Chord, Collection, and Set in Twentieth-Century Theory

Jonathan W. Bernard

On a related topic, I also want to say that I did not invent the unordered pitch-class set. That was the creation of a far higher power—and I don't mean Milton Babbitt.

—Allen Forte1

Over approximately the past three decades, during a period that can be said to commence with the appearance in 1964 of Allen Forte's article ''A Theory of Set-Complexes for Music" and to continue with the publication nine years later of The Structure of Atonal Music, the discipline of music theory, developing into its modern (and present-day) form, has come to accept Forte's formulation of the pitch-class set, together with his enumeration of set classes and the bases he laid down for relating sets of like and unlike cardinalities and for applying them to analysis, as a kind of fundamental standard for the study of the pitch dimension of twentieth-century music: a standard to which various modifications and additions have been proposed, and some even widely adopted, without altering its essence.2 The great relevance and multifarious applicability of the pitch-class set, already amply demonstrated in our professional literature, has understandably left many theorists less curious than they might otherwise be about its prehistory; having now almost the status of a "paradigm"—to use that term that music theorists

This essay was written during a period of sabbatical leave (1994–95) from the University of Washington, whose support is hereby gratefully acknowledged. I would also like to express my thanks to Robert Wason, Daniel Harrison, Elizabeth West Marvin, Catherine Nolan, and John Covach for their bibliographic assistance and other advice rendered at various stages of my work on this essay; and to the students of my graduate seminar in the history of theory at the University of Washington in Spring 1992, in which many of the writings treated in this essay were read and fruitfully discussed.

1 Allen Forte, "Banquet Address: SMT, Rochester 1987," Music Theory Spectrum 11 (1989): 95–99.

2 Allen Forte, "A Theory of Set-Complexes for Music," Journal of Music Theory 8 (1964): 136–83; Forte, The Structure of Atonal Music (New Haven and London: Yale University Press, 1973).

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