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.