repetition

the repetition domain governs how a core motif or sequence is reproduced over time without altering its intrinsic content. as part of the interplay layer, it enables structural cohesion and recognizability by mapping a motif onto itself through temporal copies, echoes, inversions, and hierarchical nests. all behaviors are pre-resolved and purely additive-no runtime modifications or reactive feedback.

each form uses parameters a and b in [0,1], remapped to perceptually relevant variables. forms are irreducible and non-overlapping:

• copy

  • behavior: repeats the motif identically at regular intervals.
  • analogy: photocopy
  • a: number of repeats (1–8)
  • b: interval between repeats (as a proportion of motif length)

• echo

  • behavior: generates successive echoes with diminishing amplitude.
  • analogy: sound bouncing in a canyon
  • a: feedback amount (controls decay rate, 0–0.9)
  • b: delay between echoes (as a proportion of motif length)

• mirror

  • behavior: interleaves the original motif with a time-reversed version.
  • analogy: reflected image
  • a: mix of original vs mirrored (0 = only original, 1 = only mirrored)
  • b: offset before mirrored motif begins

• nested

  • behavior: recursively repeats the motif within scaled time layers.

  • analogy: russian nesting dolls

  • a: number of nesting levels (1–4)

  • b: duration scaling per level (0.5–1.0)

• copy

  • a: maps to repeat count (via 1 + floor(7·a))
  • b: controls spacing ratio between each repetition

• echo

  • a: feedback gain (0 = full decay, 0.9 = near-infinite)
  • b: delay time relative to motif length

• mirror

  • a: balance between original and mirrored version
  • b: time offset of mirrored entry

• nested

  • a: number of levels of recursion

  • b: duration shrinkage per nesting level

• completeness: captures the core types of repetition - literal, decaying, reversed, and nested.
• irreducibility: each form represents a unique behavioral subspace not derivable from combinations of others.
• perceptual clarity: parameters directly reflect musically interpretable quantities.
• structural purity: all repetitions are additive and statically resolved; no feedback or conditional behavior.

• transformational repetitions (e.g. transposition, rhythmic stretching): handled in the variation domain.
• stochastic or reactive repeats: non-deterministic variants belong to field or variation.
• dynamic or timbral evolution across repeats: addressed in dynamics, decorators, or envelopes.

the repetition domain defines how motifs reappear without transformation. its four forms-copy, echo, mirror, and nested-provide a compact, orthogonal set of strategies for creating recognizable structure through recurrence. fully deterministic and irreducibly distinct, they anchor the interplay layer with time-based cohesion.