The 1.06 frequency ratio in the cochlea: evidence and outlook for a natural musical semitone

Abstract

A frequency ratio of about 1.06 often appears in cochlear mechanics, and the question naturally arises, why? The ratio is close to that of the semitone (1.059) in music, giving reason to think that this aspect of musical perception might have a cochlear basis. Here, data on synchronised spontaneous otoacoustic emissions is presented, and a clustering of ratios between 1.05 and 1.07 is found with a peak at 1.063 ± 0.005. These findings reinforce what has been found from previous sources, which are reviewed and placed alongside the present work. The review establishes that a peak in the vicinity of 1.06 has often been found in human cochlear data. Several possible cochlear models for explaining the findings are described. Irrespective of which model is selected, the fact remains that the cochlea itself appears to be the origin of a ratio remarkably close to an equal-tempered musical semitone, and this close coincidence leads to the suggestion that the inner ear may play a role in constructing a natural theory of music. The outlook for such an enterprise is surveyed.