Deriving the Weber fraction from loudness functions

In a previous paper [W. S. Hellman and R. P. Hellman, J. Acoust. Soc. Am. 91, 2380(A) (1992)], Weber fractions for intensity discrimination were derived from their concomitant pure tone loudness functions in normal hearing. The calculational procedure employed a generalized McGill–Goldberg model. This work extends these findings to more frequencies, to broadband noise, to tones masked by high-pass noise, and to forward masking. Weber functions generated by the model are compared to empirical data for the various experimental conditions and stimuli. In all cases, the calculated Weber functions capture the overall shape of the measured intensity-jnd data over a wide stimulus range. Not only does the model produce the near-miss relation for pure tones in quiet, it also predicts Weber’s law for broadband noise, a rising characteristic in the Weber function above 60 dB SPL for a tone in high-pass noise, and the midlevel hump observed in forward masking. These results show that there is sufficient information in the loudness function to recover the associated intensity-jnd function. This implies that loudness is the primary decision variable for intensity discrimination.