Metric Cubes in Some Music of Brahms

Abstract

The metric cube is a kind of graph of meters proposed as a complement to the types of metric spaces that have already been put forth in music-theoretic scholarship, particularly by Richard Cohn. Whereas Cohn's most recent kind of metric space (2001) can compare meters only if they interpret the same time span, metric cubes permit the comparison of meters that interpret different time spans. Furthermore, a metric cube posits a different kind of adjacency relation: while Cohn's most recent metric space connects two meters if their ordered pulse representations differ by only one pulse, a metric cube connects two meters if their ordered factor representations differ by only one factor. Metric cubes, and metric operations that act on the contents of a cube, reveal patterns of metric structure in three works by Brahms: the first movement of the Third Symphony op. 90, the third movement of the Second Symphony op. 73, and the last two movements of the Second String Quartet op. 51/2. These analyses also suggest correspondences in these movements between metric relationships and relationships of key, harmony, and form.