Invariants in auditory frequency relations

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Abstract
A group theoretic description of auditory frequency is shown to have important implications for understanding invariants in sound patterns. Frequency can be mathematically conceived in terms of a logarithmic spiral which involves two generative group parameters. The spiral representation not only underlies the logarithmic relationship between the frequency of a tone and its stated musical pitch but it affords an objective basis for invariants that summarize other well‐known auditory relationships including distinctions which involve different tuning systems. The spiral analysis represents a new and potentially useful tool for describing auditory invariants with important implications for emerging theories of music perception and issues in psychophysical scaling of tonal patterns.

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