Musical octaves and pitch

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.