Introduction to Post-Tonal Theory, Third Edition. Joseph N. Straus.
©2005 Pearson Education Inc., Upper Saddle River, New Jersey.
I have wanted to review this book for many years, as I initially learned about set theory from the first edition of Post-Tonal Theory. In 2004, I took a course in contemporary music theory which used the third edition, and had a chance to go through this revised and expanded edition as a student. From this new perspective the book remains a fundamental overview and reference, perhaps the best currently available on the subject.
The third edition has gone to considerable lengths to clarify and simplify the often-daunting task of explaining the highly mathematical realm of contemporary set theory, using inventive diagrams and a wealth of new techniques for ordering sets. Straus has increased the number of examples drawn from actual compositions. As the book progresses from abstract explanations of set theory to new chapters on centricity and triadic post-tonality, there is a stronger sense now than in the earlier editions of how certain set theory collections arise from actual tonal considerations, as opposed to pure mathematics. The chief progenitor of set theory, dodecaphonic composition, is put into better perspective as merely one more way of utilizing sets. The new book includes analysis of recent works from Adams to Gubaidulina to Zwilich, in addition to the canon examples (Schoenberg, Webern, Bartok etc.) from earlier editions.
One crucial issue remains the same for me in the latest edition: in practice, theorists and composers using set theory often seem to be putting the cart before the horse, musically speaking. Common-practice theory developed over a period of centuries as a means of explaining the coalescence of various modal means of writing into a discernible language, the basis of which is equal temperament. Thus, common-practice theory explained harmonic/melodic logic after the fact, and spoke of techniques which arose first in the ear. These were usually based in some way on the overtone series–aural logic, you might say.
Set theory is the logical extension of dodecaphonic writing. Such writing was essentially the first in Western music to order harmonic/melodic patterns primarily by mathematical means. Although certain tone rows–Berg’s Violin Concerto for example–seem to have arisen from aural needs (his row of rising thirds sounds to me as though it has a great deal of harmonic logic), in that same row Berg breaks the logic at the end for rhetorical reasons–to include the four notes of the Bach chorale–rather than aural. In addition, the mathematical limitations of the row prohibit Berg continuing by thirds, even if he so desired. As set theory has evolved beyond the dodecaphonic, composers seem to rely on it in a mathematical way, forgetting that aural logic was the primary basis for systems of the past. Modern sets often seem to be somewhat arbitrarily chosen in terms of their relationship to the overtone series.
What is the best compromise between these traditional and contemporary theories? Look back to the overtone series and the ear, and use set theory primarily as an a posteriori means of ordering. Is discussing this issue within the province of this book? Perhaps composers and theorists will have to resolve this elsewhere, as Straus’ book is an overview, not a theoretical tract. However, I hope to see any such work reflected in future editions. The chapters on centricity and triadic post-tonality are a good start.
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