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Vassilakis, P.N. (2000b).  Auditory roughness estimation of complex spectra.  Proceedings of the 6th ICMPC.  C. Woods, G. Luck, R. Brochard, F. Seddon, and J. A. Sloboda, editors (CD-ROM).  Keele, England: Keele University.

Abstract
  
Background: During the last thirty years, a number of models quantifying auditory roughness have been proposed and have been employed in a series of studies, demonstrating a relatively low degree of predictive power. Correct estimation of the degree of sensory dissonance (roughness) of a pair of sines is an important step towards quantifying inharmonicity and needs to be re-addressed.
Aim: This study demonstrates that all existing models estimating sensory dissonance of complex tones have underestimated the contribution of the relative amplitude values of the sines involved, while overestimating the contribution of their absolute amplitude values. Additionally, it is shown that inappropriate implementation of amplitude modulation (AM) depth to control the variation of a signal’s amplitude has further misguided the experimental examination of the above mentioned contributions.
Main contribution: Whenever AM depth values are used as a measure of the degree of a signal’s amplitude-variations, AM implementation produces an error reflecting the nonlinear relationship between presumed and applied amplitude variations. To apply an intended degree of amplitude variation, an adjusted coefficient has to be inserted in the usual AM implementation equation, modifying the coefficient that estimates the nature and degree of contribution of amplitude to sensory dissonance. An adjusted ‘roughness’ model that is in agreement with existing roughness-estimation data is introduced and its implications to dissonance studies are discussed.
Implications: The proposed AM-implementation adjustment has implications to all studies correlating changes in the degree of amplitude variation with changes in some perceptual measurement. In general, all psychometric functions based on the miscalculation of amplitude variation have been distorted proportionally to the identified error. If and how this distortion influenced the interpretation of the provided functions will vary according to the importance attributed by each study to each specific function’s shape. Careful examination and (if necessary) reinterpretation of research results is required in order to evaluate the significance the proposed adjustment may have to the tone-perception models these studies inform.