The consonance of an interval depends on the timbre of the sound, not just the frequency ratio

Sethares’ central thesis: sensory consonance and dissonance are not fixed properties of frequency ratios but depend on the spectrum (timbre) of the sounds being played. Two tones with a 2:1 ratio sound consonant when both have harmonic spectra because their partials align — but if the spectra are stretched so that partials fall at 2.1× ratios, the 2:1 octave becomes dissonant while the 2.1 pseudo-octave becomes the new consonant interval. This means the Western preference for octaves, fifths, and thirds is not a universal acoustic law but is matched to harmonic timbres. Any interval can be made consonant or dissonant by appropriately sculpting the spectrum. This principle explains why gamelan music (inharmonic metallophones) uses pelog/slendro rather than 12-tet, and opens the door to designing new instruments with matched tuning systems.

Examples

Playing a simple I-V-I chord with harmonic timbres in 12-tet sounds consonant. Replace the timbres with 2.1-stretched inharmonic partials while keeping 12-tet tuning: the chords become uniformly dissonant. Switch to a 2.1-stretched scale matched to those timbres: consonance returns.

Assessment

Given two different spectra (one harmonic, one with partials at 1×, 2.1×, 3.1×, …), predict which scale will produce the most sensory consonance for each, and explain why the octave is not automatically the most consonant interval for the inharmonic spectrum.