# density
allocates onset slots statically over a time segment, independent of onset content.
can be applied to both metrical (`grid`) and non-metrical (`field`) domains.
forms define how many events occur, and where they are placed.
this domain does not generate sounds or triggers directly - it defines slot positions over a segment.
these slots may then be used by `voicing`, `pattern`, or other event-assigning domains.

## overview
* `0` even grid
  * description: uniformly spaced allocation points
  * real-world analogy: mechanical metronome
  * notes:
    * `a` maps to number of divisions (1…max)
    * `b` is unused
    * equally applicable over `grid` or `field` durations
* `1` prob-weighted
  * description: gaussian-shaped emphasis curve biases slot positions
  * real-world analogy: phrasing swell, human rhythmic tension
  * notes:
    * `a` controls spread (σ of gaussian)
    * `b` controls center offset (0 = start, 1 = end)
    * deterministic - no randomness involved
* `2` euclidean
  * description: distributes `k` pulses over `n` steps with maximum evenness
  * real-world analogy: west african bell cycles, groove quantizers
  * notes:
    * `a` controls `k` (number of pulses)
    * `b` controls `n` (number of steps)
    * adapts to either `grid` steps or a resampled `field` segment

## parameter behavior summary
* even grid
  * `a`: number of evenly spaced divisions
  * `b`: unused
* prob-weighted
  * `a`: gaussian spread (σ)
  * `b`: center offset (position of emphasis)
* euclidean
  * `a`: pulse count (`k`)
  * `b`: step count (`n`)
* all parameters: `a, b ∈ [0, 1]`

## why these were chosen
* even grid: for uniform time-filling or pulse distribution
* prob-weighted: to shape phrasing and density contours
* euclidean: to produce discrete, interleaved structures with musical balance
each form spans a distinct class of allocation behavior: uniform, sculpted, and discrete-even.
they cover both continuous and step-based segment types, regardless of origin (`grid`, `field`, or otherwise).

## what is not included
* dynamic or time-varying density (handled by modulation or `variation`)
* probabilistic allocation (excluded by static scheduling)
* runtime decisions, feedback, or adaptation (violates system determinism)
* generative density patterns (belongs in `pattern`, `generative`, or `interaction`)

## conclusion
`density` determines how many events occur and where they are allocated within a time segment.
it separates slot layout from content, enabling modular layering with any onset stream.
these three irreducible forms provide a compact vocabulary for static event spacing, fully aligned with the system's deterministic, additive model.