envelope

• 0: flat

  • description: constant amplitude throughout note duration
  • implementation: single linear segment at y = 1

  • parameters:

    • a = unused
    • b = unused

• 1: natural ramp

  • description: curved rise into sustain, mimicking natural energy buildup (e.g. bow, breath, mallet)

  • implementation:

    • exponential attack curve
    • followed by linear sustain

  • parameters:

    • a = attack duration (0 = fast, 1 = slow)
    • b = curve shape (0 = steep, 1 = smooth); remapped to exponential gamma

• 2: synthetic click

  • description: narrow impulse followed by flat sustain

  • implementation:

    • power-rise to peak
    • short exponential decay
    • flat linear sustain

  • parameters:

    • a = click duration (0 = instant, 1 = wide)
    • b = spectral tilt (0 = sharp, 1 = smooth); mapped to both power and exponential gamma

• 3: tilt envelope

  • description: flexible attack and release curvature

  • implementation:

    • attack: bezier arc with curvature from a
    • release: bezier arc with curvature from b

  • parameters:

    • a = attack bend (0 = linear, 1 = curved); remapped to [–1, 1]
    • b = release bend (0 = linear, 1 = curved); remapped to [–1, 1]

• 4: multiphase

  • description: dynamic shape with attack, decay, and sustain

  • implementation:

    • power curve for attack
    • exponential decay to sustain
    • flat sustain

  • parameters:

    • a = relative attack time
    • b = relative decay time
    • both are normalized and rescaled to fit within note length

• 5: legato crossfade

  • description: overlapping transitions between notes

  • implementation:

    • linear hold phase
    • exponential fade-out

  • parameters:

    • a = fade length

    • b = fade start position (0 = note end, 1 = full blend)

• flat

  • a = unused
  • b = unused

• natural ramp

  • a = attack time
  • b = exponential gamma (0.01 to 100)

• synthetic click

  • a = impulse width
  • b = dual tilt (mapped to power gamma and exponential gamma)

• tilt envelope

  • a = attack bend (mapped to –1 to +1)
  • b = release bend (mapped to –1 to +1)

• multiphase

  • a = attack ratio
  • b = decay ratio
  • both time-normalized and rescaled to full duration

• legato crossfade

  • a = crossfade length

  • b = fade overlap point

• flat - minimal reference for debugging and pure tone testing
• natural ramp - models breath/bow-based gestures with curvature control
• synthetic click - produces short impulses with fine shape control
• tilt envelope - general-purpose shape with direct curvature mapping
• multiphase - covers physical gestures with distinct attack and decay
• legato crossfade - enables smooth melodic transitions without retriggering each shape:
• covers a distinct perceptual gesture
• uses only two parameters
• supports continuous variation across the space it defines
• cannot be mimicked by another shape in the set

• multi-stage or sample-driven envelopes
• velocity- or controller-modulated shaping (covered by performance layer)
• gated, looping, or reactive envelopes (covered under dynamics)
• stochastic or expressive variation (delegated to modulation or timing layers) excluded features are delegated to other layers to preserve static determinism and parametric clarity.

the envelope domain defines a single, global amplitude contour per note. each envelope family:

• uses two normalized parameters a, b ∈ [0, 1]
• is statically scheduled
• produces a spline_path descriptor composed of linear, exponential, power, or bezier-arc segments
• guarantees continuous, musically useful variation across its space together, these six forms span a wide expressive range of onset, sustain, and release behaviors while remaining compact, stateless, and composable within the system. the envelope operates in coordination with:
• envelopes - for per-partial shaping
• dynamics - for intra-note time variation
• decorators - for local augmentations this layered approach ensures full control over amplitude shape from event level to fine-grain spectral detail.