PERCEIVED ROUGHNESS OF TWO SIMULTANEOUS HARMONIC COMPLEX TONES - MIŚKIEWICZ, Andrzej; ROGALA, Tomira; SZCZEPAŃSKA–ANTOSIK, Joanna (Archives of Acoustics, 2007)
Two experiments were carried out to determine the dependence of perceived roughness onthe frequency ratio of two simultaneous harmonic complex tones. In the first experiment, thefrequency ratios of the tone pairs corresponded to 35 within-octave intervals of various musicaltuning systems. In the second experiment 12 intervals were used; six of them ranged from10 cents below to 10 cents above an equally-tempered fourth and the other six encompasseda similar range centred around the equally-tempered fifth. In both experiments the amountof roughness was assessed by absolute magnitude estimation. Results show that roughnessconsiderably varies with the frequency ratio of a pair of harmonic complex tones, which is awell-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 integerfrequency ratios. This effect is attributed to slow beats that arise between the harmonicsof two complex tones when the frequency ratio of an equally-tempered interval slightlydeparts from integer ratio. Such beats, heard as fluctuations, impart a smooth character tothe sound.