Musimetrics by Vilson Vieira, Renato Fabbri, and Luciano da Fontoura Costa.
Can the arts be analyzed in a quantitative manner? We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each characteristic and their correlations were analyzed. A bootstrap method was applied to simulate hundreds of artificial composers influenced by the seven representatives chosen. Applying dimensionality reduction we obtained a planar space used to quantify non-numeric relations like dialectics, opposition and innovation. Composers differences on style and technique were represented as geometrical distances in the planar space, making it possible to quantify, for example, how much Bach and Stockhausen differ from other composers or how much Beethoven influenced Brahms. In addition, we compared the results with a prior investigation on philosophy. The influence of dialectics, strong on philosophy, was not remarkable on music. Instead, supporting an observation already considered by music theorists, strong influences were identified between subsequent composers, implying inheritance and suggesting a stronger master-disciple evolution when compared to the philosophy analysis.
The article concludes:
While taking the first steps on the direction of a quantitative approach to arts and philosophy we believe that an understanding of the creative process could also be eventually quantified. We want to end this work going back to Webern, who early envisioned these relations: “It is clear that where relatedness and unity are omnipresent, comprehensibility is also guaranteed. And all the rest is dilettantism, nothing else, for all time, and always has been. That’s so not only in music but everywhere.”
You are going to encounter multivariate statistics in a number of contexts. Where are the weak points in this paper? What questions would you ask? (Hint, they don’t involve expertise in music history or theory.) If you are familiar with multivariate statistics, what are the common weak points of that type of analysis?
I remember multivariate statistics from their use in the 1960′s/70′s in attempts to predict Supreme Court (US) behavior. The Court was quite safe and I think the same can be said for composers in the Western canon.