Power Series Template Matching Model for Pitch Perception

Abstract

The problem of pitch perception has been the subject of a long debate between place theory and time theory. Here, we propose a Power Series Template (PoST) model to answer the problem of how and why pitch perception comes about. The sensitive measurement of acoustic signals requires efficient Sound Amplification, which inevitably accompanies mode coupling due to the perturbative non-linearities. Under reinforcement learning for Sound Localization with the second- and third-order modes as default teacher signals, a chain of coincidence is generated. After learning in Sound Localization is completed, two power series templates of 2n and 3m are generated, and the 2f1 - f2 coupling of the elements contained therein fills the blanks of matchable harmonics up to N=10 in the template, providing the well-known harmonic template. When complex tones containing multiple harmonics are input into the trained network, two power series are evoked from each harmonic, and from their intersection, the brain acquires the fundamental of the complex tone as the pitch. Based on this template model, consistent explanations are given for the problems of missing fundamental, pitch shift, pitch and chroma, and resolvability jump without the help of time theory.