Musical Ratios in Sounds from the Human Cochlea

The physiological roots of music perception are a matter of long-lasting debate. Recently light on this problem has been shed by the study of otoacoustic emissions (OAEs), which are weak sounds generated by the inner ear following acoustic stimulation and, sometimes, even spontaneously. In the present study, a high-resolution time–frequency method called matching pursuit was applied to the OAEs recorded from the ears of 45 normal volunteers so that the component frequencies, amplitudes, latencies, and time-spans could be accurately determined. The method allowed us to find that, for each ear, the OAEs consisted of characteristic frequency patterns that we call resonant modes. Here we demonstrate that, on average, the frequency ratios of the resonant modes from all the cochleas studied possessed small integer ratios. The ratios are the same as those found by Pythagoras as being most musically pleasant and which form the basis of the Just tuning system. The statistical significance of the results was verified against a random distribution of ratios. As an explanatory model, there are attractive features in a recent theory that represents the cochlea as a surface acoustic wave resonator; in this situation the spacing between the rows of hearing receptors can create resonant cavities of defined lengths. By adjusting the geometry and the lengths of the resonant cavities, it is possible to generate the preferred frequency ratios we have found here. We conclude that musical perception might be related to specific geometrical and physiological properties of the cochlea

Musical-interval structure of long-lasting TEOAE components.

<p>(a) Distribution of ratios of OAE frequencies found for individual ears (black line) and distribution of ratios determined from randomly drawn OAE frequencies (gray line); (b) difference (black line) between the curves shown in <i>a</i>. The gray line shows the 75th percentile of the distribution of ratios of randomly drawn frequencies.</p

Experimentally found ratios of resonant frequencies in otoacoustic emissions compared with musical ratios of the Just scale.

<p>Δ difference between experimental and theoretical ratio.</p>*<p>not significant.</p

Time–frequency representation of TEOAEs for the left and right ears of one subject.

<p>The amplitudes of resonant modes are color coded. The vertical bars connect resonant modes having small-integer ratios.</p