Coherent Tone-Systems: A Study in the Theory of Diatonicism

Abstract

Looking back at the second half of the present century, a future historian of music theory might cite 1962 as the year modem diatonic theory came into being: the newly founded Perspectives ofNew Music published in 1962 an article by Milton Babbitt entitled Twelve-Tone Rhythmic Structure and the Electronic Medium, including a brief yet thoughtprovoking allusion to the major/minor scale-system.' When Babbitt introduced the integer model of pitch around the mid 1950's, his primary aim was to place the study of post-tonal music on a more rigorous, scientific basis; indeed, the model has since become a standard component in post-tonal theory, as testified by the work of theorists as Allen Forte, David Lewin, Robert Morris, George Perle, and John Rahn. Babbitt may have not foreseen that the integer model would also inaugurate an important line of research concerned with tonal, rather than post-tonal, music. In any event, today there exists a sizable body of literature on diatonic and related tone-systems considered in terms of Babbitt's integer model (or extensions thereof); representative works include Gamer (1967a), Balzano (1980; 1982), Clough and Myerson (1985), Brinkman (1986), Agmon (1989), Carey and Clampitt (1989), Clough and Douthett (1991), and Rahn (1991).2 One might assume that three decades or so of rigorous diatonic re-

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