cyclic, bounded pitch structures-finite sets with internal order, repetition, or symmetry, regardless of musical tradition.
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.
each form produces a cyclic or bounded pitch map, accessed by an index:
ring_scalebehavior: 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)symmetry_setbehavior:* 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)grid_arpeggiobehavior: 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)loop_melodybehavior:* 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)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 modulationgeneralization 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.
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.
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.