density

the density domain expresses event potential: it lays out empty positions over time where events may occur, without deciding what or who will fill them. this separation enables density to act as a modular infrastructure for patterning, phrasing, and textural variation. all forms are fully deterministic and parameterized by a, b ∈ [0, 1]. outputs are slot times (not events) and may be consumed by pattern, activation, role, or other downstream domains.

• even spacing

  • description: places n equally spaced slots over a segment
  • analogy: pulse train, mechanical clock
  • a: number of divisions (1 = 1 slot, 1.0 = max resolution)
  • b: unused

• probabilistic emphasis

  • description: biases slots toward center using static gaussian curve
  • analogy: crescendo or phrasing bulge
  • a: curve spread (σ: narrow → wide)
  • b: center offset (0 = early, 1 = late)

• euclidean spacing

  • description: distributes k pulses across n steps with maximal balance

  • analogy: groove quantizer, bell cycle

  • a: k pulses (0 = 1 pulse, 1 = full fill)

  • b: n steps (1 to max subdivisions)

• even spacing

  • a: number of evenly spaced divisions (mapped to integer range)
  • b: unused

• probabilistic emphasis

  • a: gaussian spread (σ)
  • b: center of emphasis

• euclidean spacing

  • a: pulse count (mapped to integer k)

  • b: step count (mapped to integer n)

each form spans a distinct class of allocation logic:

• even spacing - baseline structure, clock-like regularity
• emphasis curve - dynamic contour, phrasing, or focus
• euclidean - discrete, maximally balanced pulse groupings together, these cover uniform, sculpted, and interleaved slot strategies - across metrical (grid) and non-metrical (field) domains.

• dynamic density changes over time (handled by variation, mutation, or trajectory)
• random or adaptive allocation (violates determinism)
• trigger generation or voice assignment (handled by activation, role, etc.)
• hierarchical slot grouping (handled in structure layer)

density defines where events could happen - and how many. it separates temporal layout from content or behavior, enabling deeply modular design. these three compact forms span the fundamental classes of onset distribution, all fully deterministic and free of runtime dependencies - making density a foundational part of structured sonic composition in the 声音 system.