inertia

this domain encodes per-voice temporal momentum - simulating concepts like:

• delayed entry or recovery
• fatigue or buildup
• lingering presence
• gradual fade or resistance to change unlike constraint, which is quota-based, or pressure, which is momentary, inertia tracks internal state over time - without using feedback or runtime logic. instead, all inertia curves are precomputed, based on incoming trigger structure or segment duration.

• 0 exponential rise/fall

  • description: smooth ramp-up and decay around trigger activity
  • analogy: steam pressure, mental focus, energy

  • notes:

    • a: rise time (0 = fast, 1 = slow)
    • b: decay time (0 = fast, 1 = slow)

• 1 decay on silence

  • description: maintains level while active, decays only on inactivity
  • analogy: presence that “fades out” after last event

  • notes:

    • a: decay time
    • b: hold threshold (0 = decay immediately, 1 = delay longer)

• 2 burst memory

  • description: rapid gain from each trigger, slow fade
  • analogy: bubbling energy, bursting behavior

  • notes:

    • a: burst size per trigger
    • b: decay time

• 3 refractory window

  • description: temporary suppression after each trigger
  • analogy: neural refractory period, fatigue

  • notes:

    • a: suppression strength (0 = light, 1 = full mute)
    • b: duration of suppression (0 = short, 1 = long)

• 4 crossover lag

  • description: voice competes with others and takes time to rise

  • analogy: filling a gap, bubbling to surface

  • notes:

    • a: inertia to enter (0 = instant, 1 = slow)

    • b: inertia to exit (0 = instant fade, 1 = long fade)

• exponential rise/fall

  • a: rise time
  • b: decay time

• decay on silence

  • a: decay curve
  • b: silence hold

• burst memory

  • a: gain per trigger
  • b: fade curve

• refractory window

  • a: mute strength
  • b: mute duration

• crossover lag

  • a: fade-in resistance

  • b: fade-out resistance

each form captures a distinct musical inertia archetype:

• rise/fall: general energy tracking
• decay-on-silence: persistence after activity
• burst memory: impulse-driven texture
• refractory: suppression and fatigue
• crossover: layered emergence of voices together they model both gradual processes and discrete resistances, essential to simulate presence, absence, buildup, and competition.

• feedback loops or runtime tracking (state must be precomputed)
• probabilistic decay or noise
• input-dependent state branches (e.g. "if 3 triggers in 5 beats…")
• dynamic reweighting (handled by upstream domains)

inertia adds a structured sense of presence, resistance, and memory to the onset engine. it enables musical elements to feel organic, “settled,” or “bubbling up” - without requiring runtime feedback. by shaping how voices linger, resist entry, or recover from activity, inertia supports naturalistic behaviors in both regular and chaotic textures.