Spiral Detection of Periodicity and the Spiral Form of Musical Scales

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Abstract
The purpose of this paper is to suggest that the neural part of the auditory system employs a temporal mechanism, referred to as a spiral processor, to determine whether sounds are periodic, and that this type of mechanism would explain the form of consonance observed in Western music. Pitch is our perception of periodicity in a sound wave, and harmony is the set of rules that explain which pitches go well together. The octave, the diatonic scale and its modes are the basic ingredients of harmony in Western music. For over a hundred years we have known that the logarithmic spiral (base 2) provides a good description of the cyclic aspect of musical scales, that is, the octave. But the implications for the internal structure of the octave, that is the diatonic scale and its two main modes, have largely been ignored. A periodic sound like a musical note generates regular streams of pulses in primary auditory neurones. As these pulse streams flow through the spiral processor they form a pattern of spokes radiating from the centre of the spiral. The shape of the pattern is fixed; the orientation of the pattern determines the pitch. The primary intervals of the diatonic scale are produced by pairs of notes whose main spokes coincide, and the intervals fall naturally into two groups, major and minor.

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