Pitch perception models - a historical review

This paper analyzes theories and models of pitch from a historical perspective. Pythagoras is credited with the first ”psychophysical” model, the monochord, that he used to formulate a law that links a physical quantity (ratio of string lengths) to a psychological quantity (musical interval). The relation between pitch itself and frequency emerged progressively with Aristoxenos, Boethius, Mersenne and Galileo. The anatomist Du Verney first proposed the idea of resonance within the ear, and of a ”tonotopic” projection from the ear to the brain. The notion of frequency analysis, formalized mathematically by Joseph Fourier, was developed by Helmholtz into a beautiful theory of hearing that bridged mathematics, physiology and music. Helmholtz unfortunately followed Ohm in postulating that pitch is determined by one particular frequency component, the fundamental, thus sparking a controversy that has drained energy of hearing scientists for decades, opposing tenants of ”spectral pitch” to tenants of ”temporal pitch”. Today the terms of the disagreement have shifted, and the disagreement is now between models based on ”pattern matching” (originated by de Boer but already hinted to by Helmholtz) and those based on ”autocorrelation” (originated by Licklider, but already implicit in earlier work). Despite the disagreements, there are deep connections between these various theories of pitch, and between them and the many methods that have been proposed for the artificial equivalent of pitch perception: fundamental frequency estimation. Using a historical perspective I will try to make apparent these relations between models and methods. The aim is to help us go beyond the controversies and develop a better understanding of how we perceive pitch.