Timbre, Dissonance and Spectrum-Matched Tuning

This module builds toward a single act of instrument design: choosing a scale that 12-TET cannot reach — a xenharmonic temperament, a stretched octave, a gamelan-flavoured seven-step division — and synthesizing a timbre that makes it sound consonant. In a live-coding set this is the difference between “microtonal” reading as out-of-tune and reading as a coherent harmonic world: on a SuperCollider rig you control every partial of every SynthDef, so you can do what acoustic builders cannot and sculpt the spectrum to fit the tuning.

The arc starts perceptual. You first learn why roughness happens at all — beating partials inside the critical band — and drill reading dissonance curves for harmonic spectra until spotting minima is automatic. Then the central inversion of perspective: consonance belongs to the spectrum-scale pair, not to frequency ratios, and a spectrum and scale are “related” when the curve’s minima land on the scale steps. Stretched timbres and their pseudo-octaves, plus harmonic entropy as the tonalness counterpart to roughness, give you the vocabulary to reason about inharmonic sounds. Early exercises are forward-direction and supported: given a spectrum, find its scale. The capstone flips this unsupported — solve the inverse spectrum-from-scale problem for your chosen tuning, then realise it with the partials-on-the-temperament-grid technique from the SuperCollider spectral-tuning atom, A/B-ing matched against mismatched chords.

The required atoms are exactly what gates that build: the roughness model, curve reading, the matching principles, the inverse method, and the SC realisation. Supporting atoms widen the frame — gamelan, Thai 7-tet and pelog show the principle operating in real traditions, the five-CDC taxonomy and the naturalism/relativism debate sharpen your claims, and dissonance scores extend the measurement from chords to whole performances.