Why do some intervals sound sweet and others harsh? Not magic — when two tones’ overtones sit close but not equal, they BEAT, and fast beats are heard as roughness. The consonant intervals are the valleys where the overtones line up. Slide the interval and ▶ play the two tones.
A Plomp-Levelt dissonance curve, computed live. Two complex tones (six harmonics each) are compared at a frequency ratio from 1 to 2; every pair of partials contributes roughness by the Plomp-Levelt model — maximal near a critical-band fraction of their spacing, zero when they coincide or are far apart. Summed, the curve dips at the simple ratios where partials align — unison 1:1, fifth 3:2, fourth 4:3, major third 5:4, octave 2:1 — and rises to rough peaks between them. Consonance is not a rule imposed on music; it is where the overtones stop beating. A fail-loud self-check throws unless the roughness at the fifth (3:2) is lower than at a detuned neighbour. Press ▶ to hear the two tones at the current ratio.
Six harmonics and the standard Plomp-Levelt roughness kernel; real consonance judgements add culture, register and harmonic context. The partial-beating sum is computed exactly.