| Peer-Reviewed

The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited)

Received: 18 September 2017     Accepted: 8 October 2017     Published: 21 November 2017
Views:       Downloads:
Abstract

Mechanical, acoustical, and neurophysiological investigations in music, acoustics, and auditory perception repose on the Pythagorean string ratio theory of musical pitch intervals (6th century B.C). Recently, the mechanical validity of the string ratio theory and its psychological import have been challenged and denied on grounds of invariance. In this regard, Essien (2014) demonstrated experimentally that, contrary to established tradition in physics of sound, the tension of a string is not constant when string length is modified even though the balanced-force exerted on the string is held constant. The data revealed the existence of two sources of force in a vibrating string: (1) The oppositely-directed force applied externally to the string (labelled Fex); (2) The force that is the intrinsic property of the string (labelled Fin). The latter is the missing parameter in Pythagorean auditory psychophysics. The omission lured researchers into acoustics and neurophysiology of pitch without an invariant physical correlate of pitch. Essien’s (2014) data showed that all transformations to string length or the balanced-force exerted on a string are various ways to modify the string’s resistance to deformation. Thus, the force in a string varies inversely with string length even though Fex is held constant. In the present paper, string length is shown to have very little or no effect at all on a string’s vibrational frequency and subjective pitch. Because psychoacoustic theories of hearing are founded on the string ratio theory, the data not only offer the missing psychological element that deprived the string ratio theory of a scientific status, but also refute both Ohm’s acoustical law (1843) and Helmholtz’s resonance theory (1877). The force in a string is portrayed as the mechanical parameter in control of pitch regardless of vibrational frequency or spectral structure. Implications for future research in musical acoustics and auditory perception are discussed.

Published in American Journal of Modern Physics (Volume 7, Issue 1)
DOI 10.11648/j.ajmp.20180701.11
Page(s) 1-13
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Invariance, String Tension, String Ratios, Pitch Perception, Mechanics of Spectral Change

References
[1] Mol, H. Fundamentals of Phonetics. Mouton & Co. The Hague. 1963.
[2] Carterette, E. C. Some historical notes on research in hearing. Handbook of Perception, Vol. 4, 1978, pp 3-39.
[3] de Cheveigné, A. Pitch perception models. Springer Handbook of Auditory Research, Vol. 24, 2005: pp 169-233.
[4] Stephen, R. W. B. and Bates, A. E. Wave Motion and Sound. Edward Arnold & Co. London. 1950.
[5] Ohm, G. S. Ueber die Definition des Tones, nebst daran geknüpfter Theorie der Sirene. und ähnlicher tonbildender Vorrichtungen. Ann. Phys. Chem. 1843. Vol 59, pp 513-565.
[6] Helmholtz, H. L. F. On the Sensation of Tone; as a Physiological Basis for the Theory of Music. Translated from the German version of 1877 and revised by Ellis, A. J. Dover Publications New York. 1877.
[7] Dorman, M. F. and Wilson, B. S. The design and function of cochlear implants: Fusing medicine. Neural science, and engineering. American Scientist, Vol 92 (5), 2004, pp 436-445.
[8] Cariani, P.; Micheyl, C. Toward a theory of information processing in auditory cortex. Springer Handbook of Auditory Research, Vol. 43, 2012, pp 351-390.
[9] Gibson, J. J. The Ecological Approach to Visual Perception. Houghton-Mifflin. Boston. MA. 1979.
[10] Bregman, A. S. Auditory Scene Analysis: The Perceptual Organization of Sound. The M. I. T. Press. Cambridge, Massachusetts; London. 1990:
[11] Neuhoff, J. G.: Ecological Psychoacoustics: Introduction and History. In Neuhoff, J. G. Ed.: Ecological Psychoacoustics, 2004, pp 1-13.
[12] Yost, W. A. Perceiving sounds in the real world. An introduction to human complex sound perception. Frontiers in Bioscience, Vol 12, 2007, pp 3461–3467.
[13] Obata, J. and Tesima, T. Experimental studies on the sound and vibration of drum. J. Acoust Soc. Am. Vol 6, 1935: pp 267-274.
[14] Gaver, W. W. What in the world do we hear? An ecological approach to auditory event perception. Ecological Psychology, Vol 5, 1993, pp 1-29.
[15] Gaver, W. W. How do we hear in the world? Exploration in ecological acoustics. Ecological Psychology, Vol 5, 1993: pp 285-313.
[16] Carello, C.; Anderson, K. L.; Kunkler-Peck, A. J. Perception of object length by sound. Psychological Science, Vol 9, 1998, pp 211-214.
[17] Lutfi, R. A. Human sound source identification. Auditory Perception of Sound Sources. Springer Handbook of Auditory Research, Vol. 29, 2008: pp 13-42.
[18] Bucur, V. Material Properties and the Modes of Vibration of Piano Soundboard. In: Handbook of Materials for String Musical Instruments. Springer, Cham; 2016, pp 175-248.
[19] Gunther L. Tuning, Intonation, and Temperament: Choosing Frequencies for Musical Notes. The Physics of Music and Color. Springer, New York, 2012.
[20] Bucur V. Measuring Vibration Modes of Violins’ and Other Instruments’ Plates. In: Handbook of Materials for String Musical Instruments. Springer, Cham; 2016, pp 133-173.
[21] Fechner, G. Elements of Psychophysics. Vol. 1. Translated from the German by Adler, H. E. Holt, Rinehart & Winston. New York. London. 1860.
[22] Bell, E. T. The Development of Mathematics. McGraw-Hill. New York. London. 1945.
[23] Essien, A J. The tension theory of pitch production and perception. Proceedings of Second International Conference on Acoustics. Acoustical Society of Nigeria. University of Nigeria, Nsukka, Nigeria. 13-16 October 2014.
[24] Kinsler, L. E. Vibration. McGraw-Hill Encyclopaedia of Science and Technology, 1971: Vol. 14, 361-366. New York. McGraw-Hill.
[25] Colton, R. H. ‘Physiological mechanisms of vocal frequency control: The role of tension’, J. of Voice, 1988. Vol. 2, no. 3, pp. 208-220.
[26] Higgins, R. A. Materials for Engineers and Technicians (5th Edition). Amsterdam. Newnes-Elsevier. 2010.
[27] Gillam, E. Materials under Test. London: Newnes-Butterworths. 1969.
[28] Cross, R. and Bower, R. ‘Measurements of string tension in a tennis racket’, J. Sports Engineering, 2001. Vol. 4, no. 3, pp. 165-175.
[29] Turcotte, R. A., Pearsall, D. J. and Montgomery, D. L. ‘An apparatus to measure stiffness properties of the hockey skate boots’, Sports Engineering, 2001. Vol. 4, no. 1, pp. 43-48.
[30] Dmytro, B, Volodymyr, B. Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. American Journal of Modern Physics. Vol. 6, No. 6, 2017, pp. 117-121. doi: 10.11648/j.ajmp.20170606.11.
[31] Essien, A. J. The Ecological Foundation of Hearing Sciences: The basis for theories of music, speech, and auditory analysis. New Generation Publishing Company, London. 2017
[32] d’Alessandro, C., Rosset, S.; Rossi, J-P. The pitch of short duration fundamental frequency glissandos. J. Acoust Soc. Am., Vol 104, 1998, pp 2339-2348.
[33] Plomp, R. Pitch of complex tones. J. Acoust Soc. Am. 41, 1967, pp 1526-1533.
[34] Collier, R. Intonation analysis: The perception of speech melody in relation to acoustics and production. European Conference on Speech Communication and Technology. Vol. 1, 1989: pp 38-44.
[35] Moore, B. C. J. Aspects of auditory processing related to speech perception. The Handbook of Phonetic Sciences, 2010, pp 454-488.
[36] Radocy, R. E. Some unanswered questions in musical perception. Contributions to Music Education. Vol. 6, 1978, pp 73-81.
[37] Békésy, G. von. Hearing theories and complex sounds. J. Acoust Soc. Am, Vol 35, 1963, pp 588-601.
[38] Békésy, G. von. The missing fundamental and periodicity detection in hearing. J. Acoust Soc. Am 1972, Vol 51, pp 631-637.
[39] Stevens, S. S.; Volkman, J.; Newman, E. B. A scale for the measurement of the psychological magnitude pitch. J. Acoust. Soc. Am. 1937: Vol 8, 185-190.
[40] Schouten, J. F. The residue: A new component in subjective sound analysis. Proceedings. Koninkl. Ned. Akad. Wetenschap Vol 43, 1940, pp 356-363.
[41] Schouten, J. F.; Ritsma, R. J.; Cardozo, B. L. Pitch of the residue. J. Acoust. Soc. Am. Vol 34, 1962, pp 1418-1424.
[42] Small, A. M. Periodicity pitch. Foundations of Modern Auditory Theory, Vol. 1, 1970: pp 3-54.
[43] Winter, I. M. The neurophysiology of pitch. Springer Handbook of Auditory Research, Vol. 24, 2005, pp 99-146.
[44] Plack, C. J.; Oxenham, A. J. Overview: The present and future of pitch. Springer Handbook of Auditory Research, Vol. 24, 2005, pp 1-6.
[45] Plack, C. J.; Oxenham, A. J. The psychophysics of pitch. Springer Handbook of Auditory Research, Vol. 24, 2005; pp 7-55.
[46] Ullman, S. Against direct perception. The Behavioural and Brain Sciences, Vol 3(3), 1980, pp 373-415.
[47] Seebeck, A. Ueber die Sirene. Ann. Phys. Chem. Vol 60, 1843, pp 449-481.
[48] Haggard, M. P. Understanding speech understanding. Structure and Process in Speech Perception, 1975, pp 3-15.
[49] Humphries, C. Liebenthal, E. and Binder J. R. ‘Tonotopic organization of human auditory cortex Neuroimage’, 2010. Vol. 50, no. 3, pp. 1202–1211.
[50] Read, J. C. A. ‘The place of human psychophysics in modern neuroscience, Neuroscience, 2015. Vol. 296, pp 116-129.
Cite This Article
  • APA Style

    Akpan Jimmy Essien. (2017). The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited). American Journal of Modern Physics, 7(1), 1-13. https://doi.org/10.11648/j.ajmp.20180701.11

    Copy | Download

    ACS Style

    Akpan Jimmy Essien. The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited). Am. J. Mod. Phys. 2017, 7(1), 1-13. doi: 10.11648/j.ajmp.20180701.11

    Copy | Download

    AMA Style

    Akpan Jimmy Essien. The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited). Am J Mod Phys. 2017;7(1):1-13. doi: 10.11648/j.ajmp.20180701.11

    Copy | Download

  • @article{10.11648/j.ajmp.20180701.11,
      author = {Akpan Jimmy Essien},
      title = {The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited)},
      journal = {American Journal of Modern Physics},
      volume = {7},
      number = {1},
      pages = {1-13},
      doi = {10.11648/j.ajmp.20180701.11},
      url = {https://doi.org/10.11648/j.ajmp.20180701.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20180701.11},
      abstract = {Mechanical, acoustical, and neurophysiological investigations in music, acoustics, and auditory perception repose on the Pythagorean string ratio theory of musical pitch intervals (6th century B.C). Recently, the mechanical validity of the string ratio theory and its psychological import have been challenged and denied on grounds of invariance. In this regard, Essien (2014) demonstrated experimentally that, contrary to established tradition in physics of sound, the tension of a string is not constant when string length is modified even though the balanced-force exerted on the string is held constant. The data revealed the existence of two sources of force in a vibrating string: (1) The oppositely-directed force applied externally to the string (labelled Fex); (2) The force that is the intrinsic property of the string (labelled Fin). The latter is the missing parameter in Pythagorean auditory psychophysics. The omission lured researchers into acoustics and neurophysiology of pitch without an invariant physical correlate of pitch. Essien’s (2014) data showed that all transformations to string length or the balanced-force exerted on a string are various ways to modify the string’s resistance to deformation. Thus, the force in a string varies inversely with string length even though Fex is held constant. In the present paper, string length is shown to have very little or no effect at all on a string’s vibrational frequency and subjective pitch. Because psychoacoustic theories of hearing are founded on the string ratio theory, the data not only offer the missing psychological element that deprived the string ratio theory of a scientific status, but also refute both Ohm’s acoustical law (1843) and Helmholtz’s resonance theory (1877). The force in a string is portrayed as the mechanical parameter in control of pitch regardless of vibrational frequency or spectral structure. Implications for future research in musical acoustics and auditory perception are discussed.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - The Mechanical Invariance Factor in Musical Acoustics and Perception (Revisited)
    AU  - Akpan Jimmy Essien
    Y1  - 2017/11/21
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajmp.20180701.11
    DO  - 10.11648/j.ajmp.20180701.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 1
    EP  - 13
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20180701.11
    AB  - Mechanical, acoustical, and neurophysiological investigations in music, acoustics, and auditory perception repose on the Pythagorean string ratio theory of musical pitch intervals (6th century B.C). Recently, the mechanical validity of the string ratio theory and its psychological import have been challenged and denied on grounds of invariance. In this regard, Essien (2014) demonstrated experimentally that, contrary to established tradition in physics of sound, the tension of a string is not constant when string length is modified even though the balanced-force exerted on the string is held constant. The data revealed the existence of two sources of force in a vibrating string: (1) The oppositely-directed force applied externally to the string (labelled Fex); (2) The force that is the intrinsic property of the string (labelled Fin). The latter is the missing parameter in Pythagorean auditory psychophysics. The omission lured researchers into acoustics and neurophysiology of pitch without an invariant physical correlate of pitch. Essien’s (2014) data showed that all transformations to string length or the balanced-force exerted on a string are various ways to modify the string’s resistance to deformation. Thus, the force in a string varies inversely with string length even though Fex is held constant. In the present paper, string length is shown to have very little or no effect at all on a string’s vibrational frequency and subjective pitch. Because psychoacoustic theories of hearing are founded on the string ratio theory, the data not only offer the missing psychological element that deprived the string ratio theory of a scientific status, but also refute both Ohm’s acoustical law (1843) and Helmholtz’s resonance theory (1877). The force in a string is portrayed as the mechanical parameter in control of pitch regardless of vibrational frequency or spectral structure. Implications for future research in musical acoustics and auditory perception are discussed.
    VL  - 7
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Member of the Acoustical Society of Nigeria, University of Nigeria, Nsukka, Nigeria

  • Sections