Some Combinational Properties of Pitch Structures
Harry Howe · Perspectives of New Music · 1965
In this paper I shall develop some ideas having to do with properties and relations of sets of less than twelve pitch-classes and their applications to combinational musical systems.1 In this part of the paper I will discuss the historical background of some of these ideas, how they differ from those of other approaches, and some of the reasons for these differences. I will also describe the methods by which I arrived at these results and their advantages. The second part of the paper presents complete formal definitions of all of the essential terms for the concepts employed in the paper. Although several of these are familiar from other theoretical studies and ordinary language, some of them are defined in new or unfamiliar ways in order to effect the convenient description of meaningful relations. The third part of the paper considers properties and relations of these concepts which follow from their definitions, and the final part discusses the consequences of accepting some of these concepts and illustrates the way in which they can be applied to a specific example. Most of the factual materials presented in this paper deal with work