Much of what we call “pitch-class set theory” today originally served as the introduction to a theory. An inventory of classes of musical objects, and of relations between these classes, its function was to prepare the ground for a model of large-scale pitch organization in music of the twentieth century: the pitch-class set complex. This model was the main focus of Allen Forte's seminal article “A Theory of Set-Complexes for Music” from 1964 and of his book The Structure of Atonal Music from 1973.

Set-complex theory deals with the analysis of entire compositions, or movements and sections of compositions. More specifi cally, it deals with the question of how these can be unifi ed in terms of PC sets. This requires a PC set relation that links several PC sets across boundaries of cardinality (unlike Tn/TnI equivalence), but also sets a clear limit to their number (unlike the various “absolute” similarity measures, like ASIM, ATMEMB, and REL). In other words, it should delineate a cross-cardinality “family” of PC sets. Such a relation is the inclusion relation. “Inclusion” means that one set is contained in another; the two sets are related as subset and superset. It is on this relation that the PC set complex is primarily based.

Over the years, the set complex faded into the background somewhat. Ironically, it never had the appeal of the ideas that once built up to it; even a topic so notoriously abstruse as PC set similarity aroused more interest and discussion. Although set-complex theory failed to make a lasting impact on the study of post-tonal music, Forte remained dedicated to the aim of fi tting PC set relations into a larger pattern. In the late 1980s, he embraced the PC set genus as a source of overarching coherence in music (Forte 1988a). This, too, is a “family”-like concept based on PC-set inclusion. However, it is both more restrictive and more universal in scope than the set complex. It is more restrictive, because one usually distinguishes a relatively small number of distinct PC-set genera;1 and it is more universal in scope, because genera “exist” independently from individual musical works. The set complex is defi ned contextually (like the subject of a fugue, the theme of a variation cycle, or a twelve-tone series), while the genus is defined communally (like “sonata form,” the Dorian mode, or C major).