Predicting intensity discrimination from power-law modifications of the loudness function

Several modifications of Stevens’ power law have been introduced to account for the steepening of the loudness function below about 40 dB SPL. The relation between intensity discrimination (ΔI/I) and loudness is determined for three proposed modifications: (a) Ls=K(I−I0)n, (b) Ls=K(In−I0n), and (c) Ls=k([I+cI0]n−[cI0]n), where I0 is the sound intensity at threshold. Below 15 dB SPL Eqs. (a) and (b) generate a rapidly decreasing function for intensity discrimination, whereas the function derived from Eq. (c) rises with a slope of −1 in log–log coordinates. The slope of the measured intensity-discrimination function is compatible with results predicted for pure tones from Eq. (c) but not with those predicted from Eqs. (a) and (b). [Work supported in part by NIH.]