Roughness of Two Simultaneous Harmonic Complex Tones On Just-Tempered and Equal-Tempered Scales

Abstract

This study is focused on the perceived roughness of two simultaneous harmonic complex tones with ratios between their fundamental frequencies set to create intervals on just-tempered (JT) and equal-tempered (ET) scales. According to roughness theories, ET intervals should produce more roughness. However, previous studies have shown the opposite for intervals in which the lower fundamental frequency of the complex was equal to 261.6 Hz. The aim of this study is to verify and explain these results by using intervals composed of complexes whose spectral components were generated with either a sine starting phase or with a random starting phase. Results of the current study showed the same phenomenon as previous studies. To examine whether the explanation of the phenomenon lies in the function of the peripheral ear, three roughness models based upon this function were used: the Daniel and Weber (1997) model, the synchronization index (SI) model, and the model based on a hydrodynamic cochlear model. For most of the corresponding JT and ET intervals, only the Daniel and Weber (1997) model predicted less roughness in the ET intervals. In addition to this, the intervals were analyzed by a model simulating the auditory periphery. The results showed that a possible cause for the roughness differences may be in the frequencies of fluctuations of the signal in the peripheral ear. For JT intervals the fluctuations in the adjacent places on the simulated basilar membrane had either the same frequency or integer multiples of that frequency and were synchronized. Since a previous study showed that synchronized fluctuations in adjacent auditory filters lead to higher roughness than out of phase fluctuations (Terhardt, 1974), this may cause more roughness across JT and ET intervals.