The category of 1:1 ratio caused by assimilation of two neighboring empty time intervals

We investigated the perception of temporal patterns of two neighboring empty time intervals, t₁ and t₂, in this order. In a previous study, we reported that bilateral assimilation took place during t₁ and t₂, as well as unilateral assimilation. [Miyauchi, R. & Nakajima, Y. (2005). Bilateral assimilation of two neighboring empty time intervals. Music Perception, 22, 411-424]. The points of subjective equality (PSEs) of t₁ and t₂ approached each other. We speculated that these temporal patterns would yield nearly 1:1 ratios perceptually despite the change in the physical temporal ratio between t₁ and t₂. However, we were uncertain whether these temporal patterns were really perceived as having 1:1 ratios. In the present study, we conducted three experiments. In Experiment 1, we measured subjective similarities of two temporal patterns and analyzed the results by hierarchical cluster analysis and multidimensional scaling. The temporal patterns, where the physical ratio between t₁ and t₂ was varied systematically, were divided into three clusters, and one cluster consisted of the temporal patterns within a range of -80 ms ≦ t₁ - t₂ ≦ 60 ms. This cluster was asymmetric in time around 0 ms. In Experiments 2 and 3, we presented each of the temporal patterns in isolation. We asked the participants whether the subjective durations of t₁ and t₂ were the same or not. When the total duration was equal to or less than 540 ms, the range in which the participants perceived the neighboring durations as equal corresponded to the asymmetric range established in our previous experiments. When the total duration was 720 ms, a different tendency appeared. The results indicated that bilateral assimilation and unilateral assimilation indeed contributed to the formation of the asymmetric 1:1 category when the total duration was equal to or shorter than 540 ms.