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For both the German and Turkish rhythm samples described above, the relative frequencies by which events occur at specific metrical phases are used to construct two sets of expectation templates. As the rhythm spaces explored in simulation consist of three-interval patterns, each template also reflects an expected three-interval pattern, but is derived from interval patterns within a metrical cycle. At time t, the observer infers a distribution over possible generating templates m. This distribution starts with the prior distribution and is updated based on event observations at each dt time step.

In Experiment 3 we simulate enculturated bias in iterated reproduction of rhythms by listeners from several musical cultures, using three-interval rhythms from the same rhythm space as Experiment 2 24, 25. In the Discussion section we highlight the contributions of pPIPPET to cross-cultural research in musical rhythm perception and expand on the proposed implementation of PIPPET in the brain. Behavioral studies examining phenomena such as categorical rhythm perception through entrainment are limited by practical constraints to studying two- or three-interval rhythmic patterns. In the present work, we derived expectation templates from empirical samples of musical rhythms, according to the relative likelihood of different onset patterns within a metrical cycle (i.e. metrical phase).

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Rhythms related by small-integer-ratios (integers less than 3) are marked with crosses and labeled. B) Colors correspond to cyclic permutations of the pattern which has been inferred (i.e. the expectation template which maximizes pm), and transparency the entropy. This figure, and other ternary plots presented in this work, were made using the python-ternary package 47. A listener’s event-based expectations in PIPPET are modeled by positing that they expect events to occur as an inhomogenous point process, with probability λ(φ), referred to as an expectation template. This consists of a summation of Gaussian distributions, each centered around a mean phase at which an event is expected, and scaled according to expectation strengths and precisions.