The perceptual relevance of balance, evenness, and entropy in musical rhythms

Abstract

There is an uncountable number of different ways of characterizing almost any given realworld stimulus. This necessitates finding stimulus features that are perceptually relevant -that is, they have distinct and independent effects on the perception and cognition of the stimulus. Here, we provide a theoretical framework for empirically testing the perceptual relevance of stimulus features through their association with recognition, memory bias, and aesthetic evaluation. We deploy this framework in the auditory domain to explore the perceptual relevance of three recently developed mathematical characterizations of periodic temporal patterns: balance, evenness, and interonset interval entropy. By modelling recognition responses and liking ratings from 177 participants listening to a total of 1,252 different musical rhythms, we obtain very strong evidence that all three features have distinct effects on the memory for, and the liking of, musical rhythms. Interonset interval entropy is a measure of the unpredictability of a rhythm derived from the distribution of its durations. Balance and evenness are both obtained from the discrete Fourier transform (DFT) of periodic patterns represented as points on the unit circle, and we introduce a teleological explanation for their perceptual relevance: the DFT coefficients representing balance and evenness are relatively robust to small random temporal perturbations and hence are coherent in noisy environments. This theory suggests further research to explore the meaning and relevance of robust coefficients such as these to the perception of patterns that are periodic in time and, possibly, space.

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“…For convenience, we denote with p conditions that show "significant" tracking of periodicities at an a = 0.05 level (evidence ratios . 19; see Milne and Herff, 2020). The results of Table 2 are derived by performing the hypothesis tests shown in Table 3 on the fitted model shown in Table 4.…”

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“…• Evidence ratios of 10-30 (or of 1/10-1/30) are "strong" evidence for the tested hypothesis • Evidence ratios above 30 (or of 1/30 and beyond) are "very strong" evidence for the tested hypothesis As explained in Milne and Herff (2020) and Escudero et al, (2020), an evidence ratio of 19 is roughly similar to an alpha of .05 in NHST. Hence, we report only those effects with an evidence ratio of 19 or above unless specified otherwise.…”

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“…For convenience, we denote effects with "*" as those which can be considered 'significant' at an a = .05 level. This corresponds to odds ratios >= 19 (odds 95/5 = 19) (Milne & Herff, 2020). show a higher intercept at the beginning of the experiment compared to older participants.…”