Syncopation as Probabilistic Expectation: Conceptual, Computational, and Experimental Evidence.

Abstract

Definitions of syncopation share two characteristics: the presence of a meter or analogous hierarchical rhythmic structure and a displacement or contradiction of that structure. These attributes are translated in terms of a Bayesian theory of syncopation, where the syncopation of a rhythm is inferred based on a hierarchical structure that is, in turn, learned from the ongoing musical stimulus. Several experiments tested its simplest possible implementation, with equally weighted priors associated with different meters and independence of auditory events, which can be decomposed into two terms representing note density and deviation from a metric hierarchy. A computational simulation demonstrated that extant measures of syncopation fall into two distinct factors analogous to the terms in the simple Bayesian model. Next, a series of behavioral experiments found that perceived syncopation is significantly related to both terms, offering support for the general Bayesian construction of syncopation. However, we also found that the prior expectations associated with different metric structures are not equal across meters and that there is an interaction between density and hierarchical deviation, implying that auditory events are not independent from each other. Together, these findings provide evidence that syncopation is a manifestation of a form of temporal expectation that can be directly represented in Bayesian terms and offer a complementary, feature-driven approach to recent Bayesian models of temporal prediction.