Harmonic complex tones elicit a pitch sensation at their fundamental frequency (F0), even when their spectrum contains no energy at F0, a phenomenon known as "pitch of the missing fundamental." The strength of this pitch percept depends upon the degree to which individual harmonics are spaced sufficiently apart to be "resolved" by the mechanical frequency analysis in the cochlea. We investigated the resolvability of harmonics of missing-fundamental complex tones in the auditory nerve (AN) of anesthetized cats at low and moderate stimulus levels and compared the effectiveness of two representations of pitch over a much wider range of F0s (110-3,520 Hz) than in previous studies. We found that individual harmonics are increasingly well resolved in rate responses of AN fibers as the characteristic frequency (CF) increases. We obtained rate-based estimates of pitch dependent upon harmonic resolvability by matching harmonic templates to profiles of average discharge rate against CF. These estimates were most accurate for F0s above 400-500 Hz, where harmonics were sufficiently resolved. We also derived pitch estimates from all-order interspike-interval distributions, pooled over our entire sample of fibers. Such interval-based pitch estimates, which are dependent on phase-locking to the harmonics, were accurate for F0s below 1,300 Hz, consistent with the upper limit of the pitch of the missing fundamental in humans. The two pitch representations are complementary with respect to the F0 range over which they are effective; however, neither is entirely satisfactory in accounting for human psychophysical data.

The pitch of harmonic complex tones plays an important role in speech and music perception and the analysis of auditory scenes, yet traditional rate-place and temporal models for pitch processing provide only an incomplete description of the psychophysical data. To test physiologically a model based on spatiotemporal pitch cues created by the cochlear traveling wave (Shamma, 1985), we recorded from single fibers in the auditory nerve of anesthetized cat in response to harmonic complex tones with missing fundamentals and equalamplitude harmonics. We used the principle of scaling invariance in cochlear mechanics to infer the spatiotemporal response pattern to a given stimulus from a series of measurements made in a single fiber as a function of fundamental frequency F 0 . We found that spatiotemporal cues to resolved harmonics are available for F 0 values between 350 and 1100 Hz and that these cues are more robust than traditional rate-place cues at high stimulus levels. The lower F 0 limit is determined by the limited frequency selectivity of the cochlea, whereas the upper limit is caused by the degradation of phase locking to the stimulus fine structure at high frequencies. The spatiotemporal representation is consistent with the upper F 0 limit to the perception of the pitch of complex tones with a missing fundamental, and its effectiveness does not depend on the relative phase between resolved harmonics. The spatiotemporal representation is thus consistent with key trends in human psychophysics.

Pitch differences between concurrent sounds are important cues used in auditory scene analysis and also play a major role in music perception. To investigate the neural codes underlying these perceptual abilities, we recorded from single fibers in the cat auditory nerve in response to two concurrent harmonic complex tones with missing fundamentals and equal-amplitude harmonics. We investigated the efficacy of rate-place and interspike-interval codes to represent both pitches of the two tones, which had fundamental frequency (F0) ratios of 15/14 or 11/9. We relied on the principle of scaling invariance in cochlear mechanics to infer the spatiotemporal response patterns to a given stimulus from a series of measurements made in a single fiber as a function of F0. Templates created by a peripheral auditory model were used to estimate the F0s of double complex tones from the inferred distribution of firing rate along the tonotopic axis. This rate-place representation was accurate for F0s above about 900 Hz. Surprisingly, rate-based F0 estimates were accurate even when the two-tone mixture contained no resolved harmonics, so long as some harmonics were resolved prior to mixing. We also extended methods used previously for single complex tones to estimate the F0s of concurrent complex tones from interspike-interval distributions pooled over the tonotopic axis. The interval-based representation was accurate for F0s below about 900 Hz, where the two-tone mixture contained no resolved harmonics. Together, the rate-place and interval-based representations allow accurate pitch perception for concurrent sounds over the entire range of human voice and cat vocalizations.

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