Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

Figure 7:

The circle of fifths (lined out) appears also in performed WTC (upper). The analyzed data are the overall intensities of pitch classes in the Fugues of Bach’s WTC II in the recording of Glenn Gould shown in Figure 1. The same procedure as in Figure 3 (middle) is applied to project the 24-dimensional pitch class vectors onto a two-dimensional plane, spanned by the two most prominent factors. These two factors of performed WTC II capture an even higher percentage (88.54 %, lower) of the variance of the data than those for the score data of WTC I (cf. Figure 5).

We choose a recording of Glenn Gould playing the Preludes and Fugues of Bach’s WTC, Book II. We calculate accumulated cq-profiles (Purwins et al., 2000b) from the set of the 24 Fugues of WTC II in all Major and minor keys (cf. Figure 1). Instead of containing frequencies of co-occurrences (cf. Table above) or symbolic durations (cf. Section 3.1 and Figure 3), the co-occurrence table now consists of

3.2 Circle of Fifths in Performance