Harmonic fusion and pitch shifts of mistuned partials

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Abstract
A model is proposed to explain pitch shifts of components mistuned from a harmonic series [W. M. Hartmann and S. L. Doty, “On the pitches of the components of a complex tone,” J. Acoust. Soc. Am. 99, 567–578 (1996)]. An internal random variable depends on the frequency of the partial and determines both its pitch and the probability that it will fuse within the complex. The model accounts for the sign of the pitch shifts (positive for positive mistunings, negative for negative mistunings), the fact that they saturate and become smaller for large mistunings, and, given reasonable assumptions on the underlying distributions, their overall shape and magnitude. No assumptions are required concerning the pitch extraction mechanism (place, time, etc.) other than that a common source of variability affects cues to both pitch and harmonic fusion.

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