Is Time Theory Necessary to Answer Resolved and Unresolved Harmonics Problems in Pitch Perception?

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 questions 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, with the second- and third-order nonlinearities as default teacher signals for sound localization in auditory scene analysis, a chain of coincidence is generated. After learning is completed, two power series templates of 2n and 3m are generated, and the \(2f_{1} - f_{2}\) 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. On the other hand, this harmonic template has deficiencies for N>10. These deficiencies result in the deterioration of the fundamental discrimination threshold (F0DT) that appears in the pitch perception of harmonic complex tones above the 10th order. Based on this template model, consistent explanations are given for the problems of the missing fundamental, octave equivalence, pitch shift, pitch and chroma, and resolvability jump without the help of time theory. This research contributes to our understanding of auditory perception and has implications for fields such as music theory, cognitive science, and auditory neuroscience.