Pitch of harmonic two-tone complexes of unequal amplitudes

Abstract

Melodic interval identification experiments were performed using dichotic two-tone complexes of successive random harmonics with intensity ratios of lower to higher tone of 20, 10, 0, −10, and −20 dB. Experimental confusion matrices were correlated with theoretical matrices computed from Goldstein's optimal processor theory, Wightman's pattern transformation theory, and from an analytic pitch theory which assumes that a two-tone complex has one of two pitches, corresponding to the pure tone frequencies, with the likelihood of each pitch dependent on the relative loudness of the tone components. Results indicate that the best predictions are achieved by a combination of the optimum processor mode and the analytic mode. At low harmonic numbers, the optimum processor theory alone accounts very well for the data, while at higher harmonic numbers a combination of optimum processor and analytic theories yields the best correlation with observed data. At harmonic numbers higher than about six, correlation between data and any theory or combination of theories is clearly less than perfect, suggesting that pitch behavior at higher harmonics has some randomness which is not accounted for by any of the current pitch theories. [Work supported by NIH, Grant NS11680-03.]