Beats in Cochlear Models

Abstract

The effect of beats in cochlear models upon cochlear fluid was studied. The elliptical orbits of motion expanded and contracted synchronously with the beat rate. Thereby, a partial rectification became apparent which, occurring in opposite directions in the 2 scalae across the partition, constituted the beat. This latter phenomenon was caused by the stiffness gradient of the cochlear partition. The effect of beats upon the traveling wave pattern along the partition in cochlear models was also studied. Stroboscopic examination revealed that the beat frequency modulated the 2 primaries thus producing 2 additional side bands. However, the displacement pattern of the membrane when viewed by high-speed motion photography did not give any evidence of these 5 frequencies. Only the intertone and the beat were present. The model is apparently a pattern analyzer of complex sound. In terms of cochlear fluid motion, it is able to resolve complex Lissajous by a spatial filter action along the partition into simple Lissajous. Any deviation from steady Lissajous, which ordinarily result from primaries in relation of integral numbers, produces beats. Thus beats of imperfect unison as well as the mistuned consonances have essentially the same cause: a cyclic phase change between the 2 primaries.