2025-05-30

atonal

non-tonal pitch collections: chromatic continua, micro-grids, fixed serial rows, and spectral-derived sets-none rely on scalar centricity or cyclic resolution.

introduction

the atonal domain lives in the pitch layer and emits unordered or order-agnostic pitch indices. where tonal supplies bounded, internally repetitive sets, atonal offers unbounded or non-cyclic spaces whose structure does not presume a tonic or recurrence. all forms are deterministic, two-parameter, and culturally neutral; they simply map an integer (or fractional) index n to a pitch degree inside each form's particular, non-tonal logic.

overview

each form realises a different non-tonal strategy:

0. chromatic_stack

behavior:* linear ascent through semitone steps, with optional stride > 1 analogy:* playing every (or every second/third) key on a piano forever parameters:*

  • a – stride size: 1 → 3 semitones
  • b – global starting offset: 0 → 11 semitones

1. micro_grid

behavior: subdivides the semitone into d* equal micro-steps and walks that lattice analogy:* a fixed-resolution microtonal keyboard parameters:*

  • a – divisions per semitone: 2 → 16
  • b – micro-offset within the first semitone: 0 → (d − 1) steps

2. serial_row

behavior: maps index n mod 12 to a twelve-tone row; higher n* repeat with constant order analogy:* schoenbergian tone row perpetually cycling parameters:*

  • a – row seed (hash selects one of 4096 pre-computed prime rows)
  • b – row transform: 0–0.25 prime, 0.25–0.5 retrograde, 0.5–0.75 inversion, 0.75–1.0 retrograde-inversion

3. spectral_fan

behavior:* flattens selected harmonics of a fundamental into ascending order (no octave wrap) analogy:* picking non-octave partials from a harmonic spectrum parameters:*

  • a – base harmonic number: 1 → 16
  • b – density exponent: sparse (few partials) → dense (many)

parameter behaviour summary

chromatic_stack*:

  • a → integer stride (1–3)
  • b → start semitone (0–11) micro_grid*:
  • a → integer micro-divisions (2–16)
  • b → fractional lattice offset (0…d − 1) serial_row*:
  • a → deterministic row selection
  • b → one of four row transformations spectral_fan*:
  • a → first harmonic included
  • b → power-law density shaping (controls how many partials populate one octave)

why these were chosen

orthogonal coverage* of non-tonal practice:

  • equal-tempered chromaticity (chromatic_stack)
  • finer equal partitions (micro_grid)
  • fixed permutation sets (serial_row)
  • inharmonic harmonic-series extractions (spectral_fan) irreducibility:* each embodies a distinct structural idea-stride, micro-lattice, permutation, spectral sieve-none can recreate the others without extra parameters or state. two-parameter purity:* every salient perceptual dimension is navigable with exactly a and b. cultural neutrality:* no reference to keys, modes, or functional harmony. determinism:* all mappings are pre-computable and context-free.

what is not included

cyclic or mode-based pitch sets: covered by tonal*. evolving or stochastic rows/sets: belong in generative*. frequency mapping or temperament: handled downstream by tuning*. randomised jitter/glissandi:* considered a temporal modulation, not a pitch-collection logic.

conclusion

the atonal domain equips the system with a compact yet comprehensive arsenal of non-tonal pitch structures-chromatic, microtonal, serial, and spectral-each fully deterministic, structurally unique, and immediately usable across the broader architecture of additive, form-based sound creation.