The Cycle-7 Complex: Relations of Diatonic Set Theory to the Evolution of Ancient Tonal Systems

Abstract

recent application of set theory' and the concepts of pattern matching and position finding2 to the diatonic set 7-35 has served to refocus attention on the manner in which pitch and interval classes operate within a tonal hierarchy. To quote Richmond Browne, The notions of interval content and intervallic context will serve as vehicles for ... position finding and pattern matching operations in tonal usages of the diatonic set. Content and context, like position finding and pattern matching, are in some senses dialectically related ways of looking at the same data.3 Little attempt, however, has been made toward the possible employment of these principles in a historical perspective-in particular, the evolution of musical systems in early civilizations. It is conceivable that the resultant wedding of old and new could shed illumination on the question of com-