Scaling of Pitch Intervals

Abstract

A literature review showed that in bisecting a musical interval Ss tend to yield the arithmetic mean if the interval is large, but the geometric mean if the interval is small. Since fractionation judgments (“half-pitch”) front which pitch scales may be derived would typically utilize quite hide intervals, and thereby tend to yield the arithmetic mean, a major discrepancy has arisen between such pitch scales and the pitch scale of our musical heritage, which is based upon the principle of the geometric mean. A number of experiments were performed using half-pitch and bisection judgments, and several variants of the method of equal appearing intervals. From these it was concluded that when equal appearing interval judgments are used with a standard interval no larger than about a musical third, a reliable psychological pitch scale emerges which agrees well with the common pitch scale of the piano keyboard. However, if the standard interval is as large as a musical fifth, the pitch scale begins to tend toward that derived from fractionation.