density

• id 0 even grid

  • description: uniform spacing of allocation points

  • real-world analogy: mechanical metronome

  • notes:

    • a maps to integer resolution (1…max_steps)

    • b is unused

    • generates evenly spaced slots across the active segment

    • equally valid over grid or field backends

• id 1 prob-weighted

  • description: emphasis curve biases slot positions using a static probability distribution

  • real-world analogy: human accent pattern or focused swell

  • notes:

    • a maps to gaussian σ (spread)

    • b maps to center offset (0…1, relative to segment)

    • produces a weighted distribution over the full time base

    • deterministic: uses static density curve, no randomness

• id 2 euclidean

  • description: distributes k pulses into n steps with maximal evenness

  • real-world analogy: west african bell patterns, groove quantizer

  • notes:

    • a maps to k (pulse count, 1…n)

    • b maps to n (step count, 1…max_steps)

    • generates interleaved pulse slots over discrete divisions

    • input steps can derive from either grid bars or a resampled field

• even grid

  • a: resolution (number of divisions)

  • b: unused

• prob-weighted

  • a: spread (σ of gaussian curve)

  • b: center offset (position of emphasis)

• euclidean

  • a: pulse count (k)

  • b: step count (n)

• even grid: for uniform, metronomic distribution over time
• prob-weighted: for sculpted density and dynamic phrasing
• euclidean: for maximal spacing under discrete constraints

each is distinct in timing logic and form, and each adapts equally to metrical (grid) or non-metrical (field) segment durations.

• time-varying density (handled via parameter modulation)
• generative or algorithmic density (belongs in pattern/generative domains)
• adaptive or reactive allocation (excluded by system determinism)
• feedback or runtime decision logic (violates static scheduling)

density defines how many events happen and where, across any time segment—whether grid-aligned or freeform. these three families—uniform, sculpted, and interleaved—form a compact and irreducible toolkit for static onset allocation. fully compatible with the system’s deterministic, parametric, and additive-only design.