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Timbre Perception of Changes in Musical Instrument Geometry using Physical Modeling Techniques

The perception of timber is complex (Krumhansl 1989). Investigations concerning the relation between physical properties of sounds and their cognitive counterparts have been done mostly using the statistical method of a Multidimensional Scaling Technique (MDS) (for an overview see Bader 2002). Here musical sounds are presented to subjects in pairs of all possible combinations. Listeners are asked to rate the similarity of the two sounds of each pair on an interval scale. The MDS then computes an n-dimensional space trying to fit the distances of the sounds onto the spacial dimensions. This creates a room, where the spacial directions are cognitive or perceptional dimensions, orthogonal one to each other. These dimensions need to be compared then to physical parameters present in the sounds. The most cited work here may be Grey (1977). He compared musical instrument sounds and found, that they are judged according to three dimensions:(1) their brightness which physically is a spectral centroid calculated by the formula c = ∑ n f(n)A(n) ∑ n A(n) . with frequencies f and their amplitudes A summed over all n frequencies found in the spectrum of the sound; (2) fluctuations in the quasi-steady-state of the sound; (3) inharmonic components in the initial transient of the sound.