Composition with Arrays

Abstract

A M US I CA L system, as opposed to a method of composition, consists of a well-defined set of operations upon musical configurations. The latter, however, are not necessarily fully specified musical passages, but may be specified only as to certain features. For example, the tonal system according, at least, to one plausible construction of itconsists of operations upon configurations specified as to pitch and rhythm, but not as to timbre or dynamics. Moreover, according to H. Schenker, the initially given configurations are not even specified rhythmically (except with regard to order), so that presumably certain operations must, according to this view, consist of specification of rhythmic features; thus the configurations to which the system's operations are applied need not all be of the same degree of concreteness. Nor is it necessary that the configurations which are resultants of a given system of operations be less than all of the possible configurations of a given degree of concreteness, or even less than all possible configurations specified to any degree. Thus for example, it seems to me that the distinction between tonal and atonal music is best construed not as a difference of whether or not such music is a resultant

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