Circle of Fifths · Geometry · Sound

Polygon Harmonics

Rotate a regular polygon through the circle of fifths. Every time one of its vertices crosses a note, that note sounds. Change the number of sides and hear geometry reorganize the twelve-note field.

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Pentagon · chromatic scale Drag the wheel by hand, or start a continuous rotation.
A rotating regular polygon on the circle of fifths Twelve note targets are arranged around a circle in circle-of-fifths order. Polygon vertices trigger notes as they cross those targets. 5 SIDES

The hidden rule

The chord size is encoded in the common factors.

A twelve-note circle and a regular polygon repeatedly line up according to the numbers they share. The greatest common divisor of the side count and twelve is the number of notes that arrive at the same instant. The least common multiple is the number of distinct strike moments in one complete turn.

3 and 9 sides: three notes together → augmented triads.
4 and 8 sides: four notes together → diminished sevenths.
6 sides: six notes together → alternating whole-tone collections.
5, 7, and 11 sides: one note at a time → ordered note streams.
10 sides: two notes together → tritone-separated chromatic pairs.
12 sides: twelve notes together → the full chromatic cluster.
For the pentagon

Five and twelve share no factor greater than one, so only one vertex reaches a note at each strike. Their least common multiple is sixty, producing sixty evenly spaced single-note events per wheel turn.

Pitch classes are voiced inside one octave so the order is easy to hear. The circle itself remains in conventional fifths order: C, G, D, A, E, B, F♯, D♭, A♭, E♭, B♭, F.