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Book Review

Introduction to Post-Tonal Theory

Introduction to Post-Tonal Theory by Strauss

Fourth Edition

Joseph N. Strauss
W.W. Norton & Company, xiv + 396 pp
ISBN-10: 0393938832
ISBN-13: 978-0393938838
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It could be persuasively argued that the arithmetic (algebra and even geometry) behind post-tonal music theory contains concepts and principles which are some of the most difficult to understand in all music theory. Once the "discrete" world of key signatures (including multiple modulations, and the relationships between tonic and dominant etc) was abandoned, composers and listeners encountered modulo mathematics to arrive at (amongst other things) pitch-class equivalence; ordered and unordered pitch-class intervals; and the relationships between them. They/we have to deal with interval-class vectors and set theory further to isolate, identify and describe (the manipulation of) pitches, pitch-classes, intervals and set classes. We have to understand contours and shapes as applied to Voice Leading, Interval Cycles and Set-Class Space; geometric and graphical analysis for Centricity and Inversional Axis; and have a holistic grasp of the principles of Twelve-Tone music in all its forms.

That an understanding of such technicalities is advisable (perhaps even necessary) should be just as energetically and unapologetically asserted for listeners and music lovers who may be uncomfortable with, or even antagonistic towards, music of the past century. And certainly indispensable for those who want to gain and enjoy a deeper understanding of post tonal music in just the same way as they would seek to appreciate sonata form, or the difference between aria and recitative from earlier in the Common Practice era. Surprisingly, many of even the classic texts on atonal and post tonal music are dense, written for those already at home with the underlying science and mathematics, and – perhaps most dauntingly – jump straight in to quite abstruse material for the non-specialist. This tends to be either because it's the most crucial or prominent; or (paradoxically) because it is the hardest-going material. But such an approach helps neither the determined, nor the timid, alas, if they really lack the basic preparation to get started. They're stuck.

One such book which expected greater and more permanently internalized familiarity with why such music as that of the composers of the Second Viennese School, some Stravinsky and Bartók, was the third edition of Joseph Straus' "Introduction to Post-Tonal Theory" (0-13-1898906, 1990). It wasn't a bad book. It shouldn't be abandoned if you already have the background knowledge to work through it. But its elliptical coverage of some key material at the start did make it a challenge – especially for the beginner.

That third edition covered in barely 250 octavo-size pages what this new and significantly updated fourth edition, considered here, takes nearly 400 pages – almost a third as large again to introduce, explain and illustrate. It contains new and expanded coverage of several important facets of atonal theory including transformational theory, voice leading, and the application of set theory to rhythm. This fourth edition of Introduction to Post-Tonal Theory is still an expensive book costing at least US$75 new; but (except, perhaps, for the most advanced of specialists – and indeed not all of those) the price is very well worth it. This edition is unreservedly recommended.

This can be said with such confidence that merely to glance at random at the many tables, formulae, closely (but always clearly) annotated musical examples, superscripts, subscripts, arrows, lines and matrices is (if approached in the right spirit) to let oneself in for infinite delights. Such a "right spirit" is the assumption that Straus' is a safe pair of hands. It's an assumption you can make about the Distinguished Professor of Music Theory at the Graduate Center of the City University of New York, having taught and/or held visiting positions at the Universities of Wisconsin-Madison, Chicago, Harvard, Yale, and Princeton. Assume safely, too, that the complex will be gently peeled back to reveal small and accessible chunks of theory. That is will be illustrated comprehensively and continually taking advantage of hundreds of musical examples from the period. You won't go wrong.

Nominally Introduction to Post-Tonal Theory is divided into six overarching chapters: Basic Concepts of Pitch and Interval (11% of the book's substantive content); Pitch-Class Sets (14%); Additional Properties and Relationships (18%); Motive, Voice Leading and Harmony (18%); Centricity and Referential Pitch Collections (17%) and Basic Concepts of Twelve-Tone Music (20%). Each comprises between five and thirteen sections; each section is followed by exercises, then model and guided analyses. Most readers are well-advised to follow the order in which Straus has chosen to present his material: it can be seen even from those chapters' names that – music theory being what it is – everything really relates to everything else. But some paths through the material are more likely to sponsor successful understanding than others. Although the index of concepts is only just over five pages long (and that of composers and works less than half that), it's an index which really is comprehensive and helps for those occasions when, perhaps, something needs to be checked or explained in another context.

It has to be said, too, that one of the strengths of the book is how well it has succeeded in arranging, ordering and cross-referencing related concepts and principles. The prime example of this is surely the concept of the Class: how pitches and sequences relate to one another, to what is expected, and to what came before. Without understanding this, such atonal music would just be random to the listener. So Straus examines one or another aspect of the form(s), space(s), sequence(s), correspondences and motion of the musical idea throughout the book. He returns to the mathematics of this – though situated firmly in the musical – whenever it's necessary to build on the previous concept; and refers thereto with exemplary clarity.

Equally helpful (this is not easy theory) is Straus' use of analogy and comparison with Tonal music. In Chapter 5, for instance, the parallel which the author draws between re-inforcement using Centricity [page 232] in atonal construction and the emphasis to a tonal musical motif or cell using louder, longer or more frequent pitches may lower many reader's anxiety level. Helpfully, the essences of new (and repeated) concepts are pulled out in differently-colored boxes. The book has plenty of white space and is laid out well with contrast and visual guidance where appropriate. Short "In Brief" sections provide stepping stones and quick references… "In post-tonal triadic music, the triads may be related in a variety of nonfunctional ways, including contextual inversions (like L, P and R)", where, of course, the italicization will direct you to the carefully-sequenced and managed places through the book where contextual inversion has been introduced, explained and given clear and transparent examples. These include some perhaps surprising places in twentieth century music where one or more pitches is/are inverted around common ones.

The Fourth edition of Straus' Introduction to Post-Tonal Theory, then, is a much better book than the earlier edition(s)… longer, bigger, clearer, more comprehensive, better paced, better and more comprehensively illustrated (both musically and diagrammatically). Its explanations and the author's sense of sequence, what needs lingering over and approaching from multiple angles, what needs cross-referencing; and – importantly – which sources in the repertoire (each chapter has a page or two of annotated bibliography and further reading/listening) best draw out the current/corresponding theory. Indeed, it's pedagogically very sound in perhaps the way that only a real expert can make such a book. Thanks to their familiarity not only with the material but with those areas with which (generations of) students have found difficulty, they can be trusted to lead the reader. As a course and reference source, as a clear exposition of the main aspects of atonal music, and as a volume which works with the reader and knows they are on a "journey", Introduction to Post-Tonal Theory deserves (and seems likely) to become the leading text on its subject.

Copyright © 2018 by Mark Sealey.