A dissonance curve plots sensory dissonance vs. interval for a given spectrum, with minima at consonant intervals

For a given timbre (spectrum), the dissonance curve shows how sensory dissonance varies as a second copy of the sound is transposed upward from unison to an octave (or further). Minima in the curve correspond to intervals where partials of the two sounds avoid each other’s critical bands — these are the most consonant intervals for that spectrum. For harmonic spectra, the minima occur near just-intonation ratios (1:1, 6:5, 5:4, 4:3, 3:2, 5:3, 2:1), which is why Western scales emphasize those intervals. For inharmonic spectra (bell, bar, crystal), the minima occur at different intervals, suggesting different scales. The dissonance curve provides a principled, measurable way to determine what scale a given timbre ‘wants.‘

Examples

The harmonic spectrum dissonance curve has deep minima at 1:1, 4:3 (fourth), 3:2 (fifth), 2:1 (octave). A marimba bar spectrum has minima at different ratios — running the dissonance curve calculation reveals what tuning will sound most consonant on that instrument. Plotting dissonance curves for several different spectra shows why different instrument families have different natural intonation tendencies.

Assessment

Explain why a spectrum with partials only at 2:1 ratios (pure octaves) would produce a dissonance curve with only one minimum (at the octave). Then describe qualitatively what the dissonance curve for a harmonic spectrum looks like, and identify which minima correspond to common musical intervals.