Musical octaves and pitch

Abstract

In certain types of musical performances systematic deviations from the frequencies of the equally tempered scale have been observed. In such scales the octave interval exceeds a 2:1 frequency ratio slightly. Experiments were carried out in which musically trained subjects matched the upper octave of a reference tone with a subsequent variable tone. Both signals were complex tones. The results show that (1) generally the physical size of the perceptually pure musical octave, briefly the physical musical octave (PMO), exceeds a 2:1 frequency ratio also when complex tones are used, and (2) the PMO is intensity dependent. This intensity dependence can be explained as a consequence of a pitch-intensity dependence in complex tones. A stretched scale derived from the experimentally established average PMO at different frequencies shows striking similarities with the stretched scales observed in musical performances.