The representation of the sound of an acoustic musical instrument involves problems of great complexity, among them the mapping of the spectral characteristics of the great variety of sounds this instrument can produce. In this study, different notes in several intensity levels were performed on the clarinet, covering the whole extension of the instrument. Discreet Fourier Transform was used to measure the amplitude and frequency time-varying curves of the partials of these sampled sounds. Using techniques such as Principal Component Analysis (PCA) and spectral matching with Genetic Algorithms, a limited set of orthogonal spectral basis was extracted from these parameters. These bases defined spectral sub-spaces, which were capable to represent the all tested sounds, as well as to group the sounds in contiguous sets of notes of similar timbre characteristics. Clustering and classification was further employed with K-means and Self-Organized Maps (SOM). A re-synthesis tool was also developed to allow validation of these models for timbre representation.