Harmonic-based analysis and resynthesis of musical instrument tones, for example, using the phase vocoder method, is a valuable technique, but its data representation is very large. However, this data set is usually highly redundant. Principal components analysis (PCA) can be used to encode such data into a smaller set of orthogonal basis vectors with minimal loss of information. Techniques for applying PCA to such data are explored, and the aural impact of the method on three tones (cello, trombone, and clarinet) are studied in two perception experiments. Results show that nearly identical resyntheses can be produced with a 40-70% data reduction. A preprocessing step called variable-duration temporal partitioning (VDTP) is introduced, which also affords a natural-sounding method for time expansion and contraction of tones. An extension of the PCA technique is also introduced that implements a "timbre space," or coordinate system for interpolation among a group of musical instruments.
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