Abstract
The recent Standard ISO 226 concerning equal-loudness-level contours has been critically analysed. As a result, it is shown that the fitting and smoothing processes applied in the standard lead to parameter values defining equal-loudness-level contours that are not consistent with the chosen loudness function type. Serious mathematical and acoustical discrepancies have also been found that result in constant terms having an unnecessarily high numerical accuracy and a flawed phon definition, which leads to an erroneous loudness level representation. Therefore an extensive treatment of the logarithmic calculations (phon) of a loudness function is performed in this study. Finally, the author concludes that it would be desirable for the discrepancies in the standard (shown in the study) to be taken into account and corrected before publishing a new version of the standard.
Highlights
An international researcher group of Japanese scientists and researchers from Germany, Denmark and the United States has produced the recent determination of equal-loudness-level contours for the human auditory perception system called ISO 226:2003 (E): Acoustics—normal equal-loudness-level contours [1]. because the equal-loudness-level contours in the standard are based on a chosen loudness function, the equal-loudness-level contour complex is of special interest
It is shown that the fitting and smoothing processes applied in the standard lead to parameter values defining equal-loudness-level contours that are not consistent with the chosen loudness function type
Serious mathematical and acoustical discrepancies have been found that result in constant terms having an unnecessarily high numerical accuracy and a flawed phon definition, which leads to an erroneous loudness level representation
Summary
An international researcher group of Japanese scientists (serving as project leader) and researchers from Germany, Denmark and the United States has produced the recent determination of equal-loudness-level contours for the human auditory perception system called ISO 226:2003 (E): Acoustics—normal equal-loudness-level contours [1]. Purely mathematically, there are lots of mathematical expressions that could simulate such contours without any connection between the expression (and its parameters) and the acoustical or psycho-acoustical terms It proved [2] that the mathematical expressions based on defined acoustical quantities and Stevens’ power law were simpler than the expressions used to achieve similar contours in the standard [5]. Problems concerning interpretations of loudness functions and, in particular, loudness levels seem to be somewhat general and have disturbing effects on the standard [1]. These are treated more extensively in the technical chapters of this study, which is mostly performed by following the excellent informative part (Annex C) in the standard [1]. Possible problems arising from the non-validities of the data can not be treated in detail here
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