John Coltranes Circle of Fifths:
We know about Coltrane’s Circle of Fifths because of an interaction with Yusef Lateef in 1967. Coltrane gave Lateef the drawing, and then Lateef included it in his book Repository of Scales and Melodic Patterns. The Repository of Scales and Melodic Patterns is a 280-page book of scales, patterns, and licks that serve as a list of jazz patterns. For Lateef, Coltrane’s Circle of Fifths symbolizes his musical journey. He adds that Coltrane “embraced the concerns of a rich tradition of autophysiopsychic music.” For Lateef, the autophysiopsychic was “music from one’s physical, mental and spiritual self.”
John Coltranes circle was an attempt to draw out a relationship between the ratios and harmonies of notes and scales. The outer ring also reveals an additional shape between the tones of the Hexatonic scale. This shape is a Hexagon. Another of Coltrane’s passions was the occult, so finding the pentagon and hexagon together has always been a point of interest for analyzing his fifth. He created his circle of fifths around the same time that he was deeply studying both Indian music and Einstein. Much of Indian music is intensely complex and uses scales with intervals smaller than semitones, called microtones. Instead of dividing an octave into 12 tones, these scales use something described as “notes between notes”. To illustrate, these scales have various notes between C and C#.
Coltrane was looking deeper to inspire his jazz composition. And while he was going micro in many ways, his interests illustrate that he was also going macro. There is a story in the book ‘Coltrane: The Story of a Sound’, where Coltrane speaks to French horn player David Amram. In the anecdote, Coltrane delivers “an incredible discourse about the symmetry of the solar system, talking about black holes in space, constellations, the whole structure of the solar system, and how Einstein was able to reduce all of that complexity into something very simple. Amram explains that Coltrane was trying to do the same in his music.
In “The Jazz of Physics”, author Stephon Alexander recalls a phone conversation he had with Yusef Lateef in his late 80s. He told the veteran musician that he felt the diagram was related to quantum gravity. Quantum gravity was the attempt to unify quantum mechanics with Einsteins’ theory of general relativity. As a physicist and saxophonist himself, Alexander is uniquely positioned to see the relationship between music & mathematics. For him it all started with Coltranes Circle Of Fifths – as he sees it, Coltrane drew from the same geometric principle that motivated Einstein’s quantum theory. While Coltrane and Lateef were approaching questions about underlying patterns and order in music from a spiritual direction, Einstein’s work can be seen as something similar but using a different method.
Why Is John Coltrane's Circle Of Fifths Different?
The Standard Circle Of Fifths is something that will be familiar to most musicians. It’s a geometric representation of the notes and pitch intervals we hear in music. More specifically, it’s the relation between 12 semitones. In the Western Scale, there are twelve intervals between each octave: A, A#, B, C, C#, D, D#, E, F, F#, G, and G#.”
In classical Western music, a fifth is an interval from the 1st to the last notes in a diatonic scale. For example, the interval between C to G is called a perfect fifth. This is because the note G is seven semitones above C. Coltrane's Circle of Fifths is based around something similar but with some variations. The most notable aspect is that Coltrane uses a whole tone or hexatonic scale. The outer ring of the drawing contains the hexatonic scale of C, while the inner circle bears the hexatonic scale of B. While there is no definitive interpretation of the Coltrane Circle of Fifths, many have tried to decode it, and the closest anyone has ever come to explaining it is by drawing upon mathematics and geometry.