Intensity discrimination as the driving force for loudness. Application to pure tones in quiet

Loudness functions and their associated neural-count functions are derived for steady-state tones at 250 and 1000 Hz from measurements of intensity discrimination obtained under gated and continuous conditions. The calculations are based on a multichannel generalization of the McGill-Goldberg counting model [J. Acoust. Soc. Am. 44, 576-581 (1968)]. Using the data for just noticeable differences (jnd) in intensity as input, the generalized version gives an integral relation between the neural-count function N(x) and the intensity-jnd function, where x = I/I0 and I0 is the reference intensity. Loudness functions are generated through the prescription L(x) = AN(x)--B. To determine how the detailed shapes of the intensity-jnd functions affect the form of the loudness function within the model, integration was performed over the intensity-jnd functions with and without a power-function approximation. Over a range of intensity levels from 20-95 dB, the best agreement between the calculated and measured loudness functions is obtained from the unaltered intensity-jnd functions. Consistent with psychophysical evidence and several models of intensity coding, the results predict that the output of the whole auditory nerve is unnecessary to maintain the large dynamic range observed for loudness and intensity discrimination.