John Coltrane’s tone circle, sketched for his friend and mentor Yusef Lateef, arranges the chromatic scale in two interlocking circles that sit atop the traditional circle of fifths. The outer ring lists the notes of the circle of fourths (moving clockwise: C, F, B♭, E♭ …) while between each pair lie four chromatic notes that alternate between an inner and outer layer. As a result each pitch appears five times around the diagram, providing a visual reference for both harmonic relationships and melodic steps.
The diagram highlights symmetric harmonic shapes: stacking minor thirds yields a square that corresponds to a diminished‑seventh chord; stacking major thirds produces a triangle for an augmented triad; and stepping by whole steps creates a hexagon for the whole‑tone scale. Because the vertices of these shapes are equally spaced, any note can function as a root, giving the chords an ambiguous, unsettled quality. In particular, the augmented‑triad triangle connects the keys B, G and E♭, which are the three tonal centers of Coltrane’s ‘Giant Steps’, illustrating how the piece moves by major‑third intervals.
Beyond static shapes, the interactive widget described in the post shows how common jazz progressions map onto the circle. The basic 2⁻‑5‑1 progression (Dm7‑G7‑Cmaj7) appears as three neighboring points clockwise around the circle, reflecting the perfect‑fifth root motion. A tritone substitution replaces G7 with D♭7, visualized as a straight line across the circle that swaps the chord’s guiding tones while preserving the same resolution. Finally, the widget traces the full ‘Coltrane changes’ of ‘Giant Steps’, showing how the pattern cycles through the augmented‑triad roots with abbreviated 5‑1 movements and later expands to full 2⁻‑5‑1 approaches, offering a geometric explanation for the tune’s relentless forward motion.