On the Serial Shaping of Stockhausen's Gruppen für drei Orchester

Explains the time-structure plan of the exceedingly extensive serial organization of Stockhausen's composition "Groups for Three Orchestras" (1955-57), which constitutes the starting point and the crucial foundation of the entire piece. Notes that the composer prepared a four-color drawing of the time-structure after the completion of the work, and knowledge of it represents a standard pre-requisite to enable illumination of all aspects of the serially predetermined time structure. Addresses the unification of space and time, the main idea of "Gruppen." Discusses the serial group criteria in the space-time continuum. Contends that at the center of the compositional process stands the idea of a structural integration of the space-time dimensions, in connection with which the principle of deriving all musical qualities of the piece from a single initial series is also decisive. Includes notes, references, musical examples, and diagrams.