Abstract
Psychophysical laws quantitatively relate perceptual magnitude to stimulus intensity. While most people have accepted Stevens’s power function as the psychophysical law, few believe in Fechner’s original idea using just-noticeable-differences (jnd) as a constant perceptual unit to educe psychophysical laws. Here I present a unified theory in hearing, starting with a general form of Zwislocki’s loudness function (1965) to derive a general form of Brentano’s law. I will arrive at a general form of the loudness-jnd relationship that unifies previous loudness-jnd theories. Specifically, the “slope,” “proportional-jnd,” and “equal-loudness, equal-jnd” theories, are three additive terms in the new unified theory. I will also show that the unified theory is consistent with empirical data in both acoustic and electric hearing. Without any free parameters, the unified theory uses loudness balance functions to successfully predict the jnd function in a wide range of hearing situations. The situations include loudness recruitment and its jnd functions in sensorineural hearing loss and simultaneous masking, loudness enhancement and the midlevel hump in forward and backward masking, abnormal loudness and jnd functions in cochlear implant subjects. Predictions of these loudness-jnd functions were thought to be questionable at best in simultaneous masking or not possible at all in forward masking. The unified theory and its successful applications suggest that although the specific form of Fechner’s law needs to be revised, his original idea is valid in the wide range of hearing situations discussed here.
Highlights
Psychophysical laws attempt to relate the amplitude of a physical stimulus to its perceived magnitude, such as loudness as a function of sound pressure or brightness as a function of luminance
Was Fechner’s logarithmic law replaced by Stevens’s power law or L = Iθ, where θ is a constant (Stevens, 1961), his general approach was questioned due to failure to integrate the jnd functions of two different sounds to predict their respective loudness functions
Simultaneous masking elevates a pure tone’s threshold and affects its loudness perception, similar to loudness recruitment in sensorineural hearing loss. Both loudness balance and intensity discrimination functions have been measured in the same group of listeners for pure tones in quiet and in simultaneous noise maskers (Houtsma et al, 1980; Rankovic et al, 1988; Schlauch et al, 1995)
Summary
The situations include loudness recruitment and its jnd functions in sensorineural hearing loss and simultaneous masking, loudness enhancement and the midlevel hump in forward and backward masking, abnormal loudness and jnd functions in cochlear implant subjects. Predictions of these loudness-jnd functions were thought to be questionable at best in simultaneous masking or not possible at all in forward masking. The unified theory and its successful applications suggest that the specific form of Fechner’s law needs to be revised, his original idea is valid in the wide range of hearing situations discussed here
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