In a previous study, we presented psychophysical evidence that time-shrinking (TS), an illusion of time perception that empty durations preceded by shorter ones can be conspicuously underestimated, gives rise to categorical perception on the temporal dimension (Sasaki, Nakajima, & ten Hoopen, 1998). In the present study, we first survey studies of categorical rhythm perception and then describe four experiments that provide further evidence that TS causes categorical perception on the temporal dimension. In the first experiment, participants judged the similarity between pairs of /t1/t2/ patterns (slashes denote short sound markers delimiting the empty time intervals t1 and t2). A cluster analysis and a scaling analysis showed that patterns liable to TS piled up in a 1:1 category. The second and third experiments are improved replications in which the sum of t1 and t2 in the /t1/t2/ patterns is kept constant at 320 ms. The results showed that the 12 patterns /115/205/, /120/200/, . . ., /165/155/, /170/150/ formed a 1:1 category. The fourth experiment utilizes a cross-modality matching procedure to establish the subjective temporal ratio of the /t1/t2/ patterns and a 1:1 category was established containing the 11 patterns /120/200/, /125/195/, . . ., /165/155/, /170/150/. On basis of these converging results we estimate a domain of perceived 1:1 ratios as a function of total pattern duration (t1 + t2) between 160 and 480 ms. We discuss the implications of this study for rhythm perception and production.

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.

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.

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.

Pitch circularity as found in Shepard tones was examined by using complex tones that had various degrees of exactness in their spectral periodicities on the logarithmic frequency dimension. This dimension was divided into periods of 1400 cents by tone components, and each period was subdivided into two parts of a fixed ratio of 700:700, 600:800, 550:850, 500:900, 450:950, 400:1000, or 0:1400. Subjects made paired comparison judgments for pitch. When the subdividing ratio was 0: 1400 or 400:1000, the subjects responded to the spectral periodicity of 1400 cents, and, when the ratio was 700:700 or 600:800, they responded to the periodicity of 700 cents. Some seemingly intermediate cases between these two extremes or some qualitatively different cases were obtained in the other conditions. As we have asserted before, the human ear appears to detect a global pitch movement when some tone components move in the same direction by similar degrees on the logarithmic frequency dimension.

A new type of complex tone that demonstrates pitch circularity is described. For such tones, the spectral envelope is trapezoidal on the coordinates of logarithmic frequency and logarithmic amplitude, and remains constant. The components of each tone form a major triad within each octave. The component frequencies were increased by steps of 1/10 octave from tone to tone, until the first tone was obtained again. According to our paired comparison experiments for pitch, which were analyzed using the multidimensional scaling technique, two kinds of pitch circularities appear. One group of subjects shows a pitch circularity corresponding to the exact spectral periodicity of an octave, and the other group a circularity corresponding to the roughly viewed spectral periodicity of 1/3 octave. The human ear seems to detect a global pitch movement when some spectral components move in the same direction by similar degrees on the logarithmic frequency dimension.