2025-06-04

trajectory

defines long-scale directional motion curves over time, guiding the shape, emphasis, or activation tendency of sonic material. serves as a high-level scaffolding for phrasing, buildup, decay, tension, and resolution. trajectory provides pure temporal energy profiles that other domains (e.g. pressure, constraint, density, mutation) can reference to inform their behavior.

introduction

this domain encodes intentional temporal shape - without specifying content or voice. it is a control signal that models phrasing gravity, structural motion, or expressive evolution. unlike segment emphasis, which is local and discrete, trajectory defines continuous pressure curves over full structural spans, typically across phrases, sections, or scenes. trajectories are deterministic, precomputed, and resolution-independent. they may be sampled at any time point to obtain a value ∈ [0,1].

overview

  • 0 linear slope

    • description: ramps evenly from start to end
    • analogy: rising or falling motion

    • notes:

      • a: slope direction (0 = decrescendo, 1 = crescendo)
      • b: curve shape (0 = linear, 1 = exponential)

  • 1 bell arc

    • description: central emphasis with soft rise/fall
    • analogy: classical phrase, thunderclap, envelope

    • notes:

      • a: peak position (0 = early, 1 = late)
      • b: spread (0 = narrow, 1 = wide)

  • 2 staircase

    • description: discrete level shifts at regular intervals
    • analogy: rhythmic buildup, additive layering

    • notes:

      • a: number of steps (min 2, max 16)
      • b: step skew (0 = front-heavy, 1 = back-heavy)

  • 3 loop pulse

    • description: repeating rise/fall motion
    • analogy: heartbeat, wave, modulation

    • notes:

      • a: cycle count (1 to 16 per segment)
      • b: duty (0 = short pulse, 1 = long)

  • 4 asymmetric rise/fall

    • description: fast rise + slow decay or vice versa

    • analogy: surprise or fade

    • notes:

      • a: skew (0 = rise fast, 1 = fall fast)

      • b: curvature (0 = linear, 1 = curved)

parameter behavior summary

  • linear slope

    • a: direction (0 = down, 1 = up)
    • b: linear ↔ exponential bias

  • bell arc

    • a: center position
    • b: width

  • staircase

    • a: number of steps
    • b: weight bias

  • loop pulse

    • a: cycles per span
    • b: pulse duty ratio

  • asymmetric rise/fall

    • a: asymmetry skew

    • b: curvature

why these were chosen

each form expresses a fundamentally different kind of structural motion:

  • linear: steady directional drive
  • bell: classic phrasing envelope
  • staircase: discrete buildup patterns
  • loop: periodic modulation
  • asymmetric: expressive tilts and imbalances together they span the space of monotonic, symmetric, cyclic, and eventful structural flows - all using the system's compact 2-parameter idiom.

what is not included

  • absolute timing (trajectory is normalized over segment)
  • reactive changes or runtime shaping
  • probabilistic variation or noise
  • hierarchical chaining (handled via segmentation + reuse)

conclusion

trajectory supplies long-range structural motion - the musical “curve” behind event-level decisions. it integrates cleanly into the additive system as a modulator of behavior, not a generator of events. by defining motion fields across time, it enables phrasing, buildup, and expressive motion to emerge across voices and behaviors, without violating determinism or purity.