Analytic Approaches to Twentieth-Century Music, by Joel Lester

October 1, 1990

Analytic ApproachesAnalytic Approaches to Twentieth-Century Music, by Joel Lester. New York: Norton, 1989. xi + 304 pp. ISBN 0-393-95762-4

The marked diversity of twentieth-century music offers great challenges to those involved in the study and teaching of this repertoire. The wide range of styles and the many innovative approaches to musical structure have made the development of conceptual models for the analysis of this music problematic. The field of music theory has taken great strides in recent decades toward addressing this problem, notably with the development of pitch-class set and serial theory. As the knowledge and application of these theories have been disseminated, their analytic principles have been the focus of, or have been incorporated in, texts on twentieth-century music.

Analytic Approaches to Twentieth-Century Music by Joel Lester, a text intended for advanced undergraduate students, is one of the most recent contributions to this literature. The book is in four units: "Tonality and Twentieth-Century Music," "Pitch Structures," "Serial Music," and "Since World War II." Despite the broad scope suggested by these titles, the text is primarily an introduction to the techniques of pitch-class set and serial analysis. Its focus on the analysis of pitch is immediately evident in the proportions of the material: Unit Two (five chapters) and Unit Three (six chapters) constitute over two-thirds of the text (210 of 303 pp.). Unit One is relatively brief (four chapters, 64 pages) and is preparatory to the subsequent units. The last unit comprises a single chapter (24 pages) and offers only a very brief survey of recent music; in effect, it is an appendage to the text.

The scope and focus of the text are expressly stated in the preface. Lester's intent is to present new theories that "treat the languages of twentieth-century music on their own terms, not as distortions of the rhetoric of earlier music . . . " and to present these theories "with as little jargon as possible" (p. ix). He acknowledges that the new theories to which he refers focus on pitch structure and are based primarily on the work of Milton Babbitt, Allen Forte, and George Perle. He describes the text as introductory in nature, intended to address the problem of the widespread ignorance of twentieth-century music through discussion of a wide range of repertoire in contrasting styles; he makes no pretense that his text is a survey of twentieth-century music, noting the absence of "some composers of stature" (p. x). Despite these limitations, Lester claims that "once students learn the approaches to analysis, they can study any piece or style" (p. x). The validity of these limitations and assertions will be considered here, after an evaluation of the content and organization of the text.

The ordering and presentation of ideas and material are generally clear and pedagogically sound. The units on set theory and serial music, which are the core of the text, are especially noteworthy in this regard. Preliminary chapters in each unit present the basic principles of set and serial theory in a systematic and straightforward manner, proceeding gradually from simple to more advanced material. Discussions are consistently accompanied by musical examples and by clear illustrations of specific techniques and procedures. Each chapter in the text includes a summary of important terms and issues addressed, along with exercises that serve as useful drill for procedures. Analytic and compositional exercises are also provided, as well as suggestions for further reading. This variety of instructional material lends itself to a flexible approach to the subject matter.

In its avoidance of theorems, equations, and abstractions—features that cause an aversion to or even disdain of set theory in many musicians—the text is perhaps the most accessible introduction to the subject available. Technical jargon is kept to a minimum, a feature of the text that contributes to the author's readily comprehensible writing style and avoids inundating students with terms. Many of the standard terms are replaced or omitted. Thus, "lowest ordering" is substituted for "normal order," "common elements" replaces "invariants," "pitch-class region" is substituted for "set complex," and "secondary set" is not presented in the discussions of aggregates and combinatoriality.

While this approach to the subject matter is pedagogically commendable, certain objections may be raised concerning the treatment of terminology. First, though some of the terms such as "lowest ordering" are quite sensible, whether the substitute terms are clearer and more easily understood is debatable. Second, jargon must not be confused with widely accepted and explicit terminology; ultimately such replacements may add to the problem of excessive jargon for which theoretical and analytical writings are often criticized. Finally, if an introduction to a theory is intended to prepare a student for additional reading and study, it should present the language common to the field. Reference to alternative terminology would be a simple solution to this problem. (One instance of this occurs in the discussion of interval content, where reference is made in a footnote to Forte's "interval vector" [p. 9].) Lester's omission of some terms is perhaps less objectionable, a point that will be addressed below.

More importantly, the explanations of the terms and procedures must be thorough and consistent. Though the text is by and large successful in this regard, there are occasional problems, notable in the unit on set analysis. The effort to avoid confusing students with too much material at once sometimes results in a lack of concision or clarity. In presenting the procedures for determining "lowest ordering," the author directs that "if the last interval in step 2 [rotation, beginning with the upper pitch of the largest interval, followed by transposition] is the same size or smaller, the student should rewrite the pitches from right to left, write the complement of each number, and transpose to begin on 0" (p. 86). That the condition "same size" (referring to the intervals . . . ) may be true of sets in which the largest interval is duplicated, is implied by subsequent discussions but is never stated; that the prescribed procedures are not necessary for symmetrical sets is not addressed until the next chapter. Even then, the only explanation given is that "there are a number of sets that retain all their pitch classes [under inversion]" (p. 114). Lester's discussion of finding the lowest ordering of sets in which the largest interval is duplicated makes no reference to shortcuts for identifying prime form. Throughout this section, interval successions are not labeled in the examples and the notion of "most packed left" (to borrow John Rahn's phrase) is not identified. Further, no table of prime forms is given for checking one's work. These omissions prevent students from quickly mastering this fundamental procedure.1

Other problems occur in the discussion on inverting a pitch-class set. The procedure is explained prior to the discussion on ordering sets (p. 84) and later in the context of interval content (p. 100) with different results, a potentially confusing point for students. The differences in the use of the terms "inversion" and "complement" with reference to intervals and pitch-class sets are not clarified. Similarly, the varied use of fixed and movable 0 for pitch-class designation that is employed in the text is never formally justified. The unit on serial music is stronger with regard to clarity and ordering, though some illustrations are confusing—for example, that of Berg's rotation procedures in the Lyric Suite, III (p. 242)—and the difficulties in finding the prime series of some twelve-tone works require clarification. Schoenberg's Klavierstück, Op. 33a is used as an example, but the illustration of procedures does not conclude with the identification of PO.

The application of analytic principles and serial techniques, often in the form of model analyses, is clearly presented, with annotations that clarify the points under discussion. One very helpful feature of the text is the notation of sets or twelve-tone series that accompany musical examples. The analyses include insightful and often engaging commentary, and provide a valuable introduction to some important works of this century. However, because the model analyses usually focus on specific features of pitch organization in a given passage or work, one misses a comprehensive model that would have demonstrated the potential for a flexible application and interpretation of the analytic approaches discussed. Similarly, the inclusion of a composite list of terms and procedures would have been helpful at the end of units or in an appendix, particularly for beginning analysts. The organization of the text leaves this task to the reader. (The only appendix in the text is on determining hexachordal combinatoriality, and no glossary of analytic terms is included.)

Formal discussion of set relations and a comprehensive examination of the precompositional features of twelve-tone series are not presented. Rather, the latter chapter in Unit Two and all but the first chapter of Unit Three focus on the study of musical examples whose structural features demonstrate specific analytic principles and compositional techniques. Consequently, a large portion of the chapters consist of the analysis of various excerpts or short movements. This emphasis on an analytic rather than theoretic approach to the subject matter allows students time to absorb material and drill procedures. While this approach results in a less than complete exposition of set relations—no discussion of complement relations and set complexes is included, and the designations for equivalence and similarity relations are not presented—it avoids burdening students with additional terminology and with the abstractions and complex explanations prevalent in other discussions of set relations. Given the intended scope and audience of the text, these omissions seem justified.

The discussions of set relations are presented in two chapters entitled "Using Different Pitch-Class Sets" and "Pitch-Class Regions, Scales, Modes." In spite of the omissions cited, the analysis of the structural significance of the interval and pitch content of sets and their transpositions in various works provides an adequate introduction to the fundamental principles of set relations, proceeding from consideration of smaller sets to larger pitch-class regions. One questionable omission is a discussion of the complement relation between sets, a concept whose significance has been demonstrated in a wide range of repertoire.2 The unit on serial music, however, is more comprehensive and includes chapters on common elements (invariants), combinatoriality, derived series, multiple orderings, and other aspects of serialism.

A prominent feature of the text is the recurring use, across chapters, of works that the students are expected to listen to repeatedly. (The number of composers represented in the text is consequently rather limited; the majority of the pieces are by Babbitt, Bartók, Debussy, Messiaen, Schoenberg, Stravinsky, and Webern.) This feature has the merit of encouraging students to correlate the analytic principles presented with the aural effects of the music and to base their own analyses on a thorough familiarity with the music, points repeatedly stressed throughout the text. Granted, the relation between analysis and listening is complex and problematic, and will vary among individuals. But Lester makes no claim of teaching students "the way to listen to twentieth-century music" (p. xi), and his emphasis on coordinating analysis and listening is laudable, especially given the tendency toward an "eye-over-ear fallacy" to which set and serial analyses are particularly susceptible.

Lester's concern about this tendency may be inferred from his emphasis on aural comprehension and from his discussions on set identification and segmentation. These steps are, of course, critical in the application of set theory. The criteria for these steps are widely acknowledged as problematic, and rules are difficult to establish, especially when analyzing atonal music.3 Individual works suggest varying criteria, and contextual consideration of all parameters is paramount. (This issue is relevant, though not as critical, to serial analysis. Set analysis is also applied to serial works in the text with appropriate distinctions between ordered and unordered sets and with an emphasis on audible features of specific works.) Lester stresses these points in a valuable discussion of general guidelines. Students are cautioned against indiscriminate grouping of pitches into sets and urged to consider "those sets that enhance our hearing and understanding of the piece" (p. 90). He closes his discussion with the following remarks:

You will find that after you have identified and learned to hear the set or sets that are prominent in a passage, and after finding these pitch class sets as they occur in several ways . . . you can begin to listen for more subtle features (p. 90).

While Lester's emphasis on aural comprehension may inhibit students from identification of structurally significant sets that are not readily audible or related to the musical surface, his comments suggest a reciprocal relationship between listening and analysis that encourages thoughtful and musical analyses.

In light of its intended use as an introductory text, the scope and focus of the book must be considered from a broader perspective. In the summary of Unit Two, Lester states:

It was for some time traditional to draw clear dividing lines between tonal music, the nontonal music of this century and twelve-tone music . . . . But as the discussions in this Unit have demonstrated, these sharp distinctions are not borne out by study of the music . . . . As a result, the focus of many studies of twentieth-century music in recent years is turning toward those principles that underlie all music of our era. The study of pitch-class sets . . . gives analysts one set of tools with which to work (p. 169).

These statements raise questions concerning the limitations of the analytic approaches presented in the text and the value of alternative approaches to analysis.

Among the criticisms that have been leveled at set and serial analysis, the tendency to overlook or ignore the importance of aspects of the music other than pitch and matters of style is prominent. Lester is clearly sensitive to this issue, for his analyses offer many insightful observations concerning the treatment of other elements and their significance to structure and style. Nonetheless, these comments are subsidiary to the analysis of pitch structure. Unit One, which includes chapters on "Pitch in Tonal and Nontonal Music," "Rhythm and Meter," "Texture and Timbre," and "Form," offers only a brief overview of these topics and focuses on the differences between tonal and nontonal music. The first chapter introduces the concept of sets as a broader interpretation of the term "motive" appropriate to twentieth-century music, and explains the need for the designation of pitch and interval classes. Subsequent chapters present a condensed (though useful) survey of their topics, and introduce some of the basic techniques and terminology associated with the treatment of these elements in twentieth-century music. The exercises provided with this unit are accompanied by some interesting questions for consideration, but are primarily geared toward listening. Few analytic principles and no model analyses are presented in the text to serve as a basis for addressing these questions. As noted above, consideration of these elements is integrated throughout the text, but the preliminary ideas found in Unit One are not applied nor expanded on systematically. Thus, the value of analyzing elements other than pitch separately is not considered at any length.

Besides the somewhat attenuated coverage of elements other than pitch, what may raise concern among potential users of the text is the lack of emphasis on alternative and traditional approaches to the analysis of pitch structure. Though the usefulness of set analysis has been widely acknowledged in recent years, its acceptance has not been universal and its value remains a controversial issue. Even among adherents of set analysis, the analysis of harmony, voice-leading, and tonal relations is still deemed of value in gaining insights about musical structure not provided by set analysis, especially in works that blend tonal and nontonal elements.4

While Lester's analysis of works by composers such as Bartók, Debussy, and Stravinsky do address these subjects, he does not consider them thoroughly or analyze them consistently. His brief discussion of the tonal elements in these works serves to reinforce the value of set analysis in illuminating other aspects of pitch structure. But these discussions often raise questions concerning the use and structural function of these elements which are not analyzed in any detail. For example, in an analysis of pitch-class sets in Debussy's piano prelude The Sunken Cathedral, the author states that "the piece ends on a C-major triad, but the sense of tonality is quite extended. There are few functional harmonies, and many of the triads and seventh chords that do occur operate in a nonfunctional manner" (p. 116). Just how the tonality is extended and why the harmonies are nonfunctional is explained in only general terms; the mixture of major, modal, and whole-tone scales, the use of parallel harmonies and pedal points, the harmonic successions, voice-leading and large-scale linear connections, and the relation of these aspects to the formal structure of the work are not analyzed.

The author's assumption appears to be that students are conversant with traditional notions about this repertoire, since formal discussions of harmony and voice-leading are not found in the text. Such an assumption is questionable. In a one-page discussion of the dissolution of functional tonality, the author simply observes that:

By the beginning of the twentieth century, functional tonality ceased to be a controlling influence over harmony and voice leading in the music of some composers. . . . Many composers continued to write music that is tonal in the traditional sense, although often with new types of harmonies and voice leadings not found in tonal music from before 1900 (p. 7).5

Fifth-ordered series derived from diatonic scales and the use of whole-tone octatonic, and altered scales are addressed, but modality and other extensions of traditional harmonic resources are not discussed in a comprehensive manner. These scales are considered as "pitch-class regions analogous to key area in tonal music" (p. 109).

The preceding observations and the author's reference to new theories that do not treat the languages of twentieth-century music as distortions of the rhetoric of earlier music reveal an analytic bias that will not be shared by all readers. Many would argue that the application of analytic models based on functional tonality and an understanding of techniques that are extensions of common-practice procedures are requisite to the study of transitional works of this century, as well as to more conservative repertoire. Further, such models and techniques utilize principles with which students will be familiar and thus may be deemed essential to a beginning text on twentieth-century music.

The criticisms presented above primarily are intended to clarify the scope and focus of the text under review, and reflect the challenges in writing a text on the analysis of twentieth-century music. The extent to which modified but traditional approaches are viable remains controversial, and will vary from piece to piece and from analyst to analyst.

No text can rightfully be expected to cover all aspects of its subject: authors must set limitations on the basis of their intentions and convictions. Virtually all of the limitations of this text are clearly set forth in the preface, and Lester states that "what is included are those aspects [of the theories discussed] that I deem to be of greatest relevance to a student beginning work in this field" (p. x). The validity of his assertion that the analytic approaches presented in the text prepare students to "study any piece or style" is a matter of personal judgement. Although, as discussed above, there are some problems in the presentation of material, student response to the text in a course this reviewer recently taught was extremely favorable. The text merits consideration by those seeking a thoughtful and accessible introduction to set and serial analysis and to some representative works of the twentieth century.

1Reference is made, under "Suggestions for Further Study" (p. 107), to lists of pitch-class sets and their interval contents in Allen Forte, The Structure of Atonal Music (New Haven: Yale University Press, 1973), and John Rahn, Basic Atonal Theory (New York: Longman, 1980).

2See, for example, Richard Parks, "Complement Relations," chap. 6 in The Music of Claude Debussy (New Haven: Yale University, 1989).

3See David Beach, "Pitch Structure and the Analytic Process in Atonal Music: An Interpretation of the Theory of Sets," Music Theory Spectrum 1 (1979): 7-22; and William E. Benjamin, "Ideas of Order in Motivic Music," Music Theory Spectrum 1 (1979): 23-24.

4For summaries and a response to criticisms of set analysis see Allen Forte, "Pitch-Class Set Analysis Today," Music Analysis 4 (1985): 29-58.

5Many of the composers of stature not mentioned in the text fall into the latter group.

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