Scaling loudness over short ranges: a reply to Poulton.

Abstract

Poulton (1984) has recently reopened an old debate about the form of the function relating loudness to the sound-pressure level of the signal. Despite the large body of evidence developed on this subject by S. S. Stevens and his associates showing that a power function provides a good description of loudness judgment both for tones and, to a less exact degree, for noise, Poulton now raises again the Fechnerian idea that loudness is proportion~l to the logarithm of sound intensity or, in the terms of hIS title, that loudness judgments are linear with decibels. In our view, however, the evidence offered to support this claim is unconvincing. Two sets of data are presented. One set, published for the first time, concerns numerical judgments of loudness for a set of six intensities of white noise ranging from 80 to 85 dB(A) in steps of 1 dB. After two repetitions, intended to familiarize the subjects with the stimulus set, each stimulus was presented following the 80-dB stimulus, designated as the standard and assigned the value of 10 on the scale of loudness. The set was presented to all subjects in the same fixed irregular order three times in succession. Before considering the results Poulton obtained, it is useful to consider what outcomes are to be expected given both the power law and the logarithmic rule proposed by Poulton. First, assume a power function with an exponent of 0.7 (a value consistent with both Poulton's data and those reported by R. Teghtsoonian and M. Teghtsoonian [1978] for the same range of intensities, but using 3-kHz tones). If the standard is called 10, the succeeding five should be called 10.84, 11.75, 12.74, 13.80, and 14.96, and since, as Baird and Noma (1975), as well as Poulton and others, have noted, unpracticed subjects are inclined to restrict themselves to integral values in the region of numbers near 10, the expected judgments for the full set of six are simply 10, 11, 12, 13, 14, and 15. By comparison, Poulton's proposal that the average subject adds one unit of loudness for every decibel ~e~ns that beginning with a standard called 10, the remammg values will be called 11, 12, 13, 14, and 15. It belabors the obvious to note that the two predictions are identical. The numerical example simply makes concrete a well-