variation

the variation domain introduces controlled, deterministic stateless modifications to motifs, sequences, or parameter sets. as part of the interplay layer, it applies single-pass transformations that alter content without retaining history - including rule-based changes, fixed-seed randomness, and probabilistic thinning. all behaviors are fully resolved before synthesis and require no internal accumulation or reset logic.

each form maps parameters a and b ∈ [0,1] to perceptually meaningful controls. forms are irreducible, non-overlapping, and temporally flat:

• rule-based

  • behavior: applies a fixed transformation rule to all elements (e.g. rotation, inversion, transposition).
  • analogy: genetic mutation with a predetermined formula
  • a: selects transformation type
  • b: controls transformation intensity

• jitter

  • behavior: applies deterministic pseudo-random offsets to timing, dynamics, or other per-event values.
  • analogy: humanized variation with fixed personality
  • a: maximum perturbation magnitude
  • b: density of affected events

• filter

  • behavior: probabilistically retains or removes events using fixed-threshold logic and biasing.
  • analogy: sieve with adjustable holes
  • a: inclusion probability
  • b: clustering bias (uniform to grouped)

• rule-based

  • a: selects rule (e.g. rotation, inversion)
  • b: controls rule intensity or depth

• jitter

  • a: max deviation size
  • b: fraction of events affected

• filter

  • a: base probability of retention
  • b: degree of temporal grouping

• purity of operation: each form performs a complete, stateless transformation in one pass.
• orthogonality: no overlap between methods-transformative, pseudo-random, and reductive variation are each uniquely represented.
• reproducibility: even stochastic-seeming results are fully deterministic via fixed seeding.
• perceptual clarity: parameters control directly relevant musical attributes.

• accumulating or evolving changes over time: see the mutation domain for stateful transformations.
• reactive or conditional variations: dynamic, event-driven changes are handled in the interaction domain.
• generative algorithms (e.g. markov, unfolding grammars): these are addressed in generative pitch or pattern.
• timbre, envelope, or spatial changes: managed separately under their respective layers.
• true randomness: all pseudo-random elements are statically seeded and repeatable.

the variation domain offers a compact, deterministic toolkit for stateless transformation. its three forms-rule-based, jitter, and filter-deliver musical diversity with complete reproducibility and no internal memory. for all cases where material must change without evolving or accumulating, this domain defines the essential palette.