Perceiving and Distinguishing Simple Timespan Ratios without Metric Reinforcement

This study is an investigation of whether we can perceive proportionally consonant timespan ratios as instances of rhythmic regularity, particularly when they are not reinforced by traditional meter. ‘‘Consonant ratio’’ refers here to any small-sum ratio like 1:1, 1:2, or 1:3, affecting a successive pair of interonset intervals (hereafter ‘‘timespans’’); as opposed to larger-sum ratios like 3:4, 5:9, and 4:11. I will refer to rhythms with an abundance of consonant ratios as ‘‘simple,’’ and to those with a lack of such consonance as ‘‘complex. ’’ (With these terms, I do not mean anything inherent about perception or experience; they are intended only as descriptions of a rhythm’s quantifiable features.) My basic goal is to know how ratio characteristics will affect our sense of regularity in a musical passage, independent of the influence of meter. But ‘‘metric hierarchy’’ and ‘‘timespan ratio characteristics’’ are conceptually entangled, and that poses a difficult challenge. The present study therefore aims to sort through these practical and conceptual entanglements, outline an experimental approach to the problem, and discuss the data that we have collected in one version of that experimental approach. An ability to distinguish timespan ratio characteristics in the absence of meter would carry important implications for the study of expectancy – a key concept in most recent research in rhythm perception. Expectancy – a perceiver’s expectation of events in the future, based on patterns in the past – is often attributed to both proportional simplicity and metric hierarchy (Lerdahl & Jackendoff, 1983; Jones & Boltz, 1989; Desain 1992), but the two factors are not normally teased apart. In some theoretical approaches, the distinction of regular from irregular rhythm depends on whether events establish consonant metric patterns as cues for the expectation of a larger structure. Following Desain’s (1992) study, a number of recent experiments have confirmed that expectancy is a distinct and important outcome of metric regularity (Large & Jones, 1999; Timmers et al., 2000). Hasty’s (1997) concept of durational projection further extends this notion, beyond the obvious level of meter, and into middleground aspects of musical time. In these teleological models of rhythm, however, an opposing question arises: can there also be ‘‘individuated’’, or ‘‘metrically independent’’ objects of temporal experience, that determine anything about the way we hear rhythm? An unmetered timespan ratio is made of only three events, bracketing two timespans; the percept of that ratio is absent until the second timespan has been completed, at the moment of the third event. If a timespan ratio has any distinct quality – for example, its perceived simplicity or complexity – then that quality could be considered a property of a single timepoint. Thus, if we are capable of distinguishing a ‘‘simple’’ additive timespan ratio from a complex one, then we will have to account for that distinction in an out-of-time perceptual mode. In that case it may be necessary to supplement our expectancybased theories of rhythm with some notion of a reducible, retrospective, and ‘‘collapsible’’ temporality.