The line of fifths and the co-evolution of tonal pitch-classes

Abstract

In this study, we determine the fundamental role of the line of fifths for the organization of tonal material by applying dimensionality reduction to a large historical corpus of pitch-class counts (ca. 1360–1940). We observe a historically growing trend in the exploitation of the fifths range, i.e. the size of segments that pitch-class distributions cover on the line of fifths. Moreover, we introduce the novel concept of pitch-class (co-)evolution, which traces the changing co-occurrence of pitch classes over time and likewise reaffirms the centrality of this linear tonal space from a historical angle, allowing us also to distinguish between historical periods in terms of the usage of pitch classes.