Multidimensional scaling analysis of centroid- and attack/decay-normalized musical instrument sounds

Abstract

Ten sustained musical instrument tones (bassoon, cello, clarinet, flute, horn, oboe, recorder, alto saxophone, trumpet, and violin) were spectrally analyzed and then equalized for duration, attack and decay time, fundamental frequency, number of harmonics, average spectral centroid, and presentation loudness. The tones were resynthesized both with time-varying harmonic amplitudes and frequencies (dynamic case) and fixed amplitudes and frequencies (static case). Tone triads were presented to ten musically experienced listeners whose tasks were to specify the most dissimilar and most similar pairs in each triad. Based on the resulting dissimilarity matrix, multidimensional scaling (MDS) was used to position the instruments in two- and three-dimensional metric spaces. Two measures of instrument amplitude spectra were found to correlate strongly with MDS dimensions. For both the static- and dynamic-case 2-D solutions, the ratio of even-to-odd rms amplitudes correlated strongly with one of the dimensions. For the dynamic case, spectral centroid variation correlated strongly with the second dimension. Also, 2-D solution instrument groupings agreed well with groupings based on coefficients of the first two components of a principle components analysis representing 90% of the instruments’ spectral variance. [This work was supported by the Hong Kong Research Grants Council’s CERG Project 613505.]