Representation and classification of the timbre space of a single musical instrument

In order to map the spectral characteristics of the great variety of sounds a musical instrument may produce, different notes were performed and sampled in several intensity levels across the whole extension of a clarinet. Amplitude and frequency time-varying curves of partials were measured by Discrete Fourier Transform. A limited set of orthogonal spectral bases was derived by Principal Component Analysis techniques. These bases defined spectral sub-spaces capable of representing all tested sounds, which were validated by auditory tests. Sub-spaces involving larger groups of notes were used to compare the sounds according to the distance metrics of the representation. A clustering algorithm was used to infer timbre classes. Preliminary tests with resynthesized sounds with normalized pitch showed a clear relation between the perceived timbre and the cluster label to which the notes were assigned.