10. The uses of pc-set analysis.

What use you make of the set and set-class data you gather depends on your interests, analytical skill, and imagination. The interests of musicians using pc set analysis vary from the concrete to the abstract. On the concrete end, you can analyze a single work, exploring the structural and expressive aspects of the work's pitch organization. Broadening out, you can attempt to characterize the pitch-structural "language" found in a repertoire, perhaps the works of a single composer like Bartók or of a cultural milieu like the Second Viennese School. At the most abstract, you can explore the inherent properties of set classes, gaining insights into the 12-pc universe on which almost all of our western music is built. Such insights can be of interest to composers as well as to those who are just intellectually intrigued by the world of tones.

A basic concern for most music analysis is that the analyzed segments of the music be shown to relate to each other. It's usually felt that most pieces demonstrate coherence among their parts. Unity may also be a hallmark of many works -- a sense that their coherence is governed by one central force or principle. (To be sure, twentieth-century music does offer examples of works whose apparent aims are multiplicity rather than unity and fractured rather than coherent experience.)

A search for coherence clearly animates the basic operations of pc set analysis: the grouping of pitches into just twelve pitch classes, the categorizing of pc sets into a limited number of set classes. The same search also drives most of the terms by which pc set data are analyzed. Most are concern with relations among pcs, pc sets, and pc set classes. Again, which relations an analyst chooses to focus on is up to the analyst. There is, however, a number of standard relations whose investigation forms a common thread in many pc set analyses. Pc set theory has developed mathematical operations to handle some of these relations. In the present guide we shall touch, at least briefly, on the main types of set and set-class relations.

Page last modified 10 July 2001 / GRT