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Ever since the advent of the twelve-tone system, the problem of large-scale pitch organization has been a pressing one for twelve-tone composers. As originally formulated by Schoenberg, the twelve-tone system does not even prescribe principles of local set succession. In practice, the juxtaposition and superposition of set forms in Schoenberg's early twelve-tone music is governed primarily by such contextual criteria as segmental association (i.e., segmental invariance) between operationally related set forms.! With Schoenberg's discovery of hexachordal inversional (IH) combinatoriality, the principle of aggregate formation came to govern the superposition of set forms. In addition, IH combinatoriality provides a means of local set succession, the secondary set. Finally, IH combinatoriality, by effecting a partitioning of the group of 48 possible set forms into 12 disjunct subgroups2 characterized by hexachordal content, creates 12 possible hexachordal areas3 whose succession may be subject to various organizing principles. The reduced number (12, as opposed to 48) and generally slower rate of succession of
Rothstein et al. (1980) studied this question.