When we analyze tonal music, the basic principle of tonality -- that a single pitch class (pc) is the gravitational centre for a work's pitch structure -- generates most of the terms of reference for our analysis. For instance, in analyses of "common-practice" tonal music (much of the music written between c.1650 and c.1900), such concepts as scale steps, chord functions, and tonicization help to describe a system -- an evolving system, to be sure -- of pitch relations.
Some twentieth-century music, however, is not tonal. Not only does such music avoid the conventions of common-practice tonality; it avoids projecting any clear sense of a central pitch class. Analyzing this music is challenging. There appears to be no generalized system of non-tonal pitch structure; instead, each piece seems to create its own contextual structure. And it may be unclear just what the bases of such a contextual structure might be.
An approach that has gained favour with musicians intrigued by non-tonal music is pitch-class set analysis. Like other analytical methods, pc set analysis has a few essential features:
Just what use we make of pc set analysis depends on our interests and skills. The music of Schoenberg, Berg, Webern, Stravinsky, Bartók, Debussy, Scriabin, and their contemporaries has formed the core repertory to which pc set analysis has been applied, but it has also been used to examine later and earlier music, including tonal music. Indeed, studying pc set analysis doesn't just give us a new toolbox for probing many pieces of music; it can give us a new way of thinking about pitch design in general.
Pc set analysis builds upon the observation that, in the absence of tonality's centralizing force, pitch structure often seems to be grounded in the intervallic relationships among pitches. At times these relationships also throw certain pitches or pitch classes into prominence. Some intervallic relationships may be obvious to the listener. Many others may not be, and pc set analysis has proved useful at uncovering and categorizing these relationships.The present guide is in two parts.
This guide includes some exercises, some of which you are guided through, with answers, to give you practice in dealing with analytical concepts and operations. In addition, the guide includes a pc set-class table and an annotated bibliography of basic printed and on-line resources in pc set analysis.
|Page last modified 3 October 2001 / GRT||