Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:C2L-D

Session:

Number:429

The physical bases of the psychophysical pitch-shift effects

Florian Gomez,  Ruedi Stoop,  

pp.429-432

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.429

PDF download (315.3KB)

It has been known for a long time that the perceived pitch of a complex harmonic sound changes if the partials of the sound are shifted in frequency by a fixed amount. Based on simple nonlinear modeling, approximate rules for the shift of the pitch shift could be given (first pitch shift law). In psychoacoustic experiments, however, clear deviations from these predictions were observed (second pitch-shift effects). This raised the question of whether these deviations are due to the biophysics of the nonlinear hearing sensor, the cochlea, or an artifact generated higher up in the auditory pathway. In this article, we demonstrate that the second pitch-shift is generated in the cochlea, and that combination-tone generation, low-pass filtering and a feed-forward coupling are the key factors responsible for the phenomenon. In particular, we find that the scaling laws of Hopf cochlea combination tones explain the classical, to date poorly explained psychoacoustical data of G.F. Smoorenburg (1970).

[1] A. Cheveigné, “Pitch perception models,” in Pitch (C. Plack, R. Fay, A. Oxenham, and A. Popper, eds.), vol. 24 of Springer Handbook of Auditory Research, pp. 169-233, Springer, New York, 2005.

[2] J. F. Schouten, “De toonhoogtegewaarwording,” Philips Technisch Tijdschr., vol. 5, pp. 298-306, 1940.

[3] E. de Boer, “Pitch of inharmonic signals,” Nature, vol. 178, pp. 535-536, 1956.

[4] J. F. Schouten, R. J. Ritsma, and B. L. Cardozo, “Pitch of the residue,” J. Acoust. Soc. Am., vol. 34, no. 9B, pp. 1418-1424, 1962.

[5] D. R. Chialvo, O. Calvo, D. L. Gonzalez, O. Piro, and G. V. Savino, “Subharmonic stochastic synchronization and resonance in neuronal systems,” Phys. Rev. E, vol. 65, p. 050902, May 2002.

[6] G. F. Smoorenburg, “Pitch perception of two-frequency stimuli,” J. Acoust. Soc. Am., vol. 48, no. 4B, pp. 924-942, 1970.

[7] J. Licklider, “A duplex theory of pitch perception,” Cell. Mol. Life. Sci., vol. 7, pp. 128-134, 1951.

[8] J. Goldstein and N. Kiang, “Neural correlates of the aural combination tone 2f1- f2,” Proc. IEEE, vol. 56, no. 6, pp. 981-992, 1968.

[9] S. Martignoli and R. Stoop, “Local cochlear correlations of perceived pitch,” Phys. Rev. Lett., vol. 105, p. 048101, Jul 2010.

[10] L. Robles,M. A. Ruggero, and N. C. Rich, “Two-tone distortion on the basilar membrane of the chinchilla cochlea,” J. Neurophysiol., vol. 77, no. 5, pp. 2385-2399, 1997.

[11] R. Meddis, L. P. O'Mard, and E. A. Lopez-Poveda, “A computational algorithm for computing nonlinear auditory frequency selectivity,” J. Acoust. Soc. Am., vol. 109, no. 6, pp. 2852-2861, 2001.

[12] J. L. Goldstein, “Auditory nonlinearity,” J. Acoust. Soc. Am., vol. 41, no. 3, pp. 676-699, 1967.

[13] V. M. Eguíluz, M. Ospeck, Y. Choe, A. J. Hudspeth, and M. O. Magnasco, “Essential nonlinearities in hearing,” Phys. Rev. Lett., vol. 84, pp. 5232-5235, May 2000.

[14] S. Camalet, T. Duke, F. Jülicher, and J. Prost, “Auditory sensitivity provided by self-tuned critical oscillations of hair cells,” Proc. Natl. Acad. Sci. U.S.A., vol. 97, no. 7, pp. 3183-3188, 2000.

[15] A. Kern and R. Stoop, “Essential role of couplings between hearing nonlinearities,” Phys. Rev. Lett., vol. 91, p. 128101, Sep 2003.

[16] R. Stoop and A. Kern, “Two-tone suppression and combination tone generation as computations performed by the hopf cochlea,” Phys. Rev. Lett., vol. 93, p. 268103, Dec 2004.

[17] S. Martignoli, J.-J. van der Vyver, A. Kern, Y. Uwate, and R. Stoop, “Analog electronic cochlea with mammalian hearing characteristics,” Appl. Phys. Lett., vol. 91, pp. 064108-064108-3, aug 2007.

[18] R. Plomp, “Pitch of complex tones,” J. Acoust. Soc. Am., vol. 41, no. 6, pp. 1526-1533, 1967.

[19] J. L. Goldstein, “An optimum processor theory for the central formation of the pitch of complex tones,” J. Acoust. Soc. Am., vol. 54, no. 6, pp. 1496-1516, 1973.

[20] S. Martignoli, F. Gomez, and R. Stoop submitted (2013).