A new type of complex tone that demonstrates pitch circularity is described. For such tones, the spectral envelope is trapezoidal on the coordinates of logarithmic frequency and logarithmic amplitude, and remains constant. The components of each tone form a major triad within each octave. The component frequencies were increased by steps of 1/10 octave from tone to tone, until the first tone was obtained again. According to our paired comparison experiments for pitch, which were analyzed using the multidimensional scaling technique, two kinds of pitch circularities appear. One group of subjects shows a pitch circularity corresponding to the exact spectral periodicity of an octave, and the other group a circularity corresponding to the roughly viewed spectral periodicity of 1/3 octave. The human ear seems to detect a global pitch movement when some spectral components move in the same direction by similar degrees on the logarithmic frequency dimension.

References

References
Attneave, F., & Olson, R. K. Pitch as a medium: A new approach to psychophysical scaling. American Journal of Psychology, 1971, 84, 147-166.
Burns, E. M. Circularity in relative pitch judgments for inharmonic complex tones: The Shepard demonstration revisited, again. Perception & Psychophysics, 1981, 30, 467- 472.
Deutsch, D. Octave generalization and tune recognition. Perception & Psychophysics, 1972, 11. 411-412.
Deutsch, D. A musical paradox. Music Perception, 1986, 3, 275-280.
Krumhansl, C. L, Bharucha, J. J., & Kessler, E. J. Perceived harmonic structure of chords in three related musical keys. Journal of Experimental Psychology: Human Perception and Performance, 1982, 8, 24-36.
Krumhansl, C. L., & Schmuckler, M. A. The Petroushka chord: A perceptual investigation. Music Perception, 1986, 4, 153-184.
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypoth- esis. Psychometrika, 1964, 29, 1-27.
van Noorden, L. P. A. S. Temporal coherence in the perception of tone sequences, Ph.D. dis- sertation, Technische Hogeschool Eindhoven, Eindhoven, The Netherlands, 1975 (un- published).
van Noorden, L. Two channel pitch perception. In M. Clynes (Ed.), Music, mind, and brain: The neuropsychology of music. New York: Plenum Press, 1982.
Ohgushi, K. The origin of tonality and a possible explanation of the octave enlargement phe- nomenon. Journal of the Acoustical Society of America. 1983. 73, 1694-1700.
Ohgushi, K. Circularity of the pitch of complex tones and its application. Transactions of the Institute of Electronics and Communication Engineers of Japan, 1 984, J67-A, 423- 430 (in Japanese).
Plomp, R. Aspects of tone sensation: A psychophysical study. London: Academic Press, 1976.
Pollack, I. Decoupling of auditory pitch and stimulus frequency: The Shepard demonstra- tion revisited. Journal of the Acoustical Society of America, 1978, 63, 202-206.
Risset, J. C. Paradoxes de hauteur: Le concept de hauteur sonore n'est pas le même pour tout le monde. Proceedings of the Seventh International Congress on Acoustics, Budap- est, 1971, 20S 10, 613-616.
Ruckmick, C. A. A new classification of tonal qualities. Psychological Review, 1929, 36, 172-180.
Schroeder, M. R. Auditory paradox based on fractal waveform. Journal of the Acoustical- Society of America, 1986, 79, 186-189.
Shepard, R. N. Circularity in judgments of relative pitch. Journal of the Acoustical Society of America, 1964, 36, 2346-2353.
Shepard, R. N. Geometrical approximations to the structure of musical pitch. Psycholog- ical Review, 1982, 89, 305-333.
Singh, P. G. Perceptual organization of complex-tone sequences: A tradeoff between pitch and timbre? Journal of the Acoustical Society of America, 1987, 82, 886-899.
Teranishi, R. Endlessly ascending/descending chords performable on the piano. Reports of the Acoustical Society of Japan, 1982, H-82-68 (unpublished, in Japanese).
Terhardt, E. Psychoacoustic evaluation of musical sounds. Perception & Psychophysics, 1978, 23, 483-492.
Ueda, K., & Ohgushi, K. Perceptual components of pitch: Spatial representation using a multidimensional scaling technique. Journal of the Acoustical Society of America, 1987, 82, 1193-1200.
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