Cognitive Constraints on Metric Systems: Some Observations and Hypotheses

TLDR

Meter is a stable, recurring pattern of hierarchically structured temporal expectations, distinct from the raw interonset interval pattern in the musical surface. The paper examines how rhythmic perception and performance studies inform musical meter, hypothesizing that beat perception requires concurrent subdivision and explaining expressive differences between duplets and triplets across tempos. It reviews subjective rhythmization, spontaneous tempo, pulse perception, and durational discrimination studies, and discusses systematic relationships between tempo and larger metrical systems. Musical meter is bounded between roughly 100 ms and 6 s, with critical thresholds at ~200–250 ms, 500–700 ms, and 1.5–2.0 s, and tempo choice systematically limits the available metric patterns for listeners.

Abstract

This paper is a music-theoretic discussion of various studies on rhythmic perception and performance and their ramifications for discussions of musical meter. Meter is defined as a stable and recurring pattern of hierarchically structured temporal expectations. Metrical patterns, although related to the pattern of interonset intervals present in the musical surface, are distinct from that pattern. Studies of subjective rhythmization, spontaneous tempo, pulse perception, durational discrimination, and so forth are discussed with respect to their implications for meter. Not only do there seem to be upper and lower bounds for musical meter (from ≅100 ms to ≅6 s, depending on context), but there also appear to be important thresholds within this range (around 200–250 ms, 500–700 ms, and 1.5–2.0 s). Interactions between beats (i.e., interonset intervals between expectancies occurring at the rate perceived as the tactus), beat subdivision, and changes in tempo are discussed, and it is hypothesized that beat perception may require (at least potentially) the perception of a concomitant level of subdivision. The interactions between beat interonset interval, subdivision interonset interval, and various thresholds may also explain (in part) some of the differences in the expressive and/or motional character of rhythmic figures (duplets versus triplets) at different tempos. Last, a broader discussion of systematic relationships in larger metrical systems with respect to tempo is given. It is shown that the choice of tempo systematically constrains the number and kind of metric patterns that are available to the listener.