Rhythmic complexity and predictive coding: a novel approach to modeling rhythm and meter perception in music

Abstract

Musical rhythm, consisting of apparently abstract intervals of accented temporal events, has a remarkable capacity to move our minds and bodies. How does the cognitive system enable our experiences of rhythmically complex music? In this paper, we describe some common forms of rhythmic complexity in music and propose the theory of predictive coding (PC) as a framework for understanding how rhythm and rhythmic complexity are processed in the brain. We also consider why we feel so compelled by rhythmic tension in music. First, we consider theories of rhythm and meter perception, which provide hierarchical and computational approaches to modeling. Second, we present the theory of PC, which posits a hierarchical organization of brain responses reflecting fundamental, survival-related mechanisms associated with predicting future events. According to this theory, perception and learning is manifested through the brain's Bayesian minimization of the error between the input to the brain and the brain's prior expectations. Third, we develop a PC model of musical rhythm, in which rhythm perception is conceptualized as an interaction between what is heard ("rhythm") and the brain's anticipatory structuring of music ("meter"). Finally, we review empirical studies of the neural and behavioral effects of syncopation, polyrhythm and groove, and propose how these studies can be seen as special cases of the PC theory. We argue that musical rhythm exploits the brain's general principles of prediction and propose that pleasure and desire for sensorimotor synchronization from musical rhythm may be a result of such mechanisms.

Keywords: meter; pleasure; predictive coding; rhythm; rhythmic complexity.

FIGURE 1

Hierarchical model of 4/4 meter. Each metric level (or value) is recursively subdivided into equally spaced parts (or values) at the level below, determining the metric salience of positions within the metric framework. The higher the level in the hierarchy, the more salient the position in the meter. Numbers designate serial positions within the meter, at 16th note resolution. The dashed line specifies the level of the tactus.

FIGURE 2

Predictive coding of music. The experience and learning of music takes place in a dynamic interplay between anticipatory structures in music, such as the build-up and relief of tension in rhythm, melody, harmony, form and other intra-musical features on one side, and the predictive brain on the other. The real time brain model is dependent on cultural background, personal listening history, musical competence, context (e.g., social environment), brain state (including attentional state and mood), and innate biological factors. The brain is constantly trying to minimize the discrepancy between its interpretation model and the musical input by iteratively updating the real time brain model (or prior) by weighting this model with the likelihood (musical input) through Bayes’ theorem. This leads to a constantly changing musical experience and long-term learning.

FIGURE 3

Cross-rhythms. (A) Three-beat triple meter with four-beat pattern as counter-rhythm. (B) Four-beat duple meter with three-beat counter-rhythm. Dots below the staves designate the tactus. (C) The bistable percept of Rubin’s vase.

FIGURE 4

Areas of activity in the brain during tapping to polyrhythm. Activations of Brodman’s areas (BA) 40 and 47 in the parietal and prefrontal cortices, respectively, as associated with tapping to polyrhythms. See Vuust et al. (2006) for more detail.