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Wrong Limits and Wrong Assumptions: Kenny Norwich and Willy Wong Fail to Derive Equal-Loudness Contours

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Transactions on Engineering Technologies (WCECS 2015)

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Abstract

Using the Entropy Equation from their “Entropy Theory of Perception”, Norwich and Wong modelled loudness L versus intensity I using four unknowns. Norwich and Wong then quantified the Weber fraction by taking the differential with respect to intensity, and then replacing differentials by deltas. Subsequent re-defining of terms produced a Weber fraction equation resembling that of the late Professor Riesz. Dr. Riesz’s own equation had three parameters, which Norwich and Wong (using re-defined terms) substituted into their equation for L. They then equated the theoretical loudnesses of a comparison tone and a reference tone, generating theoretical equal-loudness contours – a previously unaccomplished feat in the literature – after also replacing one of Riesz’s parameters, initially identified with an exponent of the Entropy Equation, by Stevens’ exponent “x”. But the Norwich and Wong derivation contains fatal flaws. First, the loudness equation L cannot deal with the respective intensity limits of threshold intensity and zero intensity. Then, there are unproven relations between various parameters. To examine those relations, the present author inferred 37 values of each of x, n, and a third parameter, by the only method available: curvefitting of the Entropy Equation and of Stevens’ Law to 37 loudness-growth plots. Results clearly show that the third parameter is not constant with tone frequency, but that it does vary with maximum loudness, in a relation not noted by Norwich and Wong. And n does not equal x. In sum, Norwich and Wong fail to derive equal-loudness contours. Their mistakes exemplify what happens in mathematical biology under inappropriate limits and untested assumptions.

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Acknowledgment

My thanks to Claire S. Barnes PhD for her valuable insights.

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  1. Independent Research Scholar, Palo Alto, CA, 94306, USA

    Lance Nizami

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  1. Lance Nizami
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Correspondence to Lance Nizami .

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Editors and Affiliations

  1. IAENG Secretariat, International Association of Engineers, Hong Kong, Hong Kong

    Sio-Iong Ao

  2. Department of Computer and Communication, Engineering College, Catholic University of Daegu, Daegu, Korea (Republic of)

    Haeng Kon Kim

  3. Provost and Senior Vice-President, University of New Orleans, New Orleans, Louisiana, USA

    Mahyar A. Amouzegar

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Nizami, L. (2017). Wrong Limits and Wrong Assumptions: Kenny Norwich and Willy Wong Fail to Derive Equal-Loudness Contours. In: Ao, SI., Kim, H., Amouzegar, M. (eds) Transactions on Engineering Technologies. WCECS 2015. Springer, Singapore. https://doi.org/10.1007/978-981-10-2717-8_14

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  • DOI: https://doi.org/10.1007/978-981-10-2717-8_14

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