Influence of the diatonic tonal hierarchy at microtonal intervals.

Previous studies have shown that listeners' perceptions of tones within a musical context are influenced by a hierarchy of tonal functions. This study investigated the influence of this hierarchy on the perception of microtones finer than the chromatic tones. Following the probe tone method introduced by Krumhansl and Shepard (1979), listeners rated each of the 48 eighth tones that occur within an octave interval according to how well that tone fit in with a major scale played just before the tone. Listeners discriminated in their preferences for tones separated by quarter-tone-but not eighth-tone-intervals, and their rating patterns conformed to a hierarchy of tonal functions extended to the quarter tones. A Fourier analysis of the data showed that listeners' rating patterns over the 48 eighth tones were necessarily and sufficiently estimated by a Fourier curve generated by the subset of 24 quarter tones, and that ratings for all tone frequencies not probed could be justifiably interpolated from this curve.