Perceived Roughness Of Two Simultaneous Harmonic Complex Tones

Two experiments were carried out to determine the dependence of perceived roughness on the frequency ratio of two simultaneous harmonic complex tones. In the first experiment, the frequency ratios of the tone pairs corresponded to 35 within-octave intervals of various musical tuning systems. In the second experiment 12 intervals were used; six of them ranged from 10 cents below to 10 cents above an equally-tempered fourth and the other six encompassed a similar range centred around the equally-tempered fifth. In both experiments the amount of roughness was assessed by absolute magnitude estimation. Results show that roughness considerably varies with the frequency ratio of a pair of harmonic complex tones, which is a well-known phenomenon. A new finding, that is in contrast to published theories of roughness, is that equally-tempered intervals produce less roughness than their counterparts based on integer frequency ratios. This effect is attributed to slow beats that arise between the harmonics of two complex tones when the frequency ratio of an equally-tempered interval slightly departs from integer ratio. Such beats, heard as fluctuations, impart a smooth character to the sound.