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Many natural signals, including environmental sounds, exhibit scale-invariant statistics: their structure is repeated at multiple scales. Such scale-invariance has been identified separately across spectral and temporal correlations of natural sounds (Clarke and Voss, 1975; Attias and Schreiner, 1997; Escabi et al., 2003; Singh and Theunissen, 2003). Yet the role of scale-invariance across overall spectro-temporal structure of the sound has not been explored directly in auditory perception. Here, we identify that the acoustic waveform from the recording of running water is a self-similar fractal, exhibiting scale-invariance not only within spectral channels, but also across the full spectral bandwidth. The auditory perception of the water sound did not change with its scale. We tested the role of scale-invariance in perception by using an artificial sound, which could be rendered scale-invariant. We generated a random chirp stimulus: an auditory signal controlled by two parameters, Q, controlling the relative, and r, controlling the absolute, temporal structure of the sound. Imposing scale-invariant statistics on the artificial sound was required for its perception as natural and water-like. Further, Q had to be restricted to a specific range for the sound to be perceived as natural. To detect self-similarity in the water sound, and identify Q, the auditory system needs to process the temporal dynamics of the waveform across spectral bands in terms of the number of cycles, rather than absolute timing. We propose a two-stage neural model implementing this computation. This computation may be carried out by circuits of neurons in the auditory cortex. The set of auditory stimuli developed in this study are particularly suitable for measurements of response properties of neurons in the auditory pathway, allowing for quantification of the effects of varying the statistics of the spectro-temporal statistical structure of the stimulus.

Auditory Perception of Self-Similarity in Water Sounds