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

Akpan Jimmy Essien

doi:doi:10.11648/j.ajmp.20180701.11

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

Akpan Jimmy Essien

Published in American Journal of Modern Physics (Volume 7, Issue 1)

Received: 18 September 2017 Accepted: 8 October 2017 Published: 21 November 2017

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Abstract

Mechanical, acoustical, and neurophysiological investigations in music, acoustics, and auditory perception repose on the Pythagorean string ratio theory of musical pitch intervals (6^th 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

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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

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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

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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

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@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}
}

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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  -

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Akpan Jimmy Essien

Member of the Acoustical Society of Nigeria, University of Nigeria, Nsukka, Nigeria

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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

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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

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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

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@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  -

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