Date of Degree
J. Donald Harris
Speech and Hearing Science
Determination of loudness scales for 1000 Hz stimuli by conventional ratio scaling methods have yielded loudness functions which grow as approximately the 0.54 power of sound pressure. Thus, two-fold loudness differences are equivalent to approximately 10 dB across the auditory continuum. The unidimensional representation of loudness ss a power function of sound intensity implies that if A is twice as loud as B, which, in turn, is twice as loud C, the A will be four times as loud as C. In order to test this implication across the auditory continuum loudness ratio estimates were obtained from four 7x7 matrices of 1000 Hz stimuli with differing interstimulus spacings and ranges.
Two types of data analysis were used in comparing the obtained ratio estimate results with those implied by the 10 dB rule. The first was a multidimensional representation of the d8ta based upon Shepard's Analysis of Proximities [R. N. Shepard, Psychometrika, 27, 125-14-0, 210-24-6 (1962)]. From these analyses simple two-dimensional configurations were found which adequately represented the data. In general, these configurations indicated that the obtained estimates did not conform to the configurations implied by the 10 dB rule, i.e., a straight line in space, but curved upwards indicating increasing non-additivity with increased inter-stimulus differences. It was further found that as the stimulus range of a matrix decreased, the ratio estimates associated with common stimulus pairs increased.
The second type of analysis was designed to plot the obtained ratio estimate data as a unidimensional function of intensity, which, in turn, would yield linear spatial configurations. The results of this analysis yielded loudness scales which could be directly compared to conventional power functions. It was found that for two matrices (B and C) that power functions were obtained, although the slope for Matrix C (15 dB range) was high relative to the conventional scale, while the slope of Matrix B (30 dB range) was quite similar to the conventional function. With a 60 dB stimulus range (Matrix A) a power function was not obtained.
Loudness growth was further investigated with other than moderate to intense 1000 Hz tones. Ratio estimates were obtained from four new matrices which contained either 250 Hz tones, white-noise, or low sensation level 1000 Hz and 4-000 Hz tones. Each of these matrices was analyzed by the Analysis of Proximities, and the obtained configurations compared to the results implied from earlier findings concerning the stimuli of interest.
A monaural test of loudness recruitment was suggested utilizing ratio estimates combined with the Analysis of Proximities.
Richards, Alan M., "Non-Metric Scaling of Loudness" (1971). CUNY Academic Works.