grid

• 0 simple

  • description: one constant time signature
  • real-world analogy: 4 /4, 3 /4, 5 /8
  • notes: baseline bar structure

• 1 additive

  • description: ordered sub-groups of beats inside a bar
  • real-world analogy: 7 /8 as [3, 2, 2], 11 /8 as [3, 3, 2, 3]
  • notes: irregular meters without nesting

• 2 polymeter

  • description: independent meters running in parallel, one per voice

  • real-world analogy: drum track in 4 /4 versus bass in 3 /4

  • notes: alignment options - longest-cycle, shortest-cycle, free

• 0 simple

  • a numerator (int > 0, quantised from a)
  • b denominator (power-of-two int, quantised from b)

• 1 additive

  • a interpreted as a list of group lengths (encoded externally)
  • b denominator (power-of-two)

• 2 polymeter

  • a mapping of voices → (numerator, denominator) pairs (encoded externally)

  • b alignment policy

    • 0 longest-cycle

    • 1 shortest-cycle

    • 2 free all parameters are bounded: a, b ∈ [0, 1] before conversion to discrete values.

cover the complete space of rational, periodic* beat structures

• allow asymmetric bars (additive) and cross-metric layering (polymeter)
• remain statically enumerable and repeatable, matching the project's deterministic ethos

irrational or drifting cycles (handled by field*)

• tempo or meter changes over time (structure layer)
• tuplets and micro-subdivisions (timing-deviation domain)

grid now owns the quantised, metrically periodic slice of onset space. for any timing behaviour that cannot be expressed as rational beats repeating in a cycle, defer to the field domain.