Techniques of Polytempic Polymicrotonal Composition

Cloud Ear Training Up to four independent equal-division lattices, each with its own division count, waveform, and up to six toggleable static pitches. Listen for the drift between systems — no shared overtone reference, just arbitrary equal grids sounding together. Master volume 50% + Add system Auto-advance: dyad → tetrad+ Stop all Status: loaded, waiting for taps… Each system's divisions (N-TET), waveform, and note count are independently adjustable. All systems share one base frequency (261.63 Hz) as their step-0 anchor. Mute silences a system without losing its note states; Solo silences every other system while it's active (multiple systems can be soloed at once). A compressor and master volume control keep the combined signal from crackling as you stack more voices.

No Master Clock, No Master Fundamental: Bonding Tempo to Tuning in Four Parts There's a particular kind of independence that most music, even most experimental music, doesn't attempt. It's easy to vary tempo across layers. It's easy to vary tuning across layers. It's much harder — and much rarer — to let both vary independently, in four simultaneous parts, with nothing underneath holding them together. That's the core of what I call polytempic polymicrotonality: four voices, each running its own equal-division tuning system, each locked to its own independent tempo, with no master fundamental unifying the pitch content and no master clock unifying the rhythm. Each voice is internally coherent — tuning and tempo are bonded together within that voice — but no voice answers to any other. Why this combination is rare Plenty of microtonal music exists. Plenty of polytempic music exists too — voices moving at unrelated speeds, often notated as separate tempo strata. B...

Most Alien Intervals: EDT 13 through 53 For each equal division of the octave (EDT), the three intervals whose cent values lie furthest from any interval in 12-TET are identified. Distance (Δ) is measured as the minimum absolute difference in cents from the nearest 12-TET pitch class (0, 100, 200 … 1200¢). These maximally alien intervals represent each tuning system's irreducible sonic identity — the pitches that cannot be heard as mistuned versions of familiar intervals. Criterion: Peter Thoegersen — intervals maximally distant from 12-TET equivalents as primary cells for polymicrotonal pitch grammar. EDT Step (¢) Rank 1 — Degree (¢) | Δ from 12-TET Rank 2 — Degree (¢) | Δ from 12-TET Rank 3 — Degree (¢) | Δ from 12-TET 13-TET 92.308 Deg 6: 553.85¢  |  Δ46.15¢ Deg 7: 646.15¢  |  Δ46.15¢ Deg 5: 461.54¢  |  Δ38.46¢ 14-TET 85.714 Deg 3: 257.14¢  |  Δ42.86¢ Deg 4: 342.86¢  |  Δ42.86¢ Deg 10: 857.14¢  |  Δ42.86¢ 15-TET 80 Deg 2: 16...