Academic journal article Perception and Psychophysics

Perceiving the Numerosity of Rapidly Occurring Auditory Events in Metrical and Nonmetrical Contexts

Academic journal article Perception and Psychophysics

Perceiving the Numerosity of Rapidly Occurring Auditory Events in Metrical and Nonmetrical Contexts

Article excerpt

Experiment 1 determined the fastest tempo at which participants could tap in synchrony with every nth tone (n = 2 to 9) in an isochronous sequence. Tapping was difficult with every 5th or 7th tone but easy with every 2nd, 4th, or 8th tone, suggesting that evenly divisible groups of n tones are automatically subdivided into equal groups of 2 or 3-a form of auditory stabilizing that generates metrical hierarchies commonly found in Western music. Experiments 2 and 3 sought evidence of subitizing and subdivision in timed explicit enumeration of short, rapidly presented tone sequences (n = 2 to 10). Enumeration accuracy decreased monotonically with n. Response time increased monotonically up to n = 5 or 6, but less between 2 and 3 than between 3 and 4. Thus, a single group of 2 or 3 tones perhaps can be subitized, but subdivision of larger groups into subgroups of 2 or 3 tones seems to be specific to a repetitive, metrical context.

Rate Limits of Accurate Numerosity Perception

The perception of numerosity is a topic of great scientific interest and has generated a considerable amount of research, especially in recent years (e.g., Barth, Kanwisher, & Spelke, 2003; Dehaene, 1997; Feigenson, Dehaene, & Spelke, 2004; Gallistel & Gelman, 1992, 2000; Lipton & Spelke, 2003; Whalen, Gallistel, & Gelman, 1999). One important issue being discussed in this literature is the extent to which numerical cognition in adult humans relies on nonverbal magnitude representations of number such as those used by infants and nonhuman animals. There is considerable evidence in favor of a dual number system in adult humans, with the discrete verbal counting system being overlaid upon and mapped onto a phylogenetically older analog system (Gallistel & Gelman, 1992, 2000). When people are prevented from using the verbal system, they rely on the nonverbal one, and verbal counting may always be accompanied by nonverbal representations. Most of the relevant research has been concerned with the perception of visual objects presented simultaneously, or sometimes sequentially. Relatively few studies have dealt with perceiving the number of sequential auditory events, although this is important in music performance.

For adults, counting successive objects or events is a fairly trivial task, unless time limits or other constraints are imposed. Therefore, research on numerosity perception usually concerns situations in which outright counting is difficult. In visual studies, simultaneous displays of multiple objects are presented briefly to prevent sequential counting. When presentation is sequential but in a fixed position, a high presentation rate is used to prevent participants from simply keeping count. The maximal event rate at which accurate enumeration is still possible is of theoretical interest: Does it depend on the maximal rate at which number words can be uttered or imagined? Are there differences between auditory and visual presentation? Such differences seem unlikely, if speech production is the limiting factor.

In a pair of classic studies, Taubman (1950a, 1950b) presented sequences of 1-10 short tones or light flashes at various constant interonset intervals (IOIs), and participants had to report the number of events. In the auditory study, performance was found to be perfect at an IOI of 125 msec. Errors, mainly underestimations, began to emerge at 100 msec and increased as the IOI was made even shorter. In the visual study, performance was perfect at an IOI of 500 msec. Errors, again primarily underestimations, began to emerge at 333 msec (the next shortest IOI used) and increased further at even shorter IOIs. These results reveal a striking difference in favor of the auditory modality. Massaro (1976) gives the fastest rate of subvocal (i.e., inner) speech as 6 syllables per second (IOI =167 msec), which is in accord with empirical data by Landauer (1962) for reciting or imagining the English number words for 1-10. …

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