Abstract  Pitch experiments are carried out to reveal the interdependence of octave uncertainty, spectral characteristics of timbre, and intransitivity of relative pitch. This work is related to Shepard's paper "Circularity in Judgments of Relative Pitch" [1]. As in Shepard's work we demonstrate a paradox perception of harmonic complex tones, which is due to simultaneous change of pitch and timbre. Whereas Shepard considers only complex tones with fixed spectral envelopes and partials spaced in octave distance, we use harmonic complex tones with specific amplitude relations of even and odd partials. The paradox perception is due to competitive auditory clues: pitch judgment based on spacing between adjacent pitches on one hand, and on the other hand on the lowest partial. The amplitudes of odd partials are adjusted in a range close to the audibility threshold. The resulting perception of octave uncertainty is demonstrated in a pitchadjustment experiment: The subject has to adjust a complex test tone with variable frequency to another static complex tone until pitch equality is perceived. These adjusted test tones of different spectral shapes can be connected to a sequence such that all adjacent tones seem to be equal in pitch, whereas the first and the last test tones are pure tones with one octave distance. So "intransitivity of pitch equality" is shown for an appropriate sequence of complex tones with different spectral shapes. A similar sequence of complex tones, but with ascending fundamental frequencies (two halftones per step) is used to demonstrate "intransitivity of pitch inequality" in an experiment of judgment of relative pitch. This sequence always seems to ascend in pitch, although the first and the last tone is identical. We hope that our experiment may help clarifying the interplay of different cues in pitch perception, and may aid automated pitch analysis. One practical reference of this work might be an explanation of the occurrence of octave mismatch when a male and a female singer try to sing with the same pitch.
