Mammalian pitch sensation shaped by the cochlear fluid

Journal name:
Nature Physics
Volume:
10,
Pages:
530–536
Year published:
DOI:
doi:10.1038/nphys2975
Received
Accepted
Published online

Abstract

The perceived pitch of a complex harmonic sound changes if the partial tones of the sound are frequency shifted by a fixed amount. Simple mathematical rules are expected to govern perceived pitch, but these rules are violated in psychoacoustic experiments. Cognitive cortical processes are commonly held responsible for this discrepancy. Here, we demonstrate that this need not be the case. We show that human pitch perception can be reproduced with a biophysically motivated mesoscopic model of the cochlea, by fully recovering published psychoacoustical pitch-shift data and related physiological measurements from the cat cochlear nucleus. Our study suggests that perceived pitch can be attributed to combination tones in the presence of a cochlear fluid.

At a glance

Figures

  1. Cochlear excitation for a complex two-tone stimulation (simulated).
    Figure 1: Cochlear excitation for a complex two-tone stimulation (simulated).

    a, Section connectivity scheme. b, ‘Complex’ spectrum, due to combination tone (CT) emergence. c, Cochlear excitability pattern. d, CT saliency. Left panel: Black curves: signal power of frequencies f2 and of f1. Red curve: sum of lower CT (f < f1). Right panel: Black curve: added signal power from frequencies f1 and f2. Red curve: signal power of lower CT. Blue curve: signal power of higher CT (f > f2) relative to the total signal power.

  2. Comparison of physiological and simulated combination tones.
    Figure 2: Comparison of physiological and simulated combination tones.

    a, Basilar membrane response spectrograms for two-tone stimulation of amplitudes 30, 40, 50 dB sound pressure level (SPL) (frequencies f2/f1 = 1.05 and 2f2 − f1 = fch) and biological data17 (fch = 7,500 Hz). b, Hopf-cochlea model, sixth section (fch = 5,656 Hz). Relevant forcing and lower combination tone frequencies are left of the black dashed lines. Grey dashed lines: exponential amplitude scaling (Δf = f2 − f1).

  3. Comparison of single Hopf element with compound cochlea and biological data.
    Figure 3: Comparison of single Hopf element with compound cochlea and biological data.

    a,b, Response amplitude of a pure tone with ωch (black), response of a two-tone input (equal strength of components) with ωCT1 = ωch (green). The difference (arrows) is the ‘relative strength of CT1’. Single Hopf amplifier (no fluid comprised) (a) and cochlea section 6 where fch = fCT1 (b). c, Relative strength of CT1 for two f2/f1-frequency ratios. Red: cochlea section 6, black: biological data17 (fch = 9,000 Hz). The blue arrows in b and c describe the same experimental result.

  4. Pitch extraction.
    Figure 4: Pitch extraction.

    a, Spectra for two-tone stimulation (−74 dB,f1 = 2,200 Hz, f2 = 2,400 Hz) at three cochlea sections. The lowest audible combination tone (CT) (hearing threshold: −53 dB, blue line) is the response at 1,400 Hz (section 14, circled). The perceived pitch is the residue pitch (red arrow) associated with the spectrum at this location. b, Psychoacoustical lower hearing frequency limit of CTs (ref. 6) (dashed black line). Simulation: Lowest CTs above the implemented amplitude threshold (solid red line) and highest CTs below the limit (unconnected red circles). The three characteristics differ by less than the section width.

  5. Pitch-shift experiment.
    Figure 5: Pitch-shift experiment.

    a, Two-frequency stimulation f2 = f1 + 200 Hz. Black stars: psychoacoustic data6 (partial sound levels 40 dB sound pressure level, two subjects). Red circles: Hopf cochlea (sections as indicated, tones at −74 dB each). Black lines: false predictions by equation (2) for k = k, k = k + 1/2 (dashed) and k = k + 1, respectively. b, Response of a cell of the cat ventral nucleus20 (‘On-L-cell’, fch = 1,100 Hz) to a three-frequency stimulation ((fc − fmod), fc, (fc + fmod); fmod = 200 Hz) at 50 dB SPL. Black stars: inverse of the most frequent interspike intervals. Red circles: pitch from cochlea section 15 (fch = 1,095 Hz,−64 dB).

  6. Section diagram.
    Figure 6: Section diagram.

    A complex signal from the preceding section j − 1 stimulates the Hopf amplifier of section j of resonant frequency the responsiveness of which is characterized by the Hopf parameter μ(j). The two components of the signal are then filtered by Butterworth filters with cutoff frequency and passed to the next section. To form the cochlea, the sections are connected in series (Fig. 1a). Signals are measured at the output of a section.

References

  1. Helmholtz, H. von. Die Lehre von den Tonempfindungen als physiologische Grundlage Für die Theorie der Musik (Vieweg, 1863).
  2. Ohm, G. S. Über die Definition des Tones, nebst daran geknüpfter Theorie der Sirene und ähnlicher tonbildender Vorrichtungen. Ann. Phys. Chem. 59, 513565 (1843).
  3. Seebeck, A. Beobachtungen über einige Bedingungen der Entstehung von Tönen. Ann. Phys. Chem. 53, 417436 (1841).
  4. Turner, R. S. The Ohm–Seebeck dispute, Hermann von Helmholtz, and the origins of physiological acoustics. Br. J. Hist. Sci. 10, 124 (1977).
  5. Martignoli, S. & Stoop, R. Local cochlear correlations of perceived pitch. Phys. Rev. Lett. 105, 048101 (2010).
  6. Smoorenburg, G. F. Pitch perception of two-frequency stimuli. J. Acoust. Soc. Am. 48, 924942 (1970).
  7. Cheveigné, A. in Pitch (eds Plack, C., Fay, R., Oxenham, A. & Popper, A.) 169233 (Springer, 2005).
  8. Seebeck, A. Beobachtungen über einige Bedingungen der Entstehung von Tönen. Ann. Phys. Chem. 53, 417436 (1841).
  9. Schouten, J. F. De toonhoogtegewaarwording. Philips Technisch Tijdschr. 5, 298306 (1940).
  10. de Boer, E. Pitch of inharmonic signals. Nature 178, 535536 (1956).
  11. Schouten, J. F., Ritsma, R. J. & Lopes Cardozo, B. Pitch of the residue. J. Acoust. Soc. Am. 34, 14181424 (1962).
  12. Chialvo, D. R., Calvo, O., Gonzalez, D. L., Piro, O. & Savino, G. V. Subharmonic stochastic synchronization and resonance in neuronal systems. Phys. Rev. E 65, 050902 (2002).
  13. Licklider, J. A duplex theory of pitch perception. Cell. Mol. Life Sci. 7, 128134 (1951).
  14. Cariani, P. & Delgutte, B. Neural correlates of the pitch of complex tones: I. Pitch and pitch salience. J. Neurophysiol. 76, 16981716 (1996).
  15. Goldstein, J. L. & Kiang, N. Y. S. Neural correlates of the aural combination tone 2f1 − f2. Proc. IEEE 56, 981992 (1968).
  16. Goldstein, J. L. Auditory nonlinearity. J. Acoust. Soc. Am. 41, 676699 (1967).
  17. Robles, L., Ruggero, M. A. & Rich, N. C. Two-tone distortion on the basilar membrane of the chinchilla cochlea. J. Neurophysiol. 77, 23852399 (1997).
  18. Martignoli, S., van der Vyver, J-J., Kern, A., Uwate, Y. & Stoop, R. Analog electronic cochlea with mammalian hearing characteristics. Appl. Phys. Lett. 91, 064108 (2007).
  19. Martignoli, S., Gomez, F. & Stoop, R. Pitch sensation involves stochastic resonance. Sci. Rep. 3, 2676 (2013).
  20. Rhode, W. S. Interspike intervals as a correlate of periodicity pitch in cat cochlear nucleus. J. Acoust. Soc. Am. 97, 2414 (1995).
  21. Barral, J. & Martin, P. Phantom tones and suppressive masking by active nonlinear oscillation of the hair-cell bundle. Proc. Natl Acad. Sci. USA 77, E1344E1351 (2012).
  22. Whitham, G. Linear and Nonlinear Waves (Pure and Applied Mathematics Interscience Publishers, 1999).
  23. Kern, A. & Stoop, R. Essential role of couplings between hearing nonlinearities. Phys. Rev. Lett. 91, 128101 (2003).
  24. Kern, A., Heid, C., Steeb, W-H., Stoop, N. & Stoop, R. Biophysical parameters modification could overcome essential hearing gaps. PLoS Computat. Biol. 4, e1000161 (2008).
  25. Kern, A. A Nonlinear Biomorphic Hopf-Amplifier Model of the Cochlea PhD thesis, ETH Zurich (2003).
  26. Stoop, R. & Kern, A. Two-tone suppression and combination tone generation as computations performed by the Hopf cochlea. Phys. Rev. Lett. 93, 268103 (2004).
  27. Steele, C. & Taber, L. Comparison of WKB calculations and experimental results for three-dimensional cochlear models. J. Acoust. Soc. Am. 80, 10071018 (1979).
  28. Wiesenfeld, K. & McNamara, B. Period-doubling systems as small-signal amplifiers. Phys. Rev. Lett. 55, 1316 (1985).
  29. Wiesenfeld, K. & McNamara, B. Small-signal amplification in bifurcating dynamical systems. Phys. Rev. A 33, 629642 (1986).
  30. Derighetti, B., Ravani, M., Stoop, R., Meier, P. F. & Brun, E. Period-doubling Lasers as Small-Signal Detectors. Phys. Rev. Lett. 55, 17461748 (1985).
  31. Eguíluz, V. M., Ospeck, M., Choe, Y., Hudspeth, A. J. & Magnasco, M. O. Essential nonlinearities in hearing. Phys. Rev. Lett. 84, 52325235 (2000).
  32. Camalet, S., Duke, T., Jülicher, F. & Prost, J. Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl Acad. Sci. USA 97, 31833188 (2000).
  33. Martin, P. & Hudspeth, A. J. Compressive nonlinearity in the hair bundle’s active response to mechanical stimulation. Proc. Natl Acad. Sci. USA 98, 1438614391 (2001).
  34. Lopez-Poveda, E. A., Plack, C. J. & Meddis, R. Cochlear nonlinearity between 500 and 8000 Hz in listeners with normal hearing. J. Acoust. Soc. Am. 113, 951960 (2003).
  35. Zwicker, E. Der ungewöhnliche Amplitudengang der nichtlinearen Verzerrungen des Ohres. Acustica 5, 6774 (1955).
  36. Cooper, N. P. & Rhode, W. S. Mechanical responses to two-tone distortion products in the apical and basal turns of the mammalian cochlea. J. Neurophysiol. 78, 261270 (1997).
  37. Cotugno, D. De Aquaeductibus Auris Humane Internae (Dissertation, Simoniana Napoli, 1761).
  38. Plomp, R. Pitch of complex tones. J. Acoust. Soc. Am. 41, 15261533 (1967).
  39. Ritsma, R. J. Frequencies dominant in the perception of the pitch of complex sounds. J. Acoust. Soc. Am. 42, 191198 (1967).
  40. Gomez, F., Saase, V., Buchheim, N. & Stoop, R. How the ear tunes in to sounds: a physics approach. Phys. Rev. Appl. 1, 014003 (2014).
  41. Van der Vyver, J-J. A Biomorphic Electronic Hopf Cochlea PhD thesis, ETH Zurich (2006).
  42. Magnasco, M. O. A wave traveling over a Hopf instability shapes the cochlear tuning curve. Phys. Rev. Lett. 90, 058101 (2003).
  43. Jülicher, F. & Duke, T. Active traveling wave in the cochlea. Phys. Rev. Lett. 90, 158101 (2003).

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