Explaining the deterioration of the relative timing accuracy for across-channel by a simple mathematical model

Abstract

The perceptual simultaneity range, within which two asynchronous pure tones are perceived to start simultaneously, and the gap detection threshold are known to be wide when the frequency separation of the tones is large. It is generally said that the accuracy of the relative timing for different frequency channels deteriorates. However, there is no clear explanation of why such deteriorations are necessary. This study aimed to show that a simple mathematical model leads to the deterioration of relative timing accuracy for two tones with different frequencies. As a result of the calculations, the model simulated the deterioration of the perceptual simultaneity range not only with the increase of the frequency separation but also with the decrease of the frequency region of two tones. The model also simulated the behavior of the gap detection threshold for two different frequencies (across-channel) with its asymmetric deterioration. Further, the model simulated the behavior of the gap detection threshold for two identical frequencies (within-channel). These results suggest that one simple mathematical model may explain the mechanisms underlying perceptual simultaneity, within-channel gap detection, and between-channel gap detection for two tones.