Cumulation of DL's for Intensity Change at Low Sensation Levels

Data which appear in the literature on normal DL's for intensity change lead to the hypothesis that, for pure tones through a sensation level of 40 dB, a linear function relates 1/jnd to the sensation level. A nonlinear difference equation expressing this hypothesis is developed here. A resultant formula allows the number of jnd's which cumulate within a range of sensation levels to be compared, provided one knows the DL magnitudes at the two limits of that range. The adequacy of this procedure was tested on six normal hearers. It was found that the number of jnd's which each subject exhibited when DL's were successively cumulated experimentally at 1000 and 4000 cps corresponded to within an average error of 4.0% to the number predicted from the formula. The maximum single error of prediction was 6.6%.