A temporal model of pitch perception based on spiral periodicity detection

Abstract

The logarithmic spiral (base 2) offers a simple passive means of detecting the regularity observed in the streams of nerve pulses produced when phase locked fibers respond to periodic sounds. That is, if time is wrapped into a spiral with time zero at the spiral's origin, then when nerve pulses‐flow outwards along the path of the spiral, the pulses of a regular stream will coalesce onto spokes emanating from the center of the spiral once per cycle. The spoke pattern has a fixed shape and it rotates around the spiral as the periodicity of the pulse stream varies. Secondary units can be used to detect coalescence on spoke patterns with specific orientations and so convert the temporal pitch information into spatial pitch information. The spoke pattern completes one revolution as the pulse rate rises or falls an octave, and the primary intervals of the Just diatonic scale produce the simplest combined spoke patterns. Thus, the logarithmic spiral provides a basis for a temporal model of pitch perception which can also predict musical harmony.