I. THE DIPTYCH — periods 24√2 s and 24φ s (never in the same phase twice)
Each family sounds at its own constant above a common drone:
the octahedral consort at the ratio √2 (the equal-tempered tritone),
the icosahedral at φ (the “golden interval”, ~833 cents, the most
irrational of ratios). Each solid’s turn re-pitches its consort by the
harmonic of its largest face; the quasiregular moments sound purest; the snub
voices waver — the audible dau. Soft plucks mark the solid-changes: two
pulse streams whose alignment drifts and never repeats.
II. THE 600-CELL — five 24-cells in one Clifford double rotation (3:5 turns)
Five voices in just pentatonic tuning, one per coloured
24-cell:
each voice’s loudness and stereo position follow its cell’s projected
size and drift — register passing perpetually among equals, no voice
leading. The 3:5 turn ratio (a Fibonacci convergent of φ) is the loop’s
audible comma. Computed from the same coordinates as the picture: the sound
cannot disagree with the motion.