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Book Review

Michiel Schuijer's superb study of pitch-class (PC) set theory begins with an anecdote:

In the late afternoon of October 24, 1999, about one hundred people were gathered in a large rehearsal room of the Rotterdam Conservatory. They were listening to a discussion between representatives of nine European countries about the teaching of music theory and music analysis. It was the third day of the Fourth European Music Analysis Conference… Most participants in the conference (which included a number of music theorists from Canada and the United States) had been looking forward to this session… A late visitor entered the room, and seated himself on a chair in the middle of the front row. He listened for a while to the discussion, his face expressing growing astonishment. Then he raised his hand and said:

"You guys are discussing methods of analyzing twentieth-century music. Why don't you talk about pitch-class sets?"

He was American. The chairman, a professor from the Sorbonne, was quick to respond:

"We do not talk about pitch-class sets, because we do not hear them!" [pp 1,2]

The dialog that followed illustrates one of the two premises on which Schuijer's book is based: that American acceptance of pitch-class set theory as an analytical tool is beneficial to composers, musicians and, ultimately, to listeners – if for no other reason than that post-tonal music can be complex; and pitch-class set theory helps us to understand and appreciate it. At least, some familiarity with it is a major advantage. Schuijer explains, though, that such an understanding in North America is best considered when viewed as part of the movement since the middle of the last century to elevate music theory into a discipline in its own right – as opposed to an adjunct to (the study of) performance practice. Here, of course, the systems of Shenker (1869-1935) for tonal music and Allen Forte (b. 1926) for atonal music predominate. That these strands have been somewhat in opposition is evidence by contributions from William Benjamin and Joseph Kerman; although we must be wary of seeing too distinct a dichotomy of trends. Rather, what they have in common (rigor, system, analysis based on theory) is to be emphasized

Schuijer is at pains to distinguish carefully and clearly between American and European (particularly British) schools of "music theory" and "music analysis", both where the former is a superset in(to) which the latter fits; and where analysis (as "dissection") itself relies on "a framework of concepts and/or protocols". It's in this second sense that Schuijer's exposition and discussion of PC set theory (the book's second raison d'être) is placed. Indeed, this European approach of situating theoretical understanding in the "service", almost, of analysis is the more sensible one. It is that embraced by Schuijer in this book. At the same time, he does not ally his discussion with those who would use either analysis or theory to "validate" or "endorse" music that's accepted as great for other reasons.

So it is against such a background, and with such ground rules established, that Schuijer then proceeds to examine how and why pitch-class theory works; what it is; what its relevance to music is; where and how it might develop and – again, in the seventh of the book's eight chapters – how such otherwise apparently abstract matter can and does relate to performance. This is an appropriate way to tackle what can be complex and intimidating to non-specialists. The earlier heat has been to some extent taken out of the debate and the work of Forte and the likes of Milton Babbitt gained greater acceptance in both musical traditions. After all, to understand PC theory is also to see that even the most conventional of tonal music is amenable of such a description: a common triad (C-E-G) uses a pitch class set; it is instructive to examine, say, a Bach chorale or a Mozart piano sonata in the light of the kind of manipulations and analyses which PC theory sponsors.

Michiel Schuijer teaches at the Conservatory of Amsterdam; his research interests tend to concentrate on the relationships between music history and music theory. So, even were Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts not the detailed, clear and perceptive study that it is, the topic(s) under discussion in the book would be central to our appreciation of contemporary music because of PC theory's intimate reliance on theory (as defined above) – thanks, in no small part, to the role of the computer in musical composition, production and analysis (in the broader sense).

So the book is actually the best of both worlds. If you're more interested in the historical narrative and the processes and persons that threw up PC set theory, this is an excellent place to start. The 30 or so pages of the first chapter, and the aforementioned seventh, as well as the eighth chapters (or about a third of the book's substantive content in toto) deal extensively with the "history". The rest of the book takes the reader carefully, gently and in admirable detail through the acoustics, mathematics, philosophy and many algorithms of pitch classes and their use in music.

In the first aspect (the wider cultural context) there is no better introduction, although of course Forte's own seminal The Structure of Atonal Music (ISBN-10: 0300021208 ISBN-13: 978-0300021202) us essential. As it is, and is Joseph Straus' Introduction to Post-Tonal Theory (ISBN-10: 0131898906 ISBN-13: 978-0131898905), to an understanding of the basic concepts. Schuijer's Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts picks up where Straus (to which it often refers).

In dealing with the basic objects and entities of PC theory, the algorithmic operations necessary to manipulate musical elements with it, equivalence, similarity, and inclusion, Schuijer covers his ground admirably. The book is amply illustrated – not only with notation, of course; but also diagrams, tables, formulae, quotations, illustrations, examples and lists. There is an exhaustive bibliography, well-designed footnoting and more than adequate index. The standard of proof-reading seems to be well up to Boydell/University of Rochester's usual extremely high standards and the design – for such a complex and intensely apparently theoretical subject – particularly conducive to its understanding.

At times, it seems as though there is more to learn, understand and absorb in contemporary music than at any period in history. Trends, theories, analyses (in all senses of both those words), explanations and methods of writing and making music are many and multiform. In this understandably expensive book, Schuijer makes a very compelling case for treating the concepts, mathematics and actually very approachable systems of Pitch Class theory as one of the pre-eminent ways of looking at post tonal music – once you've understood the basic elements. Moreover, he makes his case with style, authority and the deft guidance of a true teacher. Highly recommended.

Copyright © 2011 by Mark Sealey.

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