Integration of Energy at Threshold with Gradual Rise-Fall Tone Pips

Short-tone thresholds were tested with an array of ten stimuli so chosen to incorporate a wide range of parameter variations. It was shown that the average data could be very well fitted with the function (I−I0)T = k, where I is the stimulus intensity at threshold, I0 and k are constants, while T is the equivalent stimulus duration. This equivalent duration was derived for gradually rising and falling tone pips, and was shown to be computable as T = 2r/3+P, where r is the rise-fall time and P is the peak time. It was shown that the above model predicted individual thresholds with considerably greater accuracy than other alternative descriptions. The theoretical implications of the model are the existence of a definite lower limit of stimulus intensity (I0), below which the stimulus power does not contribute toward threshold recognition, and the constancy of the effective utilizable energy at threshold (k). This latter quantity did not vary more than 0.5 dB from stimulus to stimulus.