Isography and structure in the music of Boulez.

Neither the full context surrounding Pierre Boulez's multiplication operation nor its repercussions in terms of the structure of the music have been well understood. Boulez's multiplication operations are tied to specific transpositional schemes. These transpositional schemes are contextual and depend on the intervallic configuration of the factors of the multiplication. Thus, they create important isomorphic relationships that cut across different levels of musical structure. This article presents examples from two pieces by Boulez: Structures II and Troisieme Sonate. The examples demonstrate that, because of the trajectories that Boulez chooses to move through his precompositional tables and the specific ways that the multiplication products are realized on the musical surface, the isomorphic relationships that are essential to the tables are also key determinants of structure in this music. [ABSTRACT FROM AUTHOR]