A harmonious note on pitch: Scales of pitch derived from subtractive model of comparison agree with the musical scale

Abstract

Subjects judged "ratios" and "differences" in pitch between pairs of tones that varied in frequency. Half of the subjects listened to stimuli that ranged from 191 to 844 Hz; the other half received a range that varied from 191 to 3740 Hz. For both ranges, the rank orders of judgments in the two tasks were essentially the same. If subjects actually use ratio and difference operations on the same scale values, the factorial design should yield different rank orders for each task. Instead, it was concluded that subjects use the same comparison operation for both tasks but map the subjective comparisons to overt responses differently for each dependent variable. If the comparison operation is subtraction, the data are consistent with the hypothesis that subjective pitch is a log function of frequency; that is, differences on the musical scale predict both the "ratio" and "difference" judgments. This result may resolve the previous discord between musicians and psychophysical psychologists on the subjective scaling of pitch. © 1984 Psychonomic Society, Inc.