# tonal
cyclic, bounded pitch structures-finite sets with internal order, repetition, or symmetry, regardless of musical tradition.

## introduction
the tonal domain belongs to the pitch layer and generates static pitch sets: finite, repeatable pitch structures used as sources for melodic, harmonic, or pattern-based material.
unlike `atonal` (which emphasizes chromatic grids or unordered sets) or `generative` (which evolves over time), `tonal` defines closed, internally constrained pitch behaviors.
these forms are abstract, deterministic, and culturally neutral-capable of expressing traditional modes or entirely novel configurations with equal ease.

## overview
each form produces a cyclic or bounded pitch map, accessed by an index:

### 0. `ring_scale`
 behavior: circular scale of n degrees repeating every m* semitones
 analogy:* generalized diatonic or synthetic mode
 parameters:*
  * `a`: number of degrees per cycle (3 to 12)
  * `b`: total span in semitones (6 to 24)

### 1. `symmetry_set`
 behavior:* builds sets with reflective or rotational symmetry around a central pitch
 analogy:* scale as a geometric object (e.g. palindromic, radial)
 parameters:*
  * `a`: symmetry type (mirror, radial, rotational)
  * `b`: span or folding depth (center outwards)

### 2. `grid_arpeggio`
 behavior: traverses an n*-dimensional pitch grid along a structured path
 analogy:* arpeggiating chords across pitch planes (e.g. stack + rotate)
 parameters:*
  * `a`: grid axis ratio (e.g. 3:2, 4:3)
  * `b`: traversal path type (linear, zigzag, spiral)

### 3. `loop_melody`
 behavior:* cycles through a fixed, user-defined pitch sequence with controllable loop offset
 analogy:* a sequencer rotating through a melodic cell
 parameters:*
  * `a`: loop phase offset (0 to sequence length)
  * `b`: pitch bend or variation depth (±3 semitones)

## parameter behavior summary
 *ring\_scale**
  * `a`: number of scale degrees (step count)
  * `b`: total interval span (defines coarseness)
 *symmetry\_set**
  * `a`: symmetry structure (mirror vs. radial fold)
  * `b`: how deep or wide the symmetry reaches
 *grid\_arpeggio**
  * `a`: grid shape (intervallic ratio between axes)
  * `b`: traversal path shape over the grid
 *loop\_melody**
  * `a`: sequence index offset (wraps)
  * `b`: per-step transposition or contour modulation

## why these were chosen
 generalization over tradition: instead of encoding specific modes or chords, these forms define general structural constraints* (cycle, symmetry, grid, loop) that include traditional scales as special cases.
 structural integrity:* each form expresses a unique way to constrain or repeat pitch space, irreducible to others.
 two-parameter sufficiency:* all behavior is navigable with just `a` and `b`, preserving the system's parametric purity.
 cultural neutrality:* avoids style-imposed assumptions-usable for both familiar and entirely synthetic pitch designs.

## what is not included
 chromatic/microtonal collections:* handled in `atonal`.
 evolving or probabilistic materials:* belong to `generative`.
 tuning/frequency assignment:* deferred to `tuning`.
 user-defined note names or keys:* not part of pitch logic-these are display-level concerns.

## conclusion
the tonal domain defines compact, cyclic pitch sets through structural primitives-cycles, symmetries, grids, and sequences.
its forms serve as deterministic sources for both familiar tonal contexts and non-traditional pitch materials, supporting the project's goal of generating all structured sound, not mimicking any particular musical idiom.