Multidimensional scaling of musical timbre constrained by physical parameters
Stephen E. McAdams, Suzanne Winsberg · The Journal of the Acoustical Society of America · 1999
A new multidimensional scaling technique [S. Winsberg and G. De Soete, Br. J. Math. Stat. Psychol. 50, 55–72 (1997)] is applied to the analysis of dissimilarity judgments on musical timbres in both group and individual data. This technique constrains the resulting spatial model such that the order of items along a given perceptual dimension preserves their order along a previously established physical dimension. The fit between perceptual and physical dimensions is achieved with spline functions and yields what may be interpreted as the auditory transform of the physical dimension needed to obtain the perceptual one. A reanalysis of ten timbre spaces from the literature shows that this kind of model does not work as well on group data as it does on individual data due to differences in the nature of underlying dimensions and in the form of the auditory transforms for different listeners. Further, an analysis of individual data sheds light on the reasons why higher dimensions in published timbre spaces are so often difficult to interpret.