The color of music: spectral characterization of musical sound filter by a cochlear model

In music research, attention is more and more focused on the main factors of sound perception; in particular, the capability of discriminating music sound features, notably attacks and periodic components, both of which are believed to generate timbre sensation. In this paper it is argued that the frequency spectrum of the stationary part of instrument sounds are coded, at some stage, within the nervous system, into a small number of parameters. Somewhat as in vision the light spectrum of a uniformly painted area is coded by the retina into three fundamental colours, the sound parameters seem to represent what may be called ``instrument sound colours''. The analysis is carried out on music sound samples pre-filtered by a non--linear model of the human cochlea. The main reason for this approach lies in that the non--linear filtering performed by the cochlea works so as to reduce significantly the information content of acoustic input. Some properties of the model, particularly those related to the efficacy of non--linearity in tone masking and noise suppression, are evidenced by a few examples. The reliability of the model in sound colour characterisation, also in the case of noise--added sounds, is also investigated. A principal--component analysis of cochlear responses to sounds generated by 21 musical instruments seems to indicate that the spectra of the stationary parts of instrument sounds are perceived as combinations of three fundamental components.