One might perceive that two tones start simultaneously when they start with a small onset asynchrony. We refer to such a small range of asynchrony as a perceptual simultaneity range (PSR). The PSR for various combinations of two tones’ frequencies has been measured by the authors. The results were as follows: the PSR follows the V-curve as a function of the frequency separation of two tones. The shape of the V-curve depends on the frequency region of two tones. However, if the frequency separation is converted into the auditory peripheral distance (Bark), the breakpoint and the left line of the V-curve overlap irrespective of the two-tones’ frequency region. This study aimed to present an approximate formula of the PSR V-curve, as a psychoacoustic function. The constraints of the formulation are the following. The V-curve consists of two segmented lines along the Bark distance. The breakpoint is located at 0.5 Bark, as estimated by previous studies. The left line of the V-curve is irrelevant to the frequency region, while the right line of the V-curve is affected by the frequency region. Consequently, the approximate formula was obtained as equations in two cases below and above the Bark distance = 0.5 Bark.
Satoshi Okazaki (Wed,) studied this question.