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John Coltrane playing saxophone.

John Coltrane’s Drawing of the Mathematical Soul of Music


The saxophonist and composer explains, in a geometric drawing, that intimate connection between music and mathematics.

In the last verse of his “Other Poem of the Gifts,” Jorge Luis Borges thanked the “divine labyrinth of effects and causes” for “music, the mysterious form of time.” To this idea, we might add that music also exists as a sublimated expression of mathematics and geometry. This, the saxophonist and composer John Coltrane once affirmed with his own drawing.

The visual experiment is believed to have been created by Coltrane during a period when he undertook an in-depth study of Indian music along with a study of some of the theories of Albert Einstein. The circle, which may be said to resemble a clock, incorporates some of Coltrane’s theoretical innovations into a well-known musical scheme. The drawing was presented in 1967 to fellow saxophonist and professor, Yusef Lateef, Coltrane’s colleague and tutor. Lateef always perceived a kind of spiritual path in Coltrane’s music.

Sketch of the Coltrane Circle

Known as “The Coltrane Circle” or “Coltrane’s Circle of Tones,” the diagram is based on the circle of fifths which, in musical theory, is a geometric representation of the relationships between the 12 semitones of the chromatic scale, their notations (flat or sharp), and their relative shades. The outer ring portrays the hexatonic or whole-tone scale of the note Do, and the inner ring portrays the hexatonic scale of Si. The series of terms and structures is easily understood by those who’ve studied musical theory. For those of us who haven’t, the graphic is a beautiful enigma, visually and intuitively explaining the relationship between music and mathematics.

Despite the depth of his study, Coltrane spoke very little on musical theory. His knowledge in the field is reflected rather more in his legendary compositions. For this very reason, Coltrane’s circle is a rare, valuable and surprisingly beautiful work. A five-pointed star drawn in union with all the Do notes of the scale.

Perhaps every musical composer is, in one way or another, also a mathematician. Coltrane’s circle, a symmetrical code or a mandala adorned with numbers and letters, expresses precisely what is, at once, both paradoxical and obvious.

*Images: 1) remix from the album cover Settin’ The Peace / Creative Commons; 2) Creative Commons

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