# 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.