Coordination of Interval Sizes in Seven-Tone Collections

Abstract

In the Appendix to his book on The Structure of Atonal Music, Allen Forte lists 38 seven-pc subsets of the twelve-semitone set (1973 and cf. 1964). These 38 sets are listed in Figure 1. In the present study, each of these 38 7-pc subsets of the twelve-semitone aggregate is referred to as a seven-tone collection. In recent years, much attention has been paid to collections in general and in particular to the so-called collection. (The diatonic is 7-35 in Forte's numbering, which is followed in Figure 1.) Authors who have dealt with the diatonic include Eric Regener (1974: 199-201), Robert Cogan and Pozzi Escot (1976: 140-41), Richmond Browne (1981), Robert Gauldin (1983), John Clough and Gerald Myerson (1985: 249-62), and, most recently, Richard Cohn (1988: 29-30). The so-called chromatic heptachord (7-1 in Forte's numbering) has also been studied, notably and in connection with so-called deep scales, by Milton Babbitt (1965: 54), Hubert S. Howe (1965: 52), and Carlton Gamer (1967: 3946). As well, Richmond Browne (1981: 5, 9) has remarked, in passing, on what might be termed the harmonic minor collection (7-32) and what could be called the ascending melodic minor collection (7-34).

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