An increasing number of corpus studies relies on pitch-class distributions
in order to infer characteristics of musical pieces under a historical
perspective (Albrecht & Shanahan, 2013; Albrecht & Huron, 2014; Quinn &
White, 2017; Weiß, Mauch, & Dixon, 2018; Yust, 2019; Harasim, Moss,
Ramirez, & Rohrmeier, 2021).
This contribution shows that the line of fifths (LOF; Temperley, 2000) is
the fundamental underlying tonal space in a large historical corpus (ca.
1360-1940) of Western classical pieces in MusicXML format. Modeling the
pieces’ pitch-class distributions as vectors in a high-dimensional
simplicial space and visualizing them via Principal Component Analysis
reveals that the distance to the center of the LOF as well as the
distinction between the natural (F, C, G, D, A, E, B) and the altered tonal
pitch-classes (e.g., Abb, Db, F#, C##) are the most important factors for
the dispersion of the data. These findings are robust with respect to
different dimensionality reduction methods. Moreover, we introduce the
concept of pitch-class coevolution and demonstrate that the LOF also
underlies striking changes in the usage of pitch-classes between different
historical periods.
Any empirical study is based on certain implicit or explicit modeling
assumptions, some of which are given by the encoding of a corpus, e.g.
whether enharmonic equivalence is assumed (e.g. MIDI-encoding) or not (e.g.
MusicXML encoding). Relying on pitch-class distributions without assuming
enharmonic equivalence, our findings emphasize the structural importance of
the LOF for the organization of the pitch-class content of tonal music
across a large historical timespan.