Calculating Tonal Fusion by the Generalized Coincidence Function

  • Martin Ebeling
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 37)

Abstract

Models of pitch perception in the time domain suggest that the perception of pitch is extracted from neuronal pulse series by networks for periodicity detection. A neuronal mechanism for periodicity detection in the auditory system has been found in the inferior colliculus (Langner 1983). The present paper proposes a mathematical model to compute the degree of coincidence in the periodicity detection mechanism for musical intervals represented by pulse series. The purpose of this model is to study the logical structure of coincidence and to define a measure value for the degree of coincidence.

The model is purely mathematical but has a strong relation to physiological data presented by Langner. As the sensation of consonance depends mostly on pitch, frequency is the only parameter to be regarded in the model. The integration of other parameters and the adaptation to further physiological data should be easy but still lies ahead.

The model is a mathematical basis for a concept of consonance based on pitch perception models in the time domain. In contrast to the concept of the sensory consonance it does not refer to the percept of roughness, which nevertheless is important for the perceived pleasantness of consonances.

Keywords

Autocorrelation Function Acoustical Society Inferior Colliculus Basilar Membrane Cochlear Nucleus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aures, W.: Ein Berechnungsverfahren der Rauhigkeit. Acustica 58, 268–281 (1985)Google Scholar
  2. Aures, W.: Der sensorische Wohlklang als Funktion psychoakustischer Empfindungsgrößen. Acustica 58, 282–290 (1985)Google Scholar
  3. Cariani, P.A., Delgutte, B.: Neural Correlates of the Pitch of Complex Tones. Journal of Neurophysiology 76(3), 1698–1734 (1996)Google Scholar
  4. de Cheveigné, A.: Pitch perception models. In: Plack, C., Fay, R.R., Oxenham, A.J., Popper, A.N. (eds.) Pitch — Neural Coding and Perception, pp. 169–233. Springer, New York (2005)Google Scholar
  5. Ebeling, M.: Verschmelzung und neuronale Autokorrelation als Grundlage einer Konsonanztheorie. Peter Lang Verlag, Frankfurt a. M. (2007)Google Scholar
  6. Goldstein Julius, L., Scrulovic, P.: Auditory-nerve spike intervals as an adequate basis for aural spectrum analysis. In: Evans, E.F. (ed.) Psychophysics and Physiology of Hearing, pp. 337–345. Academic, London (1977)Google Scholar
  7. Hartmann, W.M.: Signal, Sound, and Sensation. Springer, New York (2000)Google Scholar
  8. v. Helmholtz, H.: On the sensations of tone. Tr. Ellis, Alexander J. Dover, New York (1885); reprint 1954Google Scholar
  9. Hesse, H.-P.: Musik und Emotion. Wissenschaftliche Grundlagen des Musik-Erlebens. Springer, Wien (2003)Google Scholar
  10. Kaernbach, C., Demany, L.: Psychophysical evidence against the autocorrelation theory of auditory temporal processing. Journal of the Acoustical Society of America 104(4), 2298–2306 (1998)CrossRefGoogle Scholar
  11. Kameoka, A., Kuriyagawa, M.: Consonance Theory. Journal of the Acoustical Society of America 45(6), 1451–1469 (1969)CrossRefGoogle Scholar
  12. Langner, G.: Evidence for neuronal periodicity detection in the auditory system of the guinea fowl implications for pitch analysis in the time domain. Experimental Brain Research 52, 333–355 (1983)CrossRefGoogle Scholar
  13. Langner, G.: Neuronal mechanisms underlying the perception of pitch and harmony. Annals of the New York Academy of sciences 1060, 50–52 (2005)CrossRefGoogle Scholar
  14. Langner, G.: Temporal Processing of Periodic Signals in the Auditory System: Neuronal Representation of Pitch, Timbre, and Harmonicity. Zeitschrift für Audiologie 46(1), 8–21 (2007)Google Scholar
  15. Langner, G., Schreiner, C.E.: Periodicity Coding in the Inferior Colliculus of the Cat. Journal of Neurophysiology 60(6), 1799–1822 (1988)Google Scholar
  16. Licklider, J.C.R.: A Duplex Theory of Pitch Perception. Experimenta VII/4, 128–134 (1951)CrossRefGoogle Scholar
  17. Meddis, R., Hewitt, M.J.: Virtual pitch and phase sensitivity of a computer model of the auditory periphery. Journal of the Acoustical Society of America 89(6), 2866–2894 (1991)CrossRefGoogle Scholar
  18. Papoulis, A.: The Fourier Integral And Its Applications. McGraw-Hill, New York (1962)MATHGoogle Scholar
  19. Parncutt, R.: Harmony. A psychoacoustic approach. Springer, Berlin (1989)Google Scholar
  20. Parncutt, R.: A model of the percetual root(s) of a chord accounting for voicing and prevailing tonality. In: Leman, M. (ed.) Music, gestalt, and computing — Studies in cognitive and systematic musicology, pp. 181–199. Springer, Berlin (1997)Google Scholar
  21. Patterson, R.D., Allerhand, M.H., Giguère, C.: Time-domain modelling of peripheral auditory processing: A modular architecture and a software platform. Journal of the Acoustical Society of America 98(4), 1890–1894 (1995)CrossRefGoogle Scholar
  22. Plomp, R., Levelt, W.J.D.: Tonal consonance and critical bandwidth. Journal of the Acoustical Society of America 35, 548–560 (1965)CrossRefGoogle Scholar
  23. Rhode, W.S.: Interspike intervals as correlate of periodicity pitch in cat cochlear nucleus. Journal of the Acoustical Society of America 97(4), 2414–2429 (1995)CrossRefGoogle Scholar
  24. Stumpf, C.: Tonpsychologie. Knuf, Hilversum (1890); reprint (1965)Google Scholar
  25. Terhardt, E.: On the Perception of Periodic Sound fluctuations (Roughness). Acustica 30, 201–213 (1974)Google Scholar
  26. Terhardt, E.: Ein psychoakustisch begründetes Konzept der Musikalischen Konsonanz. Acustica 36, 121–137 (1976/1977)Google Scholar
  27. Tramo, M.J., Cariani, P.A., Delgutte, B., Braida, L.D.: Neurobiological Foundations for the Theory of Harmony in Western Tonal Music. In: Zatorre, R.J., Peretz, I. (eds.) The Biological Foundations of Music. Annals of the New York Academy of Sciences, vol. 930, pp. 92–116 (2001)Google Scholar
  28. Voutsas, K., Langner, G., Adamy, J., Ochse, M.A.: A brain-like neural network for periodicity analysis. IEEE Trans. Syst. Man Cybern. B: Cybern. 35, 12–22 (2005)CrossRefGoogle Scholar
  29. Wever, E.G.: Theory of Hearing. Wiley, New York (1949); reprint 1965Google Scholar
  30. Wiener, N.: Generalized Harmonic Analysis. Acta Mathematica 55, 117–258 (1930)MATHCrossRefMathSciNetGoogle Scholar
  31. Yost, W.A., Patterson, R., Sheft, S.: A time domain description for the pitch strength of iterated rippled noise. Journal of the Acoustical Society of America 99(2), 1066–1077 (1996)CrossRefGoogle Scholar
  32. Zhang, X., Heinz, M.G., Bruce, I.C., Carney, L.H.: A phenomenological model for the responses of auditory-nerve fibers. I. Nonlinear tuning with compression and suppression. Journal of the Acoustical Society of America 109(2), 648–670 (2001)CrossRefGoogle Scholar
  33. Zwicker, E., Fastl, H.: Psychoacoustics. Springer, Berlin (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Martin Ebeling
    • 1
  1. 1.Peter-Cornelius-Conservatory of musicMainz

Personalised recommendations