The Subsets of SLIDE‐ and Parallel‐Related Combinations in Twentieth‐Century Music

Abstract

In twentieth‐century music, not only do SLIDE and Parallel function as transformations between chords, but they also combine triads to form pitch‐class units from which many triadic and non‐triadic subsets are derived. By identifying these subsets, I illustrate the larger frameworks of the SLIDE and Parallel formulae and their unifying roles in the pitch‐class organisation of selected twentieth‐century pieces. After establishing the subset/superset identity, I reveal that the subsets serve two formal purposes, functioning as elements of initiation and closure in relation to the pitch‐class organisation of structural units. Moreover, I show how these subsets/supersets may engage in gradual processes and how they are tied to linear motions and correlative relations. To demonstrate these subsets’ extensive use, I provide examples from pieces written between the 1930s and the 1990s by nine European, North American and Russian composers: Britten, Cabena, Lutosławski, Martinů, Persichetti, Piston, Prokofiev, Schnittke and Shostakovich. I conclude my article by analysing a passage that incorporates all the properties discussed in the article.