Models of the perception of the pitch of tonal complexes
Theories of pitch perception, and the related literature, are reviewed, with special reference to the residue pitch of tonal complexes. A distinction is drawn between spectral-pattern theories, which propose that pitch is derived from independent internal estimates of component frequency, and periodicity theories, which propose that the pitch of tonal complexes may be derived from a residual periodicity resulting from an incomplete auditory frequency analysis. The Spectral-pattern models described by Goldstein (1973) and Wightman (1973b) are discussed in detail; computer simulation procedures, allowing the prediction of a probability density function for the estimated fundamental frequency of a tonal complex, are described for each. Contrasting predictions concerning the relation between component frequency discrimination and fundamental frequency discrimination for harmonic complexes are developed for the spectral-pattern and periodicity theories. Component frequency and fundamental frequency discrimination by human observers was measured, under a variety of conditions, for a complex containing the 4th and 5th harmonics of 200 Hz. For a comparison of the pitches of two such complexes of slightly different frequency, the relative fundamental frequency difference limen was no larger, and generally smaller, than the smaller relative component frequency difference limen. Discrimination performance was interpreted in terms of a modified version of Goldstein's (1973) spectral-pattern theory, in which an internal noise limits discrimination between signals with non-coincident components. Further experiments investigated the identification of fundamental frequency by human observers as a function of the variability of internal estimates of component frequency as estimated from the discrimination experiments. The results of these experiments were consistent with the predictions of the spectral-pattern theories. Component and fundamental frequency discrimination was also considered with respect to temporal and spatial theories of frequency discrimination. The results of the discrimination studies were consistent with a modified Energy Detection model, where discrimination is ultimately limited by an internal noise.