Categorical Rhythm Perception as a Result of Unilateral Assimilation in Time-Shrinking

In previous studies, we established an illusion of time perception that we called time-shrinking: an empty time interval, immediately preceded by a slightly shorter time interval, is underestimated. In the first experiment of the present study, we examined the perceived duration not only of the second interval (t2), but also of the first interval (tl). The empty time intervals tl and t2, making a total duration of 90,180, 360, or 720 ms, were presented such that the time ratio between them changed systematically. The points of subjective equality of tl and t2 were established by the method of adjustment. In the patterns typically susceptible to timeshrinking, that is, in which t2 was underestimated, tl was perceived almost vertically. In the second experiment, listeners had to bisect an empty duration of 180 ms, marked by sound bursts. The bisecting sound marker was positioned closer to the initial marker than to the final one. Thus, tl had to be shorter than t2 in order for a regular pattern to be perceived. In the third experiment, just-noticeable forward and backward displacements of the middle sound marker were measured by a transformed updown method. The prediction that the interval of uncertainty was closer to the initial than to the final sound marker was confirmed. The three experiments demonstrated the existence of unilateral temporal assimilation, and it is argued that this perceptual mechanism causes a category of 1:1 rhythms, despite a considerable change in temporal ratio between two contiguous time intervals.

A New Illusion of Time Perception—II

When one very short empty time interval follows right after another, the second one can be underestimated considerably, but only if it is longer than the first one. We coined the term "time-shrinking" for this illusory phenomenon in our previous studies. Although we could relate our finding to some studies of rhythm perception, we were not able to explain the illusion. The present article presents our attempt to understand the mechanism that causes the time-shrinking. Four experiments are reported. The first one ruled out the possibility that the illusion results from a difficulty in resolving the temporal structure. The second experiment showed that the listener was not inadvertently judging the duration of the first interval instead of that of the second one. In addition, this experiment yielded more information about the time window within which the illusion occurs. The third experiment showed that forward masking of the sound markers, delimiting the empty durations, could not explain the illusion either. Furthermore, this experiment revealed a clue to the mechanism of time-shrinking: competition between expected and observed temporal positions. The fourth experiment further examined the temporal conditions that give rise to the illusion and showed that categorical perception plays a crucial role in the formation of the illusion. In the general discussion, we argue that the illusion is due to an asymmetric process of temporal assimilation.

A New Illusion of Time Perception

When two very short time intervals are presented serially by sound markers (in such a way that they share a common marker) the subject's duration judgments of the second time interval can be affected by the duration of the first interval. Such a conspicuous effect has not been reported in the literature. Standard empty time intervals of 120, 240, 480, and 720 msec were preceded by a neighboring empty time interval of various physical durations, and subjects adjusted a comparison empty time interval to the same subjective duration as these standards. We found clear underestimations of the standard duration when its physical duration was 120 msec. For example, when the preceding duration was 45 msec, the relative underestimation was about 40%. Because such a stable and remarkable underestimation appeared in a very simple situation, this phenomenon may be called a new illusion. Such an illusion did not appear when the time interval to be judged was succeeded by another time interval. At present we cannot explain the illusion, but in the general discussion we attempt to relate it to some findings in rhythm perception.

Ratio Judgments of Empty Durations with Numeric Scales

A study is reported on the perception of empty time intervals marked by auditory signals. Nakajima's supplement hypothesis, which states that the subjective duration of a subjectively empty time interval is proportional to its physical duration plus a constant of ~80 ms, was examined quantitatively. Although this hypothesis has been used to explain various general aspects of time perception, from a global viewpoint, it has lacked the quantitative data necessary to describe the shape of the psychophysical functions mathematically. In the present study, subjects used two positive numbers to estimate the subjective ratio ( m: n) between the durations of two serial or separate empty intervals. The psychophysical functions for empty durations 50–600 ms long could be approximated by a straight line with a positive y-intercept, as predicted by the hypothesis. The effective range of the hypothesis could be extended to ~1200 ms. A power function (without any modifications) also gave good approximations. The reliability and validity of the supplement hypothesis are discussed.

A Model of Empty Duration Perception

An attempt to construct a general theory of duration perception is presented. First, four experiments are reported in which the supplement hypothesis, on the relation between two or three empty durations, was examined: the subjective duration of a subjectively empty time interval is directly proportional to its physical duration plus a constant of ~ 80 ms. This hypothesis could be applied to the ratio judgments of auditorily marked empty durations between 40 and 600 ms given serially. It could also explain the discrepancies between musically notated rhythms and the corresponding physical performed rhythms in very simple rhythm patterns consisting of three tones. Next, three earlier experiments on discriminations of empty durations marked by sound bursts were also reanalyzed. Within the range 40–600 ms, the absolute just noticeable difference of an empty duration was almost directly proportional to the standard duration plus a constant of about 80 ms. If the supplement hypothesis is accepted, this means that the relative just noticeable difference of the subjective duration was constant. Finally, the processing time hypothesis is presented: subjective duration is directly proportional to the physical time required to process the given empty duration. This processing is considered to begin with the detection of the first marker, and to end ~ 80 ms after the detection of the second marker.