Several studies have shown that category scales are nonlinearly related to ratio scales of subjective magnitude. A variability model has been proposed previously to account for this departure from linearity. This article examines the model in the light of the empirical relations that enter into it: the ratio scale of subjective magnitude, the corresponding category scale, and the variability of judgments in both physical and psychological units. These relations are determined, through repeated measurement with a single observer, for the psychological continuum, loudness, and its inverse, softness. The ratio scales are shown to be reciprocals, and the category scales complements. The category scale of softness is more concave downward, relative to its magnitude scale, than is the category scale of loudness. This outcome is also derived mathematically from the empirical equations relating the four scales to physical magnitude. Variability is found to increase with increasing stimulus magnitude at the same rate for both loudness and softness productions, expressed either in physical units or in psychological units. Hence, the variability model is found not to accord with the observed difference in concavity between softness and loudness category scales relative to their respective psychological magnitude scales.


The following article appeared in J. Acoust. Soc. Am. Volume 35, Issue 12, pp. 1953-1961 (December 1963) and may be found at http://dx.doi.org/10.1121/1.1918866


variability hypothesis, ratio scale, category scale, softness

Subject Categories

Voice, Loudness, Hearing


Psychology | Speech and Hearing Science


Acoustical Society of America

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©1963 Acoustical Society of America

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