Adaptive tuning adjusts pitches in real time by sliding down the dissonance curve toward nearby consonant intervals

Adaptive tuning (Sethares’ consonance-based algorithm) continuously recomputes the sensory dissonance of all currently sounding notes and adjusts their pitches to reduce that dissonance. Conceptually: the dissonance curve is a landscape with hills and valleys; each currently sounding interval sits somewhere on this landscape. The algorithm computes the gradient of the dissonance surface and moves pitches downhill toward nearby local minima (consonant intervals). The algorithm requires knowledge of the spectrum of the sounds (since dissonance curves depend on spectrum). Real-time implementation uses MIDI pitch bend to retune notes. Trade-offs: pitches wander melodically when adapting, harmonic consistency may be sacrificed, and chords with many simultaneously ‘competing’ minima can cause instability.

Examples

Two notes a tritone apart: the algorithm nudges both toward the nearest just ratio, either slightly closing to a fourth or opening to a fifth. A context (inaudible partials added to the calculation) can stabilize pitch motion and prevent excessive wandering. Sethares’ Adaptun software (Max/MSP patch) implements this in real time.

Assessment

Why does adaptive tuning produce better sensory consonance than fixed just intonation in a harmonically complex piece? What problem arises when a melody moves quickly through many different intervals, and how does the ‘context’ feature address it?