(a) Three-dimensional harmonic timbre spaces of cello strings (animated versions: Supplementary Material, Movies S1 to S4). The small circles represent the harmonic timbres of 5 repeated notes per instrument, while the radii of the mean-centered spheres are their standard deviations, indicating the uncertainty of the playing. The projections of the spheres onto the coordinate planes help to locate the actual positions in space and show the exact values of the three coordinates. (b) The orthonormal basis vectors of the harmonic timbre space (the columns of U) are the principal timbres resulting from the analysis together with the harmonic timbre coordinates of the instruments. Their components indicate increased/decreased levels of the harmonics relative to their mean levels in the collection. S_i (in units of bel) are the importance (amplification) factors of the principal timbres, equations (1)–(3).