Coltrane's Tone Circle

Exploring the circle of fifths, its jazz applications, and Coltrane's geometric approach to harmonyJohn Coltrane once sketched a diagram for his friend and mentor Yusef Lateef: the chromatic scale arranged in circles, lines and circles identifying relationships. Lateef later referenced it in his Repository of Scales and Melodic Patterns (see the original). As far as I know, Coltrane never explained the diagram in writing, and there is no consensus on exactly what it was meant to show.At its core, the drawing is the circle of fifths, familiar to most musicians. Coltrane's version fills in the circle with chromatic scales, separated into two circles of whole steps, that join the fifths. Lines then trace different harmonic relationships between the notes, uncovering shapes that reveal the chord structures behind "Giant Steps", arguably Coltrane's most famous harmonic experiment.In this post, we'll rebuild the diagram as an interactive widget and attempt to decode its harmonic secrets.§ Reading the CircleThe large notes around the outside form the circle of fourths: moving clockwise from C, each note is a perfect fourth above the last (C, F, B♭, E♭, and so on). Between each pair sit four smaller notes that climb chromatically, alternating between an outer and inner ring. Following them clockwise from C, you'll pass C♯, D, E♭, and E before arriving at F. Twelve fourths add up to sixty semitones, or five octaves, so every note appears on the ring five times.The circular band inside the chromatic scale contains scale degrees for the fourths, measured from the note at the top. The controls below allow for changing key with the arrow buttons: the circle rotates to bring the new key to the top, while the degrees stay in place. The buttons below highlight the shape of a relationship within the circle. We'll explore those shapes later in the post.Throughout the post, descriptions of the circle assume C as the root, the starting point when the page loads.§ A Note on NotationInstead of Roman numerals (I, ii, V), this post uses the Nashville number system to express diatonic relationships.

A superscript minus marks a minor chord, so 2⁻ in C is D minor. Labels like ♭9 and ♯11 are extensions rather than chords.§ The Circle of FifthsIf you start on any note and keep stacking perfect fifths (C, G, D, A, E, and so on), after twelve steps you will land back on C, having visited every note exactly once. The sequence forms a perfect circle. On this tone circle, the sequence of fifths runs counter-clockwise. Read it the other way and each step is a perfect fourth instead (C, F, B♭, E♭, ...), because a fifth up and a fourth down arrive at the same note. The circle of fourths and fifths is the same circle.The circle allows us to quickly see how closely two keys are related. Neighboring keys share six of their seven notes: C major and G major differ only in G's F♯, and C major and F major differ only in F's B♭. Each step away swaps one more note, until you reach the opposite side of the circle. C major and F♯ major, a tritone apart, have just two notes in common, which makes them as distant as two keys can be.Jazz harmony often works by stacking fourths (quartal harmony), as opposed to the more traditional approach of stacking thirds. McCoy Tyner's piano voicings in Coltrane's quartet are a famous example, along with the "So What" chord from Miles Davis's Kind of Blue. That openness and ambiguity is an essential component of the modern, 50's and 60's, jazz sound.Stacking fourths is also why the circle has twelve positions. A fourth is five semitones, which shares no factor with the twelve in an octave, so a chain of fourths visits every note before returning to where it started. Intervals that do divide the octave evenly close the loop sooner: stack minor thirds and you're back after four notes, or major thirds and you're back after three. Those shortcuts are the shapes inside the circle.§ Symmetric ShapesMany chords are asymmetric. A major triad stacks a major third and then a minor third, and that asymmetry is how your ear determines the root of the chord. The shapes on the tone circle establish an opposing idea: divide all the notes of the octave into equidistant parts to produce different harmonic symmetries.There are only a few unique ways to do this. The circle draws the first three, with the fourth as an imaginary line across the circle to the tritone (substitution):IntervalSemitonesNotesShapeStructureDistinctMajor second26HexagonWhole-tone scale2Minor third34SquareDiminished 7th chord3Major third43TriangleAugmented triad4Tritone62LineTritone pair6Because every note is equidistant from the others, each has an equally strong claim to the root.