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.