A Scale for the Measurement of the Psychological Magnitude Pitch

Abstract

A subjective scale for the measurement of pitch was constructed from determinations of the half-value of pitches at various frequencies. This scale differs from both the musical scale and the frequency scale, neither of which is subjective. Five observers fractionated tones of 10 different frequencies at a loudness level of 60 db. From these fractionations a numerical scale was constructed which is proportional to the perceived magnitude of subjective pitch. In numbering the scale the 1000-cycle tone was assigned the pitch of 1000 subjective units (mels). The close agreement of the pitch scale with an integration of the differential thresholds (DL's) shows that, unlike the DL's for loudness, all DL's for pitch are of uniform subjective magnitude. The agreement further implies that pitch and differential sensitivity to pitch are both rectilinear functions of extent on the basilar membrane. The correspondence of the pitch scale and the experimentally determined location of the resonant areas of the basilar membrane suggests that, in cutting a pitch in half, the observer adjusts the tone until it stimulates a position half-way from the original locus to the apical end of the membrane. Measurement of the subjective size of musical intervals (such as octaves) in terms of the pitch scale shows that the intervals become larger as the frequency of the mid-point of the interval increases (except in the two highest audible octaves). This result confirms earlier judgments as to the relative size of octaves in different parts of the frequency range.