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farey clock

every fraction p∕q sits at exactly (p∕q × 360°) around the circle — radian space made visible. the farey sequence of order n contains every reduced fraction between 0 and 1 with denominator ≤ n. adjacent fractions have a beautiful property: if p∕q and r∕s are neighbors, then |ps − rq| = 1. hover a dot to light up its two neighbors and see that determinant worked out. click to hear the position as a pitch.

hover or click a fraction

order n (denominators ≤ n) F₅ — 0 fractions
root pitch