Physical basis of two-tone interference in hearing

The cochlea uses active amplification to capture faint sounds. It has been proposed that the amplifier comprises a set of self-tuned critical oscillators: each hair cell contains a force-generating dynamical system that is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. While the active response to a pure tone provides frequency selectivity, exquisite sensitivity, and wide dynamic range, its intrinsic nonlinearity causes tones of different frequency to interfere with one another in the cochlea. Here we determine the response to two tones, which provides a framework for understanding how the ear processes the more complex sounds of speech and music. Our calculations of two-tone suppression and the spectrum of distortion products generated by a critical oscillator accord with experimental observations of basilar membrane motion and the nervous response. We discuss how the response of a set of self-tuned oscillators, covering a range of characteristic frequencies, represents the structure of a complex sound. The frequency components of the stimulus can be inferred from the timing of neural spikes elicited by the vibrating hair cells. Passive prefiltering by the basilar membrane improves pitch discrimination by reducing interference between tones. Our analysis provides a general framework for examining the relation between the physical nature of the peripheral detection apparatus and psychophysical phenomena such as the sensation of dissonance and auditory illusions.