Stretching and compression in the perception of musical intervals

Perceived octaves are stretched, requiring frequency-dependent ratios that generally exceed 2:1. Small intervals seem to be compressed perceptually. Whether this compression also depends on frequency is unclear. To examine this question, six experienced string instrumentalists each made perceptual judgments of sinusoidally formed major seconds, perfect fourths, and octaves above each of four lower frequencies. The frequency ratio for each perceived interval type varied with lower frequency. The pattern of this variation differed between the octave and the other two interval types and across subjects. A consequence is that nonlinear loci in a two-dimensional space are mathematically necessary for a complete representation of an individual listener's subjectively equal musical intervals. The listener apparently quickly assimilates the intervals produced by performers to these personal interval loci.