THE DIPTYCH — periods 24√2 s and 24φ s (never in the same phase twice)
Each family is rooted on a common 55 Hz ground — the octahedral at √2 above it (left, reedy), the icosahedral at φ (right, hollow). Each solid sounds its largest face as a harmonic of that root, unreduced, so the truncation chain is heard as changing register; the quasiregular moment is filtered nearly to a pure tone; the snub wavers — the audible dau. Notes attack sharply and release into silence, so the two pulse streams can be heard drifting apart. Beneath them a steady pair of tones at 622.25 and 622.94 Hz beats once every 1.45 seconds: 8×√2 against 7×φ, the closest small ratio to the two families’ incommensurable relation — the beat rate is the size of the discrepancy. Press sound to begin.