Pitch of unresolved, two-component complex tones
Lawrence L. Feth, Honor O’Malley, Jw Ramsey · The Journal of the Acoustical Society of America · 1982
Helmholtz [On the Sensations of Tone (Dover, New York, 1954), 2nd English edition] reported that the pitch of a two-component complex tone could be shifted slightly by increasing the amplitude of one component. The pitch was shifted toward the frequency of the more intense component. Helmholtz attributed the pitch shift to a variation in the instantaneous frequency of the two-tone complex. This laboratory has previously investigated the discriminability of pairs of two-component complex tones with identical small amplitude differences between the components of a pair. Discriminability seemed to depend upon the difference in their envelope-weighted instantaneous frequency fluctuations. In the study to be reported, four subjects matched a double-sideband suppressed-carrier (DSSC) signal to each member of pairs of two-component complex tones centered at frequencies from 500 to 4000 Hz. There were small, complementary amplitude differences between components of a pair of two-tone complex signals, while the amplitudes of the two components in the DSSC signal were equal. Listeners were also asked to discriminate between pairs of these complementary two-tone complexes. Data indicate that there is a relationship between the discriminability of the complementary two-component complexes and the perceived pitch of each complex. These data were used to test several variations of a (general) weighted time-average model to relate the pitch of each fluctuating two-tone complex to its averaged instantaneous frequency. In general, the model seems to hold for center frequencies below 4000 Hz where there are moderate frequency separations between the components of a complex. The model appears to be insensitive to the choice of weighting functions and the nature of the average.