­tion with sci­ence and with spir­i­tu­al tra­di­tions of all kinds. Coltrane’s poet­ic way of speak­ing has left his musi­cal inter­preters with a wide vari­ety of ways to look at his Cir­cle, as jazz musi­cian Corey Mwam­ba dis­cov­ered when he infor­mal­ly polled sev­er­al oth­er play­ers on Face­book. Clar­inetist Arun Ghosh, for exam­ple, saw in Coltrane’s “math­e­mat­i­cal prin­ci­ples” a “musi­cal sys­tem that con­nect­ed with The Divine.” It’s a sys­tem, he opined, that “feels quite Islam­ic to me.”

Lateef agreed, and there may be few who under­stood Coltrane’s method bet­ter than he did. He stud­ied close­ly with Coltrane for years, and has been remem­bered since his death in 2013 as a peer and even a men­tor, espe­cial­ly in his ecu­meni­cal embrace of the­o­ry and music from around the world. Lateef even argued that Coltrane’s late-in-life mas­ter­piece A Love Supreme might have been titled “Allah Supreme” were it not for fear of “polit­i­cal back­lash.” Some may find the claim ten­den­tious, but what we see in the wide range of respons­es to Coltrane’s musi­cal the­o­ry, so well encap­su­lat­ed in the draw­ing above, is that his recog­ni­tion, as Lateef writes, of the “struc­tures of music” was as much for him about sci­en­tif­ic dis­cov­ery as it was a reli­gious expe­ri­ence. Both for him were intu­itive process­es that “came into exis­tence,” writes Lateef, “in the mind of the musi­cian through abstrac­tion from expe­ri­ence.”

Note: An ear­li­er ver­sion of this post appeared on our site in 2017.

Relat­ed Con­tent:

Saint John Coltrane: The San Fran­cis­co Church Built On A Love Supreme

The Secret Link Between Jazz and Physics: How Ein­stein & Coltrane Shared Impro­vi­sa­tion and Intu­ition in Com­mon

John Coltrane’s Hand­writ­ten Out­line for His Mas­ter­piece A Love Supreme

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness