ABSTRACT
Observations in music often consist of vectors. Consider, for instance, the tempo measurements for Schumann’s Tra¨umerei (Figure 2.3). In this case, the observational units are performances and an observation consists of a tempo “curve” which is a vector of n tempo measurements x(ti) at symbolic score onset times ti (i = 1, ..., p). The main question is which similarities and differences there are between the performances. Principal component analysis (PCA) provides an answer in the sense that the “most interesting”, and hopefully interpretable, projections are found. In this chapter, a brief introduction to PCA is given. For a detailed account and references see e.g. Mardia et al. (1979), Anderson (1984), Dillon and Goldstein (1984), Seber (1984), Krzanowski (1988), Flury and Riedwyl (1988), Johnson and Wichern (2002).
