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 musi­cans 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. Musi­can 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 pub­li­cal­ly 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 reli­gious expe­ri­ence. Both for him were intu­itive process­es that “came into exis­tence,” writes Lateef, “in the mind of the musi­can through abstrac­tion from expe­ri­ence.”

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Relat­ed Con­tent:

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

John Coltrane’s ‘Giant Steps’ Ani­mat­ed

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

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Comments (158)
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  • PaulR says:

    Ein­stein’s the­o­ry of quan­tum grav­i­ty? I thought quan­tum grav­i­ty was a rebut­tal against Ein­stein.
    Ein­stein, did, how­ev­er, like to make vague state­ments about God.

  • Gellert Szabo says:

    So can some­one explain the draw­ing?

  • Ccb says:

    Its a cir­cle con­sist­ing of 2 con­cen­tric whole tone scales. Not cycle of 5ths.

  • Plop says:

    The 5ths are empha­sized.

  • None says:

    You’ll note that all the cir­cle of 4ths/5ths notes have dou­ble cir­cles around them.
    This is an extrap­o­la­tion of the cir­cle.
    That said, you’re not wrong.
    here’s more…

  • Adam Rudolph says:

    NOt to take any­thing away from anyone…but the record should be seet straight. YUsef Lateef was NOT John Coltranes pro­toge. In fact they were peers who often prac­ticed togeth­er and shared many ideas. It is com­mon knowl­edge that Yusef was deep into “world music” long before coltrane and many oth­ers and that he was the one who intro­duced coltrane to schillingers sys­tem of com­po­si­tion from which giants steps was inpsired. It is not always the more famous one, of even the genius who comes up with ideas.…..this has been told to me by many who were around and on the scene at that time in detroit and nyc. dis­re­spect here.…but it is good to know the untold sto­ry.

  • Josh Jones says:

    @Adam, thanks very much for your com­ment. I’ve edit­ed the post to bet­ter char­ac­ter­ize Lateef’s rela­tion­ship to Coltrane.
    @PaulR, whoops! Right you are. Cor­rect­ed.

  • Corey Mwamba says:

    Here (as some­one who was sur­prised to see them­selves quot­ed in the arti­cle) to echo Adam Rudolph’s com­ments above.

  • Bernardo Teixeira says:

    lol Ein­stein always hate quan­tun mechan­ics!!!

  • Josh Jones says:


  • Dean says:

    Alexan­der sees “the same geo­met­ric prin­ci­ple that moti­vat­ed Einstein’s” quan­tum the­o­ry.

    Grav­i­ty was not men­tioned

  • Ray C says:

    Indeed, Ein­stein and Coltrain have some­thing in com­mon: they let math do all the ‘heavy-lift­ing’ allow­ing their imag­i­na­tions to run free.

    Melod­ic / har­mon­ic analy­sis is moot with­out con­sid­er­ing Coltrain’s keen sense of sym­met­ric rhyth­mic phras­ing – he always knew where he was going. Also knew the val­ue of time-pitch ratios as being the most organ­ic rhyth­mic phras­es demot­ing the ‘bar-struc­ture’ to being orga­ni­za­tion pur­pose only. My first expe­ri­ence with a 9 against 8 resul­tant (r 9 ÷ 8)was pure Coltrain(see Joseph Schillinger — The­o­ry of Rhythm. Runs cir­cles around any oth­er so called rhyth­mic tech­nique.).
    Try this phrase (1 = 1/8 note– its 8 bars of 9/8 )
    |: 8_1_7_2_6_3_5_4_4_5_3_6_2_7_1_8 :|

  • Roel Hollander says:

    @Josh Jones: thanks for shar­ing.

    @Corey Mwam­ba: why sur­prised? Peo­ple who take blog­ging seri­ous always make an effort to note prop­er cred­its. Your name would thus obvi­ous­ly appear.
    At least for me your arti­cle “Way of see­ing Coltrane” are of impor­tance, with­out them I most like­ly would not have come to writ­ing my blog arti­cles. And per­haps Josh Jones would­n’t have either?

  • David Hilton says:

    It looks like to me he’s drawn the cir­cle of 5ths oppo­site than most oth­er ver­sions- instead of going up in 5ths to the right he goes up 4ths to right and 5ths to the left- which imo, is a mil­lion times bet­ter. Also, Coltrane has spelled a cou­ple who­le­tone scales, the top ring spelling out a C who­le­tone scale, and the inside ring is a C# or Db who­le­tone… Trane writes both scales four times each- indi­cat­ed by the 1,2,3, 4, in box­es with a line going to the start of the afore­men­tioned scales. I don’t want to look too much longer at Coltrane’s draw­ing, it’s start­ing to hurt my brain.. haha­ha.… how­ev­er, in the inner part of the cir­cle it looks to like the small num­bers and their accom­pa­ny­ing straight lines are spelling out some chro­mat­ic scales. With all key cen­ters flow­ing out from the cen­ter of the cir­cle. Some­thing like that.

  • stelenox says:

    where are you peo­ple see­ing the 5ths and the 4ths in the cir­cle? i just can see whole tone scales, chro­ma­tisms but noth­ing relat­ed with the tra­di­tion­al cir­cle of 5ths.

    And when you peo­ple, music crit­ics and the­o­rist are going to under­stand that MUSIC is not a f—ing SCIENCE, even if we use maths indi­rect­ly or some kind of rules..

  • Niall Tracey says:

    The weird oval things con­nect­ing the two cir­cles appear to be the “cross­ing points” between the cir­cles to fol­low a major scale up to its sev­enth degree.

    If you start at one of the dou­ble-cir­cled fifths/fourths and pro­ceed clock­wise two steps, it describes do-re-mi, which are sep­a­rat­ed by who­le­tones. The mi-fa gap is a semi­tone, so you have to switch cir­cles — and the mi and fa are con­nect­ed in Coltrane’s dia­gram.

    You can then con­tin­ue on your new ring until you hit the 7th degree of the major scale, and you have the full scale, or you can cross at the 6th degree to land on the flat 7th (part of the dom­i­nant 7th chord).

    I’m not con­vinced it’s huge­ly use­ful, because it does­n’t reveal more than oth­er rep­re­sen­ta­tions, and it obscures things like minor thirds and alter­na­tive modes of the scale, but it’s inter­est­ing to see how some­one so deeply immersed in music tried to put down on paper what he had already grasped inter­nal­ly.

  • Jean says:

    Actu­al­ly, Ein­stein found­ed quan­tum mechan­ics in 1905. That’s why he had a Nobel prize in 1921. He hat­ed how Niels Bohr solved some of the para­dox­es of this quan­ta the­o­ry by say­ing real­i­ty was, at its core, not deter­min­ist. And quan­tum mechan­ics does not deal with grav­i­ty.

  • Mircan Kaya says:

    Jazz is a musi­cal genre and it is dif­fi­cult to define it with­out a broad vision that includes wide range of musi­cal gen­res span­ning over a peri­od more than a hun­dred years. One should not dis­re­gard the role of impro­vi­sa­tion in Jazz (Jass) music
    It is all about music after all and physics, math­e­mat­ics, cos­mic rules of har­mo­ny should be con­nect­ed to “music” and not to “jazz” only. This despis­es oth­er gen­res of music.
    There is math­e­mat­ics & physics in every­where. Not only in music but every­thing in the uni­verse. When it comes to music, all gen­res of music con­tain in them­selves math­e­mat­ics & physics.

  • Gil says:

    The two were very good friends. FACTS.

  • joseph kaminski says:

    Stu­pid, very nar­row mind­ed. There are a infi­nite num­ber of song and scales that do not con­form to this map. As soon as you con­sid­er dis­si­dent scales the map goes out the win­dow.

  • Al says:

    Total non­sense. This is just over rev­er­ence for Coltrane and noth­ing more. Coltrane was­n’t as pro­found as peo­ple pre­tend and that cir­cle is non­sense. It’s heart­break­ing, to me, how far off peo­ple are about har­mo­ny.

  • Chris says:

    It’s a piano key­board laid out in cir­cu­lar form. C1 being the bot­tom note on the key­bord, then pro­ceed­ing up by half step alter­nat­ing notes to the inside and out­side cir­cles. Each “C” note is num­bered as you pass it by on the key­board until you get back around to the 6th, and start again. Any two notes with no black keys between them are cir­cled. All the “C” notes are con­nect­ed with lines. All the “5ths”, cor­re­spond­ing on the oppo­site side of the cir­cle to their ton­ic notes, are con­nect­ed with lines. I’m still tying to fig­ure out what the num­bers inside the cir­cles refer to.

  • Corey Mwamba says:

    Hey Roel! It was shared by some­one on FB, and I was read­ing it; it just came as a sur­prise!

  • Daniel locht says:

    Coltrane and Lateef stud­ied with the math­e­mati­cian, jazz the­o­rist Roland Wig­gins in Philadel­phia. He intro­duced them to Nicholas Slomin­sky’s the­saurus of scales and melod­ic pat­terns which was fun­da­men­tal to Coltrane’s method­ol­o­gy .
    This looks like it is based on a 12 tone melod­ic pat­tern.

  • Chris says:

    I just real­ized I’m actu­al­ly wrong about the cir­cled notes.

  • Earnest says:

    I would love to see anoth­er blog in which you com­plete­ly dis­sect this dia­gram, note by note, line by line.

  • J-M Van Schouwburg says:

    Yusef Lateef ( William Evans) was mem­ber of the Dizzy Gille­spie Orches­tra around the same time that John Coltrane shared the sax sec­tion .…. end of the for­ties and ear­ly for­ties . Jim­my Heath was also in the Dizzy’s Orches­tra…

  • DAZ says:

    For the musi­cians inter­est­ed, here’s an old arti­cle dat­ed back when the pic­ture was post­ed by Miles Okaza­ki on Twit­ter :

    Btw, i have the dig­i­tal ver­sion of the Yusef Lateef book some­where on my hd, and if i remem­ber cor­rect­ly there are actu­al­ly 2 Coltrane draw­ings in there (pret­ty much sim­i­lar but with a twist from what from what i could recall)

  • George mann says:

    “good” music, is time­less in a sense that it tick­les some­thing in our brain. Almost as if we have heard it before? There is a mag­ic and beau­ty in music , when it is “right” it brings plea­sure and trig­gers emo­tions.
    There is some­thing mag­i­cal about math­e­mat­i­cal mod­els and algo­rithms, they are beau­ti­ful, time­less … They just work…
    They may describe some “thing” or prop­er­ty of physics, that inex­plic­a­bly IS THE TRUTH, music is the same in a sense, No one can deny the POWER of sound waves , that touch the heart in a way that can’t be explained eas­i­ly, but is are real and time­less­ly truth­ful as math­e­mat­ics itself😊

  • andrew hill says:

    Ein­stein’s physics was not quan­tum. Even though the term is old­er and due to Planck, who start­ed it all in 1900, Ein­stein, seen erro­neous­ly as the last clas­si­cal physi­cist, was not think­ing in those terms yet. The asser­tions in the arti­cle are intrigu­ing, though, and the book could be that, too.

  • Rehan says:

    Intel­lec­tu­al com­plex­i­ty in music is not a hard achieve­ment. One can have a com­put­er come up with plen­ty of com­plex­i­ty. What is hard is access­ing gen­uine inspired cre­ativ­i­ty expressed via appar­ent simplicity/complexity. Todays and the past 40, 50+ years of music is exclu­sive­ly for the gen­er­al pub­lic and aver­age musi­cians at best. No longer do we have musi­cians who can cre­ate real art for the best musi­cians in the world, just as we no longer have Shake­spear­es or Beethoven’s any more.

  • Annemie says:

    This is so visu­al­ly stun­ning, the har­mo­ny and Sacred Geom­e­try of music, chart­ed as in Astrol­o­gy in a com­bined sphere!!! Next lev­el!!!

  • Zane says:

    Does any­one else think that this looks real­ly sim­i­lar to Meta­tron’s Cube?

  • Newstetter says:

    I think you mean “dis­so­nant” scales … not “dis­si­dent.”

  • Harry Likas says:

    I see an extrap­o­la­tion of the Cir­cle of “4ths” (a square is drawn around each “4th”). Then the cir­cle was sub­di­vid­ed chro­mat­i­cal­ly up a 5 octave range. Then cir­cles were drawn to high­light the half step approach note below each 4th (lead­ing tones) and a cir­cle was drawn to high­light the half step up above each 4th (tri­tone chro­mat­ic approach).

    The Chro­mat­ic scale degrees have been num­bered 1 2 3 4 5 6 7, 1 2 3 4 5 6 7, for orga­ni­za­tion­al pur­pos­es.

    This is sim­ply a sketch of the chro­mat­ic scale, then high­light­ing the cir­cle of 4ths with­in it and cir­cling each ones lead­ing tone and chro­mat­ic tri­tone approach note. This is pret­ty basic stuff.

  • Newstetter says:

    Here’s anoth­er inter­est­ing analy­sis of this cir­cle …

    This essay address­es the appar­ent ‘mis­take’ in the left side of the cir­cle where the pat­tern of three chro­mat­ic tones is bro­ken. There is a sec­ond ver­sion of the cir­cle in the orig­i­nal note­book which ‘cor­rects’ this mis­take. The group­ings in the over­lap­ping ovals are all set up so that there is a sin­gle note between each group­ing in both the inner and out­er cir­cle, but one of the group­ings ( G, G#, A) is off and should prob­a­bly have been G#, A, Bb. There is a lot of debate about whether or not this was a mis­take or inten­tion­al, but in light of the sec­ond sketch and sim­ple log­ic, I think it’s essen­tial­ly a minor error in the sketch which was left uncor­rect­ed in the tra­di­tion of zen art, and of course Jazz, where mis­takes are also not mis­takes.

  • Newstetter says:

    Here’s anoth­er exam­i­na­tion of this cir­cle, includ­ing obser­va­tions about the appar­ent mis­take in the left hand side of the cir­cle. (two part blog post)

    The chro­mat­ic group­ings, sur­round­ed by over­lap­ping ovals, are all posi­tioned with one note between them in the inner and out­er rings, except the group­ing “G, G#, A” which is off by one place. It prob­a­bly was meant to be “G#, A, Bb” which would have been con­sis­tent with the rest of the pat­tern. There’s a lot of debate about whether this was real­ly an uncor­rect­ed mis­take or inten­tion­al. On the side of it being a mis­take, there is a sec­ond sketch in the same book show­ing a ‘cor­rect­ed’ ver­sion.

  • Louis says:

    His rela­tion to quan­tum mechan­ics was more com­pli­cat­ed than that:

  • Linda Clough Cole says:

    I won­der if any of you folks remem­ber my father, John Clough. Music the­o­rist who the­o­rized “flip flop cir­cles” Bril­liant man. I miss him.

  • Peter Callaway says:

    John Coltrane grew up Pen­te­costal which means he prayed in the Spir­it that is in tongues in the Holy Ghost.
    He was a per­fec­tion­ist.
    As far as beliefs he seemed to embrace East­ern like spir­i­tu­al­i­ty lat­er in life.
    But then why was Coltrane found dead on a park bench in Cen­tral Park in NYC?
    Tal­ent with­out restraint and strength of char­ac­ter makes ones gift some­what void.

  • Benjamin Connelly says:

    You can see the the­o­ry behind Giant Steps in this cir­cle.
    Using the inner cir­cle’s dark­ly cir­cled notes A, B, Dflat, Eflat, F G
    and the out­er cir­cles dark­ly cir­cled notes C D E Gflat Aflat Bflat

    In giant steps. All Major Chords Eflat, B, and G are in the inner cir­cle’s dark­ly cir­cled notes. All dom­i­nant sev­en chords are in the out­er cir­cle’s dark­ly cir­cled notes. Minor chords are func­tion­ing mere­ly as appendages of the dom­i­nant chords.

    Try play­ing with this: The two cir­cles allow for sub­sti­tut­ing sur­pris­ing dom­i­nant sev­en chords to move in sur­pris­ing direc­tions:
    Con­ven­tion­al: G D7 D
    Con­ven­tion­al Jazzy: G D7 to Dflat
    Using this cir­cle G Bflat7 to Eflat (see first line of giant steps for this move.)
    How bout this G E7 A ?
    Each one of the above moves uses a major chord from the inner cir­cle a dom­i­nant from the out­er and resolves down a fifth to the inner.

  • Chris troy says:

    The arti­cle referred to Ein­stein’s “quan­tum the­o­ry,” not the­o­ry of quan­tum grav­i­ty. Huge dif­fer­ence there. Also, although Ein­stein is most famous for his the­o­ry of grav­i­ty (gen­er­al relativity),he is cred­it­ed with being a pio­neer­ing of quan­tum physics. His nobel prize is for the Pho­to­elec­tric effect(quantized light/counting pho­tons).

    Also, quan­tum mechanics/physics isnt a rebut­tal against Ein­stein. We sim­ply can­not describe the behav­ior of nature at very very small scales in a “clas­si­cal” way, that is, deter­min­is­ti­cal­ly. His grav­i­ta­tion­al the­o­ry is just fine for gen­er­al pur­pos­es. In fact NASA still uses new­ton­ian gravity/mechanics some­thing even less accu­rate.

    You might be think­ing about the fact that Ein­stein did not accept the fact that the math­e­mat­ics for­mu­lat­ed to address the appar­ent­ly quan­tum nature of mat­ter was based on the sta­tis­ti­cal prob­a­bil­i­ties of it being in a cer­tain place at a cer­tain time. He believed that they sim­ply had not yet uncov­ered the vari­ables which tru­ly and pre­cise­ly deter­mine the behav­ior. He was ostra­cized for this of course.

    Quan­tum grav­i­ty is the attempt by many physi­cist, from Ein­stein to today to unite quan­tum mechan­ics and gen­er­al rel­a­tiv­i­ty. So the idea that one rebutts the oth­er is just a false mis­con­cep­tion. The prob­lem is that the two work extreme­ly well in their own domain.

    By the way i love jazz, coltrane, math­e­mat­ics, physics, this arti­cle, and of course A Love Supreme.

  • Guy says:

    It’s all the gold­en ratio

  • Jourdan Hines says:

    Call me crazy, but I think part of the dia­gram is wrong:

    As you look to the left and the 9 o’clock posi­tion one of the “hearts” is fac­ing the wrong direc­tion. The bot­tom of the heart should be the note A which points towards the inner part of the cir­cle.

    Any­one else catch this or have fur­ther com­ments on it?

  • gerald brennan says:

    And not a word about his the­o­ry or tech­nique.

  • Ahmet İşsever says:

    Becom­ing a father for those who will fol­low the deeds; which may help in the sci­ence and in state of the art achieve­ments must be that this per­son is a fine influ­ence for those.
    May they be recalled in all good­ly deeds, in the good light for-ever. Salutes in peace.

  • Raymond Foos says:

    While read­ing through the com­ments and replies i am mys­ti­fied as to how many times those indi­vid­u­als who’ve com­ment­ed or replied have mis­spelled John’s name…it’s Coltrane not Coltrain…i find it total­ly dis­re­spect­ful to do so!!!

  • Marco Raaphorst says:

    You can see the cir­cle of fiths or fourth in it.

  • bluzcat says:


  • Michael in LA says:

    John Coltrane died at Hunt­ing­ton Hos­pi­tal in Long Island of liv­er can­cer. We can argue about the cause of his can­cer and if his his­to­ry of drug abuse was a con­tribut­ing fac­tor. Your descrip­tion of him as dying des­ti­tute on a park bench is false.

  • Dolf says:

    I think “the same geo­met­ric prin­ci­ple that moti­vat­ed Einstein’s” Gen­er­al Rel­a­tiv­i­ty” might work bet­ter. Gen­er­al Rel­a­tiv­i­ty involved a lot of Geom­e­try.

    While Ein­stein argued with famous Quan­tum Mechan­ics pro­po­nents like Niels Bohr, he in fact was one of its orig­i­na­tors whether he liked it or not. Ein­stein’s paper on the pho­to­elec­tric effect showed that light was both a wave and a par­ti­cle which is one of the bedrocks of Quan­tum Mechan­ics.

  • Reg says:

    IIt seems some­one is dou­ble-guess­ing Bach and Mozart. This was far bet­ter illus­trat­ed on a train­ing card in the 1960s.Shifting singers for­mant fre­quen­cies is far more inter­est­ing.

  • franco says:

    Don’t need any kind of cheap lit­er­a­ture to unde­stand what’s he doing. You see the draw and instant­ly knows what means and how to play it. There’s no need to stu­pid misty­cal ref­er­ences, take care that peo­ple talk­ing calls bri­an eno a futur­is­tic com­pos­er…

  • tommy molotov says:

    looks more like stal­in’s notes at a debussy con­cert

  • Ziga says:

    Pure non­sense. There have always been and will always be inno­va­tors. The prob­lem is that they belong to the age they come from and not to pre-estab­lished aes­thet­ic ideals. There are plen­ty of com­posers, writ­ers, painters, poets, etc., who will be rec­og­nized for their tremen­dous inno­v­a­tive strides in this age, but the chances are that you’ll nev­er learn about them — they may not even be known out­side of a very small cir­cle of peo­ple for anoth­er hun­dred years. Shake­speare was rel­a­tive­ly unknown dur­ing his life­time and then dis­ap­peared until a revival of his work much lat­er. Bach was pret­ty much com­plete­ly for­got­ten. The oth­er thing is, if you’re look­ing for “real art” to sound like Beethoven or read like Shake­speare, it’ll nev­er hap­pen — art is evo­lu­tive — it reflects the changes that we expe­ri­ence on a socio­cul­tur­al lev­el, as well as fun­da­men­tal shifts in aware­ness. Please remem­ber that many of the artists that we’ve made into icons over the years were nev­er pop­u­lar in their own time. Pop­u­lar­i­ty is nev­er an indi­ca­tor of qual­i­ty or inno­va­tion.

  • Rehan says:

    @ Ziga, Inno­va­tion by itself is not Art. Art is a com­mu­ni­ca­tion of a ‘high­er con­scious­ness’ via mat­ter to give us a glimpse of that state. It is the best evi­dence for an ‘after life’ (whether you believe in such or not) and said high­er con­scious­ness. Inno­va­tion many times comes from tal­ent (men­tal instincts) and tend to have a ‘dead­ness’ to it. The music of Beethoven etc. does not come alive and show its true poten­tials in any of todays musi­cians. Also clas­si­cal music can­not be record­ed. Non clas­si­cal gen­eras hide behind ampli­fi­ca­tion for appeal. Not that i’m against pop music btw.

    Many years back I got to hear a musi­cian who could chan­nel the super con­scious (if you want evi­dence-not proof for the super con­scious: mind via the instru­ment (with a real vibra­to). He got this gift after an auto acci­dent. Only then did we hear what beethoven’s music was sup­posed to sound like. The entire audi­ence was pro­fes­sion­al strings play­ers from around the world (unlike the gen­er­al pub­lic who jump at any­thing). None had heard any­thing like it before or since.

    One can­not appre­ci­ate the depth of the music of Bach, Beethoven and Mozart until one has heard a real musi­cian in live per­for­mance. An extreme­ly rare event. They no longer seem to be born, or the gifts or not avail­able as they once were.

    Even the Jazz greats are sup­posed to be all dead accord­ing to some jazz musi­cian who lament­ed on the Char­lie Rose show. We’ve always known that in the clas­si­cal world. So you cant judge clas­si­cal until you’ve real­ly heard it.

  • Lucas Gonze says:

    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 cir­cle but a torus (aka donut) with a string wind­ing around it. There are ver­sions of the torus for all the symet­ri­cal inter­vals (semi­tone, whole tone, minor third, major third).

    I dia­grammed each of these, 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. He gave it to Lateef at that gig.

  • Jim says:

    Mr. Call­away, where do you get your infor­ma­tion? Clear­ly not from any fac­tu­al source. “A park bench”? “Strength of char­ac­ter”? It’s like The World Accord­ing to Sean Spicer.

  • CRB says:

    Coltrane is the cor­rect spelling.

  • Coltrane's Naima says:

    Above all else, etc! Coltrane’s lyrics, A Love Supreme and ”
    Astral Trav­el ” and Ein­stein, ” You can’t Solve A Prob­lem, Frim the Same Con­scious­ness That Cre­at­ed It, You Learn To See The World Anew.” Nuff said by two of the most cul­tur­al­ly com­pe­tent spir­i­tu­al genius giants who stepped on this plan­et ions ago, yes­ter­day, today, and tomor­rows will be rel­a­tiv­i­ty in cos­mi­cal­ly sweet eter­nal­ly.

  • Marco says:

    He got close, con­sid­er­ing he used a 2D scheme. The solu­tion to his math­e­mat­ic break­through I believe cor­re­spond to the more accom­plished “tor­sion field”; which, resem­bles the ener­gy expan­sion and com­pres­sion toward an infi­nite exter­nal rout and a sin­gle inter­nal one.

  • miroslav says:

    Ein­stein received his Nobel Prize for dis­cov­ery of the pho­to­elec­tric effect law

  • Khalisax says:

    Brilliant,well spo­ken @ZIGA

  • kai says:

    Yes! I agree. ‘any musi­cian will rec­og­nize as the “Cir­cle of Fifths’ real­ly isn’t help­ful. This isn’t what any musi­cian would recog­nise as the cir­cle of fifths. I sup­pose you could say the 5ths are cir­cled, but actu­al­ly every sin­gle note is cir­cled at some point in the draw­ing! Sure, you can pick out the 5ths if you know what they are, but I don’t think that’s what the image leads you to do that. If any­thing he’s high­light­ed C five times with numbers…which is…helpful? I pret­ty, and I imag­ine draw­ing it while you think­ing about music is prob­a­bly fun, but not espe­cial­ly use­ful!

  • Enrique says:

    Also there is a cycle of fifhts,watch care­ful­ly and you will recog­nise Ccb

  • Les says:

    Chi­nese Amer­i­can Dr Chou is the first (woman? per­son?) to hold two chairs in seper­ate depart­ments: Music and Math at Har­vard. Her sis­ter was the sec­re­tary of Edu­ca­tion in Chi­na, her moth­er wrote the first Wok cook­book and her father was the only per­son to speak all of the Chi­nese dialects (200?) . Watched him cor­rect a word on the wall­pa­per at a Chi­nese restau­rant in Berke­ly.

  • John says:

    Jean you are the only per­son who got those points cor­rect. It was the dis­cov­ery of the pho­to­volta­ic prin­ci­ple being quan­tized that won the Nobel. And quan­tum grav­i­ty was nev­er con­sid­ered in Ein­stein’s time, and only con­sid­ered as part of the attempt to rec­on­cile rel­a­tiv­i­ty with quan­tum mechan­ics.

  • Charles says:

    This is all non­sense. Coltrane was a bril­liant musi­cian, but it can be under­stood and appre­ci­at­ed (and played) with­out ref­er­ence to Ein­stein and math. Just because some­one says that musi­cians are sub­con­scious­ly math­e­mati­cians does­n’t make it true.

    The arti­cle is just a col­lec­tion of unsup­port­ed state­ments and more or less irrel­e­vant quotes. And if it “feels Islam­ic” to one clar­inetist does­n’t make it Islam­ic. Coltrane was influ­enced by music from Africa and India, to be sure. This appears to be writ­ten by some­one with lit­tle grasp of har­mo­ny, and a desire to be seen as deep. To a musi­cian who’s worked on Coltrane’s music it’s some­what embar­rass­ing to read.

  • DLH says:

    Your com­ments are elit­ist and nar­row.

  • Louise Gregg says:

    When the arts trans­form you know you have arrived in a world you are head­ing for.

  • Asa Bove Sobelow says:

    Inter­est­ing com­ments on what the Coltrane dia­gram might rep­re­sent. But HOW do you sup­pose Coltrane used it? Lis­ten­ing close­ly to his music might give insight to his use of this dia­gram to illus­trate an intel­lec­tu­al grasp of his intu­itive musi­cal under­pin­nings. To focus on the rings is to miss a more sub­tle point and drown the con­ver­sa­tion in intel­lec­tu­al spar­ring. The key is not found in the ring(s) them­selves so much as it is found in the place where all the lines con­verge in the cen­ter. To Trane, I believe, the out­er rings = human intel­lect (excel­lent for its intend­ed pur­pose, but lim­it­ed. The point where all lines con­verge = intu­ition (or per­haps for him, Spirit/Oneness). Coltrane, par­tic­u­lar­ly in his more ‘spir­i­tu­al’ work, did his sin­cer­est best, as most musi­cians do, to replace ‘think­ing’ with ‘feel­ing’ and thus, become more musi­cal­ly (per­son­al­ly?) tran­scen­dent.

  • ssingh says:

    It’s fun­ny we make all this analy­sis about music assum­ing there are only 12 notes. There are infi­nite notes, just as there are infi­nite col­ors. The 12 tone sys­tem is con­ve­nient, but mere­ly 12 points in the realm of infi­nite pos­si­bil­i­ty. If we want to find real par­al­lels between music and oth­er realms of science/experience, we must look at the oth­er aspects of sound/music. Explo­ration of the over­tone series is a good place to start! Why not tune our musi­cal scales to points on the over­tone series? Much more har­mo­nious and beau­ti­ful!



  • Philip DiTullio says:

    These con­cepts are all in the Schillinger Sys­tem of Musi­cal Com­po­si­tion.

  • James says:

    It actu­al­ly does­n’t say any­thing about ‘quan­tum grav­i­ty’ (which applies more broad quan­tum the­o­ry to the rel­a­tive­ly nar­row field of grav­i­ty). It’s actu­al­ly quite inter­est­ing to think of Coltrane’s musi­cal the­o­ry as being relat­ed to ‘quan­tum the­o­ry’, as west­ern music and instru­ments arguably under-quan­ti­fy tonal­i­ty.

  • Dennis says:

    In 1968 I was lis­ten­ing to a Coltrane album. I can­not say that I know what a “trance” is, but that’s the word I’ll use. I went into a trance. It was not some­thing I was try­ing to do.

    Dur­ing the trance, Coltrane’s music trans­lat­ed, in my mind, to words, sen­tences, para­graphs of the Eng­lish lan­guage. They had very spe­cif­ic mean­ings. When one side of the album end­ed I would even­tu­al­ly wake up out of the trance. I could not remem­ber the Eng­lish trans­la­tion that I had heard while under the trance.

    I’d flip to the oth­er side and play that side. I’d go into the trance again, and the same thing would hap­pen. And NO, I was­n’t high. Yeah, it was the ’60s, but I nev­er got involved in the drug crap.

    Of course, I have long wished to know what had hap­pened back then. Did Coltrane DESIGN his music in that man­ner? By the way, I had not known a sin­gle thing, back then, about Coltrane’s spir­i­tu­al­i­ty. To me, it was just “good jazz.”

    Any­way, this arti­cle blows me away, because, in a way, it some­what “con­firms” for me that Coltrane was some kind of eso­teric sci­en­tist or some­thing. And I won­der if some sci­en­tists and/or math­e­mati­cian could study Coltrane’s music and pos­si­bly derive, sci­en­tif­i­cal­ly, some kind of rela­tion­ship between the mathematics/physics of Coltrane’s music and the Eng­lish language–or per­haps ANY lan­guage.

    When one thinks of the idea of mor­phogenic fields, col­lec­tive con­scious­ness (or the col­lec­tive sub­con­scious), then per­haps it can be imag­ined that the expe­ri­ence that I had in ’68 could have been dupli­cat­ed by any­one, of any cul­ture, who would have heard the trans­la­tion of Coltrane’s music in their own lan­guage.

  • Ricardo says:

    It’s a nice draw­ing, for sure. But I’m afraid it’s just a mat­ter of over-hyp­ing Coltrane. Peo­ple like to talk about Coltrane or Miles Davis like they were super humans, and peo­ple feel it’s real­ly trendy to hype them.

    But actu­al­ly, as great as they were, there are thou­sands of oth­er jazz greats who are just as genius, if not more, but receive lit­tle or no atten­tion at all. I guess it’s not fash­ion­able to praise Count Basie or Dizzy Gille­spie.

    It’s a mat­ter of hype, fash­ion, and ego. To talk about Coltrane makes you look so pro­found and knowl­edge­able… it’s just an act.

  • paul niemiec says:

    Not a sin­gle per­son has men­tioned Den­nis San­dole, Coltrane’s teacher, and the per­son who showed Coltrane how to split the octave into three equal divi­sions. For a more inter­est­ing “Sacred Cir­cle”, check out Pat Mar­ti­no, who arranges the chro­mat­ic scale in a cir­cle (sim­i­lar to a clock face). Mar­ti­no lays either a tri­an­gle or a square over the cir­cle, which gives either an aug­ment­ed chord or a dimin­ished chord. Mar­ti­no then gen­er­ates every type of chord by rais­ing (or low­er­ing) suc­ces­sive notes in the aug­ment­ed or dimin­ished chords by a half-step. This is a com­plete­ly dif­fer­ent approach than gen­er­at­ing the chords out of the major scale. Note that Mar­ti­no was also a stu­dent of Den­nis San­dole, and note that again we are talk­ing about some­one who is split­ting the octave into even divi­sions of either three or four.

  • Grahame Rhodes says:

    Are you sure about the schillinger sys­tem thing? With ref­er­ence to Giant Steps though and apart from “Have You Met Miss Jones” bridge I always thought it was the Slonim­sky Melod­ic Pat­terns
    You’re right about Yusef Lateef though because Trane was inter­est­ed in Indi­an Ragas which Lay­eef showed him.
    I have nev­er read any influ­ence regard­ing Schillinger though please clar­i­fy

  • Ecta says:

    Very true. Mak­ing assump­tions about music based on West­ern modal­i­ties is eth­no­cen­tric. An exam­ple of an alter­na­tive is the Per­sian Dast­gah sys­tem.

  • Tony DeCaprio says:

    Good you men­tioned Den­nis. Thank you.

  • demetrios babalis says:

    An excep­tion­al and pio­neer­ing artist. The men­tion­ing as well as the spec­u­la­tion of the influence(s) that super­nat­ur­al myths had on John Coltrane add to our under­stand­ings. Thank you for shar­ing about these numer­ous insight­ful glimpses into John Coltrane’s life.

  • Jimmy michael says:

    It’s the cycle of 4ths, not fifths. He clear­ly has 4ths cycle cir­cled the dark­est. 4ths are V7 to I and know­ing the cycle helps tremen­dous­ly. It is also the order of flats for key sig­na­tures. Coltranes abilty to play modal is writ­ten all over this sketch.

  • Pythagoras says:

    This draw­ing is based on equal tem­pera­ment, which is a false con­struct alto­geth­er. Hard to apply pure math and look for mean­ing in some­thing peo­ple made up. Equal tem­pera­ment is a mild­ly adul­ter­ation of a tru­ly remark­able set of num­bers and ratios. Even the notion that an octave con­tains only 12 notes is instead wrong except for in west­ern tonal music. When Bach and oth­ers tweaked nature in order to con­struct instru­ments that could play in sev­er­al keys, they left the nat­ur­al math behind alto­geth­er. So this is a draw­ing of 12 equal­ly spaced ‘things’ in a cir­cle and var­i­ous geom­e­try con­nect­ing the dots. ( geom­e­try is entic­ing because it implies order with­in chaos- but it usu­al­ly has to ignore a lot of the chaos to do so. ( con­stel­la­tions much?).
    NOW, if some­one wants to re-draw this over a Just into­na­tion / har­mon­ic series with per­haps a 56- note karmic Indi­an ‘scale’ ( aka round num­ber selec­tion of har­mon­ics- halved until they all live with­in an octave, THAT would prob­a­bly blow some minds, too. I think it would look like a spi­ral galaxy in 3 dimen­sions. Per­haps a com­put­er mod­el­er would help. It prob­a­bly already being done in the con­text of weath­er mod­el­ing pro­grams.
    Any­way, I think Coltrane’s point is: it’s all mirac­u­lous and big­ger than us from a high­er pow­er and that will always hold true.

  • Philip DiTullio says:

    With regards to Schillinger’s influ­ence pure fact. Yusef Lateef stud­ied the Schillinger Sys­tem in Detri­ot and his influ­ence along with many musi­cians of the day, Juan Amal­bert, Muhal Richard Abrams, Jymie Mer­rit, Jim­my Heath …

  • Mark says:

    I’ve always thought that music is math­e­mat­ics. Just look at nota­tion, pitch is ver­ti­cal, rhythm is hor­i­zon­tal- a sim­ple graph. Grant­ed, I’m speak­ing of west­ern music. but has no one noticed that con­nect­ing all the C’s on the chart pro­duces a beau­ti­ful five point star? That’s the con­nec­tion between music and math!

  • Phil says:

    Read the arti­cle again. It cred­its right­ly so as you note that Yuseef was “peer even as men­tor” to Trane.



    Ein­stein made one ear­ly con­tri­bu­tion to quan­tum the­o­ry in 1905,before his famous papers on rel­a­tiv­i­ty. Oth­er peo­ple elab­o­rat­ed the the­o­ry. The biggest prob­lem in the­o­ret­i­cal Physics is that quan­tum mechan­ics does­n’t fit smooth­ly with gen­er­al rel­a­tiv­i­ty, even though each the­o­ry works real­ly well in its own domain. Ein­stein him­self worked on the Uni­fied Field prob­lem with­out mak­ing much progress.

    The arti­cle does­n’t say quan­tum grav­i­ty. It is pos­si­ble that the author mis­spoke, know­ing more music than physics.

  • Dave says:

    How in any way is this 8 bars of 9/8? You don’t teach music, that much is clear.

  • Mary says:

    It may be a real pos­si­bil­i­ty that Coltrane had Synes­the­sia. Many bril­liant peo­ple do. It has the brain think­ing in col­ors, or num­bers, or draw­ings to sound, taste etc. It’s like hav­ing hyper sen­si­tiv­i­ty in brain por­tals. It would explain all of it, and is not some­thing most peo­ple under­stood, or under­stand today.

  • DAVID says:

    The pen­ta­gram in John Coltrane’s draw­ing may well be the cir­cle of fifths etc BUT it may also be the orbit of Venus, the God­dess star.Why?John Coltrane was, I believe, [and one of the great “Goddesses”/psychic priest­esses has con­firmed} the rein­car­na­tion of Elijah,Christ and the Prophet Muham­mad {pbuh} and that’s what he dis­cov­ered in 1955, but nev­er said. The true Christ “Anoint­ed one/God’s mes­sen­ger“ nev­er claims any­thing for him­self — he leads by exam­ple.

    I believe John Coltrane’s “A Love Supreme” was his New Testament/Qur’an, released in the uni­verse lan­guage of music, and that his ago­nised late play­ing express­es his great sad­ness that his beau­ti­ful Bud­dhist mes­sage over many incar­na­tions had been total­ly mis­un­der­stood and led to so much hatred — he was cry­ing out for our help, for our under­stand­ing.

    It may even be that only the great psy­chic priest­ess Alice Coltrane knew who John real­ly was, that only she tru­ly under­stood?

    Think if we don’t lis­ten and stop fight­ing over reli­gious dif­fer­ences, like Pros­pero in Shake­speare’s meta­phys­i­cal mas­ter­piece The Tem­pest, we will con­demn him for­ev­er to his island of sad­ness.

  • Dragoi says:

    If you lazy iconophiles could both­er your­selves to learn even the most basic music the­o­ry — Euro­pean, Indi­an, Ara­bic, it does­n’t mat­ter which — none of this pop­py­cock would be impres­sive at all.

  • Dave Galloway says:

    Charles, I believe you are spot on. I would add my belief that his influ­ences extend­ed beyond Africa and India music. ( I am sure you know that :<)
    Not meant to be crit­i­cal at all.

  • Judy says:

    Sym­me­try is the order of our uni­verse. In the Gen­e­sis, the world was formed, Not a fairy tale but true. The Bible is noth­ing but sci­ence. We don’t want to acknowl­edge this truth, but every­thing com­pli­ments one anoth­er. Thank you for shar­ing.

  • ME says:

    You obvi­ous­ly dont under­stand the dynam­ics of dis­so­nant jazz, which was very high­ly prac­ticed and played by Coltrane. This chart is not about har­mo­ny, at all. It is about for­mat and func­tion by which he strate­gized his com­po­si­tions.

  • D Wilmington says:

    Daniel — I stud­ied spo­rad­i­cal­ly with Wig­gins at UVA in the ear­ly 90’s. I’m won­der­ing if your com­ment here sig­nals that you did, too.

  • Sakina says:

    No one choos­es the time and/or place of death.

  • Taylor di Clemente says:

    These har­mon­ic geome­tries dis­solve when one removes tem­pera­ment from the equa­tion and use nat­u­ral­ly occur­ring inter­vals. Coltrane/Slonimsky geome­tries only func­tion in the 12-tone equal tem­pered sys­tem, that is, they exist with­in a cul­tur­al bub­ble. They are more of a lin­guis­tic gram­mar than a nat­ur­al physic.

  • EricJohnLarge says:

    Is Amer­i­can indige­nous singing and drum­ming “music”. Has it or can it be ana­lyzed as “music”?

  • Ken Cory says:

    It’s just two rings depict­ing the two whole-tone scales. It’s no sur­prise that a six-note whole tone scale will repeat five times around a cir­cle of 30 notes, lead­ing to a pen­tan­gle dia­gram. Claim­ing that a dia­gram like this has a con­nec­tion to Ein­stein’s the­o­ries is like claim­ing that a tic-tac-toe dia­gram shares a deep con­nec­tion with quarks.

  • Kat says:

    Yeah– I was hop­ing for the same thing. I’m nei­ther a musi­cian nor a math­e­mati­cian, so I had hoped some­one would break down this draw­ing and explain what it’s sup­posed to be show­ing. It’s a great draw­ing (I’m a visu­al artist) so it looks fan­tas­tic to me, but I have no idea what any of this means or how it relates to any­thing.

  • Respect says:

    Love respect Namaste

  • Graeme says:

    Watch this. I always felt this cap­tures the descrip­tion of Coltrane’s cre­ation best.

  • John says:

    It’s always amus­ing to read com­men­taries pur­port­ing to find Islam­ic inspi­ra­tions or ana­logues in West­ern music. In Islam, lis­ten­ing to idle singing or the play­ing of musi­cal instru­ments for mere plea­sure is “haram,” for­bid­den; Allah will pour molten lead in the ears of such per­sons on the day of judg­ment. Here is a ref­er­ence, from the Per­ma­nent Com­mit­tee of the King­dom of Sau­di Ara­bia; oth­ers can be found.

  • Gary McDaniel says:

    I see a spi­ral, not a cir­cle.

  • Gary Steven Corseri says:

    Fascinating–how the worlds of the Arts, Physics, Quan­tum Mechan­ics, and Spir­i­tu­al­i­ty can inter­sect.

    I also per­ceive in “the Coltrane cir­cle” what Span­ish and inter­na­tion­al artist Pilar Viviente ren­ders her own way in her col­or­ful series of “Rodetes.”

    “Only con­nect,” the great Eng­lish writer, E. M. Forster advised at the con­clu­sion of his mas­ter­piece nov­el.

    We are already con­nect­ed. We are already con­nect­ed. The best artists and sci­en­tist and spir­i­tu­al­ists endeav­or to bet­ter under­stand, refine and illu­mi­nate those connections–in their own way.

  • kw says:

    he did not found quan­tum mechan­ics — in fact he railed against it for most of his career. He did estab­lish the spe­cial case of rel­a­tiv­i­ty and gen­er­al rel­a­tiv­i­ty. Neils Bohr, Max Plank and man­ny oth­ers estab­lish quan­tum mechan­ics

  • Voytek Pavlik says:

    It all depends on the music, that was cre­at­ed, as we know the sound cre­ates vibra­tion and the vibra­tion can cre­ate shape. The Pen­ta­gram shape shows what type of music the musi­cian who drew this, is cre­at­ing. As being myself some­one who cre­ates music, and cre­at­ed var­i­ous types, styles and gen­ress­ince 2009, which you can lis­ten on Spo­ti­fy for exam­ple, I under­stood the light side and the dark side of the music.

    Yes, it con­nects to some sort of spir­i­tu­al­i­ty and the divines, but as Alex Jones recent­ly stat­ed well, on Joe Rogan pod­cast, the good angels-spir­its won’t inter­vene in your free will, but the bad ones will. So, mak­ing music is like chan­nel­ing, where most of the musi­cians prob­a­bly don’t know who or what they are con­nect­ing to.

    No need to base it towards Ein­stein or quan­tum what­ev­er the­o­ries. The stuff is there, it’s hap­pen­ing, and those who are woke enough, and make things like music and arts, can feel it and know it exists.


  • Kes Terton says:

    That is just cow poop. Look hard­er. Widen your field of inquiry. That’s as stu­pid and elit­ist as say­ing, “Paint­ing is dead.”

  • Andrea Brachfeld says:

    From what I see there are 5 num­bers on the out­side of the cir­cle all point­ing to C. These five points are joined by a 5 point­ed star. The research says that the note C vibrates to the root chakra and cor­re­sponds to the vibra­tion that the earth vibrates to. As one may go up the chakras, the notes cor­re­spond­ing to each chakra fol­low the C Ion­ian scale end­ing with the 7th chakra locat­ed on the top of the head. Each one of the dark­ened cir­cles out­line the cir­cle of fifths which are sur­round­ed by the upper and low­er neigh­bors of the dark­ened notes. The out­er cir­cle of the cir­cle out­lines the whole tone scale with the start­ing note as C. The inner cir­cle out­lines the whole tone scale start­ing on A or any one of the notes of that whole tone scale. The lines in the mid­dle of the draw­ing con­nect to the tri­tones for exam­ple the C con­nects to F#, A to Eb etc. These dom­i­nant chords are inter­change­able as the thirds and sev­enths are just reversed in posi­tion. The num­bers in the mid­dle of the draw­ing on the lines are num­bered from 1–7 start­ing on for exam­ple C and end­ing on the tri­tone F# mov­ing chro­mat­i­cal­ly. Then there are num­bers under those which move back­wards from C to F#- the tri­tone . There are oth­er num­bers drawn on the lines which don’t seem to be com­plet­ed and also seem to be crossed out. So all this being said, my take is that this is a draw­ing of rela­tion­ships and con­nec­tions. I’m still not sure how this is used when play­ing but that being said, I do think of the upper and low­er neigh­bors when I am play­ing a scale or chords to give my solo con­trast and musi­cal ten­sion. By the way, thank you so much for this post! I’ve been want­i­ng to real­ly study this for a while now and this gave me the oppor­tu­ni­ty to do so!

  • Brandon Mamata says:

    I see there’s no men­tion of George Rus­sel­l’s Lydi­an Chro­mat­ic Con­cept of Tonal Organ­i­sa­tion? Prob­a­bly good to acknowl­edge the impor­tance of this text in rela­tion to Coltrane’s devel­op­ments with har­mon­ic move­ment.

  • santana says:

    That is the first time I’ve learned as much from the com­ments as from the arti­cle. Con­grat­u­la­tions you all.

  • Nancy says:

    I just wish I had a deep and thor­ough under­stand­ing of math and physics. I only have the ques­tions.

  • Menziani says:

    Thrice you mis­pelt Coltrane’s name in your text. Is this delib­er­ate or are you talk­ing about some­one else ?

  • love it says:

    love the music man

  • Adam Rudolph says:

    Yusef was in the group AFTER trade. he was rec­om­mend­ed by and replaced James moody who had a hit record out and so left dizzy.

  • Adam Rudolph says:

    Just to add to this con­ver­sa­tion and to address those of you who wish this cir­cle to be “every­thing” . Coltrane, Yusef Lateef and Eric Dol­phy spend alot of time research­ing and prac­tic­ing togeth­er. they made many dia­grams sim­i­lar to this one. No one cir­cle or dia­gram was ever meant to “show it all” I have copies of sev­er­al oth­ers of these. This one has become more know because Yusef includ­ed it in his impor­tant book “Repos­i­to­ry of Musi­cal Scales and Pat­terns” and Stephon used it — with per­mis­sion in his book. It shows only SOME aspects of the inter­val­lic research these 3 were doing and the kind of work Yusef did up into his 90s. Noth­ing is craved in stone. The idea was and is to find YOUR OWN way.

  • Adam Rudolph says:

    Brandon…there are many to acknowledge…no one worked in a vac­u­um. Coltrane devel­oped his own ideas in his research …his peers„„Dolphy, Ornette, Lateef…were all look­ing into how to orga­nize and move through inter­val­lic material.…As Yusef told me…“when you get rid of one thing, you have to replace it with some­thing else: they had moved beyond work­ing with “chord changes” thus the inter­est in inter­vals. George Rus­sell was very impor­tant to every­one and we have to also men­tion Dizzy, Bar­ry Har­ris, Monk.….I call them the R & D musi­cians. they showed us all the PROCESS. (it is not about style)

  • Tony Ridler says:

    What if, space is curved, and, if we don’t get lost, we won’t find our­selves, danc­ing!

  • Nerdelbaum Frink says:

    @andrew hill You’re absolute­ly wrong. Ein­stein’s the­o­ries of rel­a­tiv­i­ty were clas­si­cal. but those are not Ein­stein’s only con­tri­bu­tions to physics. Ein­stein essen­tial­ly devel­oped the first way to evi­dence that light is a par­ti­cle through the pho­to­elec­tric effect, which is what he won the Nobel prize for. Ein­stein devel­oped our most accu­rate clas­si­cal the­o­ry of physic with respect to some top­ics, but also was very present in the ear­ly devel­op­ment of quan­tum mechan­ics. He cer­tain­ly had issues on a philo­soph­i­cal lev­el con­cern­ing the prob­a­bilis­tic nature of the the­o­ry, but he did not have a prob­lem with its cor­rect­ness of it for the evi­dence that was avail­able. He just believed that there was some mech­a­nism behind the scenes that drove it, and so that is what lead him to work with some col­leagues to come up with the EPR para­dox, but that para­dox turned out to be the nature of real­i­ty (essen­tial­ly they came up with the con­cept of entan­gle­ment).

    That said, equat­ing Ein­stein to Coltrane is a reach­ing anal­o­gy. Music, and par­tic­u­lar­ly what we see here in this pic­ture, is cer­tain­ly math­e­mat­ics, but it is an entire­ly dif­fer­ent type and appli­ca­tion com­pared to physics, as well as orders of mag­ni­tude dif­fer­ence in com­plex­i­ty. That’s not to dimin­ish the impact­ful nature of music, as the tran­scen­den­tal effect of music on a per­son was well appre­ci­at­ed by Ein­stein, but being able to describe galax­ies is some­thing else to that.

  • Brad lee says:

    Thats prob­a­bil­i­ty. The fact that there is no such thing as grav­i­ty. Only a the­o­ry. The­o­ry is not fact . Coltrane liked his flats . His den­si­ty kept him in check . Jazzzzzzzzzzz

  • Reign Forrest says:

    That music has a huge math­e­mat­i­cal con­tent is well-known to musi­col­o­gists. That physics (includ­ing the­o­ries of rel­a­tiv­i­ty) has a huge math­e­mat­i­cal con­tent is also well-known. But to bring up Ein­stein in this dis­cus­sion about Coltrane’s artic­u­la­tion of the cir­cle of music is, IMO, sil­ly.

  • Steve C says:

    1967: Death. Coltrane died of liv­er can­cer at the age of 40 on July 17, 1967 at Hunt­ing­ton Hos­pi­tal in Long Island. His funer­al was held four days lat­er at St. Peter’s Luther­an Church in New York City.

  • Chris Jensen says:

    Music and math have always been relat­ed, there is no doubt of that. I’m not say­ing that qua­drat­ic equa­tions will make you a bet­ter play­er, but they both have pat­terns that relate to each oth­er. How­ev­er, I will take this a step fur­ther. Musi­cians and data pro­cess­ing geeks have much in com­mon. I am both. I’m not talk­ing about using win­dows, but actu­al­ly writ­ing hard core code. Music and data pro­cess­ing are linked togeth­er. What is music but two basic ele­ments .….. pitch (high or low) and dura­tion (how long the pitch is held). Data pro­cess­ing in it’s most ele­men­tal form is an elec­tron­ic switch that is either turned on or off, 1 or 0. The com­bi­na­tions of either is vir­tu­al­ly end­less. Any play­er that can impro­vise in a giv­en form, whether baroque, clas­si­cal, roman­tic, or jazz should be able to write the wildest code imag­in­able, and vice ver­sa, because they all oper­ate on the same prin­ci­ples. When I went to school for music, an aston­ish­ing amount of grad­u­ates wound up writ­ing code.

  • Linda says:

    @Dean,thank you for your obser­va­tion. I was ready to look up, Quan­tum The­o­ry, Grav­i­ty, and Mechan­ics, to see if I missed some­thing! Lol! I also did­n’t see grav­i­ty men­tioned. Just Theory..I am no physi­cist or sci­en­tist, I thought they were are dif­fer­ent actions. Well per­haps I will share my efforts with this thread. Have a Quan­tum day!😝😜😊

  • jed says:

    that which is greater than thou… are you kid­ding … god is vague by con­cept…

  • Pilar Viviente says:

    Thank you!I much appre­ci­ate. And I total­ly agree with you.😘 🌹

  • Pilar Viviente says:

    Synesthesia,indeed. I know a bit about this. 😘

  • Jenn says:

    Genius who could open his heart and pour out truths that could con­nect with us
    Was a genius

    I love lis­ten­ing to him while I paint

  • Pieter Loose says:

    this is sim­ply the cir­cle of 5ths

    every gui­tar play­er should know this

  • Douglas R Ewart says:

    1) John Coltrane, (not Coltrain).

    2) Physics is cru­cial and won­der­ful, and I have tak­en to using my Ewart Son­ic Spin­ning Tops to acquaint and illus­trate cer­tain aspects of physics and math to stu­dents, teach­ers, oth­ers and me, as I endeav­or to get more peo­ple, espe­cial­ly the young peo­ple inter­est­ed in all the sci­ences. and par­tic­u­lar­ly physics, botany, and biol­o­gy.

    That being said, it is impor­tant to study all of these aspects and sys­tems of infor­ma­tion. How­ev­er, music is big­ger than and more com­plex than physics and math. Physics and math are ele­ments of music. Music is far more com­plex than physics and math as we are yet to fig­ure it out, and I am not just talk­ing the­o­ry or sci­ence as we know it/them. Music is spir­i­tu­al, emo­tion­al, art, sci­ence, craft, feel­ing, hear­ing, tast­ing, intu­ition, intel­lect, struc­ture and more. We are yet to fig­ure out all the music’s appli­ca­tions and so on. Know­ing musi­cal the­o­ry is impor­tant to those that are inquis­i­tive and are inter­est­ed in the log­ic, sci­ence, and devel­op­ing a musi­cal reser­voir of resources, and obtain­ing a han­dle on the mul­ti­tudi­nous nature of music. How­ev­er, know­ing all the the­o­ry in the world…math and physics won’t nec­es­sar­i­ly make you a good or even inter­est­ing music mak­er that is how com­plex and yet sim­ple music is!

    Our music has been World Music for a long time, espe­cial­ly when one con­sid­ers the inter­ac­tion that took place in the Car­ribean and Latin Amer­i­ca (the Amer­i­c­as) with the indige­nous peo­ples, Africans, inden­tured ser­vants from India, Chi­na, the Mid­dle East, and Euro­pean peo­ples and cul­tures in the West­ern Hemi­sphere.

    Baba Scott Joplin, Baba Jel­ly Roll Mor­ton, Baba Yusef Lateef, and oth­ers before and after them placed a new spot­light and mag­ni­fi­ca­tion lens on the notion and con­cept of World Music.

    Thanks to all the writ­ers, blog­gers and those involved in this vital dis­course.
    Peace and Respect!

  • Frankie DiDonato says:

    All paths.. it’s spir­i­tu­al not “reli­gious”… It’s grat­i­tude to the love supreme. The lin­er notes by train in the open sleeve are about love and a supreme that tran­scends any reli­gious clas­si­fi­ca­tion. It’s short sight­ed to see it must be clas­si­fied to one par­tic­u­lar faith. Quite frankly it’s child­ish. It’s far deep­er as I believe Trane would agree.

  • Rainer says:

    The Nobel Prize in Physics 1921 was award­ed to Albert Ein­stein “for his ser­vices to The­o­ret­i­cal Physics, and espe­cial­ly for his dis­cov­ery of the law of the pho­to­elec­tric effect.” I don’t think this has any­thing to do with Quan­tum The­o­ry. As far as I remem­ber, this was a big­gy lat­er in the inven­tion of TV?

  • Guiseppe says:

    FANTASTIC, but does it make your rear end move? I remem­ber some wise words: “A well-shak­en butt is worth more than all the genius in the cos­mos.”

  • DanT says:

    That was the first thing I noticed. Call­ing it “Einstein’s quan­tum the­o­ry” is an imme­di­ate red flag. It is com­mon to throw around cer­tain names (Ein­stein, Hawk­ing, Galileo, etc) to sup­port ideas that sound “rev­o­lu­tion­ary” but have lit­tle or noth­ing to do with (even an under­stand­ing of) these people’s work. Study the thinkers, don’t hijack them.

  • DanT says:

    To Brad Lee:
    Please don’t con­fuse (sci­en­tif­ic) The­o­ry with the con­ven­tion­al use of the word. That is play­ing word games as a short­cut to mak­ing a legit­i­mate point and only serves to per­pet­u­ate igno­rance and mis­un­der­stand­ing. The equiv­a­lent term for what you are stat­ing is “hypoth­e­sis”, and we do NOT refer to a “hypoth­e­sis of grav­i­ty”. The­o­ry, when refer­ring to some­thing like “The­o­ry of Grav­i­ty” does essen­tial­ly mean “estab­lished fact”. It’s the work­ing expla­na­tion, like the instruc­tions for oper­at­ing your phone could be called “the The­o­ry of (spe­cif­ic mod­el) Phone Oper­a­tion”.

  • raul suarez fernandez says:

    it is incred­i­ble how many igno­rants are com­ment­ing here just try­ing to look smart.

  • Allen says:

    Raul, that com­ment is in itself a ‘know-it-all’ state­ment and with noth­ing behind it it also cross­es igno­rance. The state­ment, not you.

  • Allen says:

    ‘worth more’ is the key term there…

  • Allen says:

    to Guiseppe.

  • Allen says:

    Frankie DiDo­na­to says:
    June 26, 2019 at 10:13 am

    All paths.. it’s spir­i­tu­al not “reli­gious”… It’s grat­i­tude to the love supreme. The lin­er notes by train in the open sleeve are about love and a supreme that tran­scends any reli­gious clas­si­fi­ca­tion. It’s short sight­ed to see it must be clas­si­fied to one par­tic­u­lar faith. Quite frankly it’s child­ish. It’s far deep­er as I believe Trane would agree.

    I’m not Trane but I agree!!!

  • Dennis says:

    The Coltrane Cir­cle dia­gram has an error, if con­sis­ten­cy was intend­ed. On the left-hand side the A in the inner cir­cle should be linked with the B flat in the out­er cir­cle, and the G in the inner cir­cle should not be linked with the G sharp in the out­er cir­cle.

    Assum­ing this cor­rec­tion has been made, the out­er cir­cle depicts 5 sequences of notes with equal inter­vals of a tone, each start­ing on C, ascend­ing clock­wise and descend­ing anti-clock­wise. The inner cir­cle also depicts 5 sim­i­lar sequences but made up of the alter­nate notes. These sequences of notes, played on an instru­ment or sung, start­ing on any note, are known as “Aux­il­iary Aug­ment­ed” or “Whole Tone” scales.
    The inner and out­er cir­cles are linked with what I shall refer to as a “bridge”, mov­ing both clock­wise and anti-clock­wise, at every sec­ond note of the above described “whole tone” sequences.

    If a musi­cian begins play­ing a sequence of notes, for exam­ple, at the No.1 C note and plays a clock­wise sequence of notes cross­ing from out­er to inner cir­cle and back from inner to out­er cir­cle at each bridge, (a reg­u­lar sequence of repeat­ing pat­terns of inter­vals of semi-tone, tone, tone, semi-tone, tone, tone, etc.) i.e. a sequence of 36 notes con­sist­ing of C, C sharp, E flat, F, F sharp, A flat, B flat, B, C sharp, E flat, E, F sharp, A flat, A, B, D flat, D, E, G flat, G, A, B, C, D, E, F, G, G sharp, B flat, C, D, E flat, F, G, A flat, B flat, C, the sequence (or extend­ed scale) includes every note of the chro­mat­ic scale, each played three times, takes six octaves to resolve before the pat­tern repeats, and, due to the arrange­ment of semi-tones and tones, sounds some­what melod­ic rather than chro­mat­ic.
    The out­come is the same no mat­ter which note is used as a start­ing point, whether ascend­ing or descend­ing, and there is always choice whether or not to begin a sequence with a tone or a semi-tone, pro­vid­ed the pat­tern is main­tained.

    Ful­ly chro­mat­ic music is to all intents and pur­pos­es “key-less”, i.e. “free”.

    Musi­cal keys are defined by dom­i­nant sev­enth chords. (Each key has only one dom­i­nant sev­enth chord.) If a sequence of chords (as in jazz blues) are all dom­i­nant sev­enth or altered dom­i­nant sev­enth chords, the chordal foun­da­tion of the music is in as many keys as there are chords, in oth­er words it approach­es being key-less the more dif­fer­ent chords there are and it becomes key-less when all twelve dom­i­nant sev­enth based chords are employed.

    The note sequences depict­ed in the cor­rect­ed Coltrane Cir­cle rep­re­sent, in a sense, total free­dom in music with­out los­ing melod­ic qual­i­ty.


  • Dennis says:

    Nice obser­va­tions.

    Please see my obser­va­tions (July 5th 2019).

    Kind regards,

  • Anthony says:

    I love Trane’s music but hate math.

  • Jay Irwin says:

    Is it pos­si­ble he was express­ing a musi­cal rep­re­sen­ta­tion of a star? I haven’t heard any­body talk about the star. Love this thread!

  • Joe says:

    It’s a pen­ta­gram. Which is the heart of mag­ic. When you get bored of play­ing music you start to use your learn­ing-capa­bil­i­ties to study oth­er sub­jects. I heard that Char­lie Park­er was also very intel­lec­tu­al and read tons of books.

    This dia­gram reminds me of Vor­tex math, and Nico­la Tes­la’s “Map to mul­ti­pli­ca­tion.”

  • Richmond Platz says:

    I noticed the whole tone sequence being sus­pend­ed by the half tones (Half Steps.), much like what fourths reg­u­lar­ly do!

  • Richmond Platz says:

    Quan­tum The­o­ry does not, as yet, hand­shake with The­o­ry of Rel­a­tiv­i­ty! See author Mark Seifer, a the­o­ret­i­cal physi­cist.

  • Richmond Platz says:

    I believe there is no room for hatred in a world of truth. There is no life with­out death, so to speak!

  • Richmond Platz says:

    Per­haps I could say: You may be open­ing the door for hatred to enter the world of actu­al proof. I don’ believe
    Coltrane/Einstein har­bered any hatred in their basic mind­set.

  • Alsons says:

    At the end Ein­stein’s EGO waste soooo much time for unnec­es­sary things! Instead work­ing togeth­er with Bohr.…

  • Brad Parker says:

    INNER VIBES :: I’ve been study­ing this wheel, this cir­cle for maybe 50 years now… I get the con­cept but play­ing the con­cept is anoth­er world… deep bow to John Coltrane! …and now, about that dou­ble dimin­ished scale…

  • Molefi Manoto says:

    I like your style.

  • SugarCookie says:

    Thank you for your infor­ma­tion and for NOT being one of those know-it-all peo­ple. It’s beau­ti­ful work.

  • Kellie says:

    This is the sym­bol for the observed rhythm of Venus from earth. Every eight years venus ret­ro­grades in one of five con­stel­la­tions, cre­at­ing the shape of a pen­ta­gram in the heav­ens. In ancient and mod­ern astrol­o­gy Venus is asso­ci­at­ed with music. Vet­tius Valens writes of Venus, “She makes…refined arts, pleas­ant sounds, music mak­ing, sweet singing…both inven­tors and also mas­ters of these (pro­fes­sions).”

  • Katz says:

    You mean cir­cle yes?

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