amplitudes

• 0 flat

  • description: equal amplitude for all partials
  • real-world analogy: pulse trains, square waves
  • notes: reference baseline

• 1 polynomial tilt

  • description: power-law roll-off, with optional skew across spectrum
  • real-world analogy: string harmonics (1/n), pink noise
  • notes: a controls decay, b controls skew

• 2 gaussian peak

  • description: single formant-like peak centered at arbitrary partial
  • real-world analogy: vowels, woodwinds, formant synthesis
  • notes: peak center + width

• 3 beta shape

  • description: skewed bell, u-shapes, edge emphasis
  • real-world analogy: tape noise, bass thump + hiss, asymmetrical energy
  • notes: high flexibility from beta(α, β)

• 4 shelf (sigmoid)

  • description: smooth step-like drop or rise in partials
  • real-world analogy: speaker roll-off, muted trumpet
  • notes: a = cutoff, b = steepness

• 5 logistic chaos

  • description: chaotic but continuous grain structure, with scale control
  • real-world analogy: breathy sources, granular clouds
  • notes: logistic map smoothed by window

• 6 bessel (modal)

  • description: oscillatory energy with many ripples

  • real-world analogy: bells, gamelan, metal plates

  • notes: based on bessel functions

• 0

  • param a: (unused)
  • param b: (unused)

• 1

  • param a: brightness (p)
  • param b: tilt/skew across index

• 2

  • param a: peak center
  • param b: peak width

• 3

  • param a: alpha (shape)
  • param b: beta (shape)

• 4

  • param a: cutoff position
  • param b: step sharpness

• 5

  • param a: chaos strength (r)
  • param b: smoothing window (grain size)

• 6

  • param a: modal spread (x)

  • param b: decay factor all parameters are bounded: a, b ∈ [0, 1].

these seven families were selected to span the perceptual space of spectral shapes in a musically relevant and synthesis-efficient way:

• simple roll-offs and brightness control → polynomial tilt
• localized resonances → gaussian peak
• asymmetric or complex spectral bodies → beta shape
• spectral edges or low-pass rolloffs → shelf
• irregular dynamic motion → logistic chaos
• modal-like structured ripples → bessel
• reference → flat (no spectral shaping) each offers unique control and timbral identity, and cannot be easily mimicked by the others-even when arbitrarily tuned.

• dual-formant shapes - currently not implemented. could be added via two combined gaussians.
• exponential decay - steep exponential drop-offs not included explicitly; tilt with p > 5 approximates well.
• triangle / rise-fall - approximated by beta(α≈β<1); not needed as separate family.

with the current 7 implemented families, the system offers:

• a minimal yet rich coverage of natural and artificial spectral energy shapes
• two-dimensional control for each type
• no binary steps or discontinuities, making it ideal for purely additive synthesis the framework remains extensible (e.g. to multi-formant distributions), but in its current form, already provides a powerful toolset for spectral instrument design.