A Review of J. Kent Williams’s Theories and Analyses of Twentieth-Century Music (Fort Worth: Harcourt Brace and Company, 1997).

Larry J. Barnes

KEYWORDS: Williams, pedagogy, atonality, set theory, neotonality, aleatory, minimalism, new tonality

ABSTRACT: Lest we arrive at the millennium uninformed, the time to reconcile with the twentieth century’s milieu has arrived with a vengeance. In the spring of 1997, I employed J. Kent Williams’s Theories and Analyses of Twentieth-Century Music, one of several recent texts that attempt such a reconciliation. Newly published, this was the primary resource in a course designed for upper-level undergraduate music majors. Unlike two other current texts dealing with analysis of our century’s music, Williams’s offers a brave inclusiveness, paying careful homage to nearly every salient style of this century. This review deals with personal successes and concerns I encountered with this in the classroom.

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Volume 3, Number 4, July 1997
Copyright © 1997 Society for Music Theory

Initial Observations

“Day after day, making tomorrow seem like yesterday. And remember when we said there was no future? Well, this is it.”(1)

“Humans tend to construct, accept and share with others systems that explain and organize their world as perceived and known, and feel uneasy without such explanation and organization.”(2)

[1] The recently published text, Theories and Analyses of Twentieth-Century Music by J. Kent Williams, suggests that, lest we arrive at the millennium uninformed, the time has arrived to reconcile with a vengeance the now-fading twentieth-century milieu. We appear to be in a period of intense, self-absorbed retrospection. Blank Reg’s casual paraphrase of nihilistic philosophy in the ill-fated ABC-TV series “Max Headroom” signaled that popular media had finally arrived at the cynical conclusions of Schopenhauer. We seem more intrigued than usual with a kind of fascination with relics—not the truths an icon represents, but instead an interest in any contemporary, personal, even scatological, use of the object itself. Ancient myths and legends have surfaced as facades for video games and films. Political figures stand and wait nervously while we dig up the back yards of their previous neighborhoods. A hasty search is on not for an object’s true meaning but for any immediate and personal use that object might afford; in the absence of any forthcoming evidence as to the object’s cultural significance, a meaning is conveniently attached that serves our immediate needs.

[2] The motionless music of New Age puts forward the message that the predicted age of no momentum has indeed arrived. And the “in your face” Punk defiance reluctantly gave some ground in the late eighties to the “pity me” of Grunge and Kurt Cobain, donating its vulgarities to the underground, where a steady stream of previously obscene words, disconnected from function, seems to soothe rather than shock. This dull stasis has now reached even Rap, that brash, defiant needle-rocking signal of rage from the Bronx, giving way to Detroit techno, clean and pressed computer samples in a post-disco environment run by white boys. We have chosen to dilute emotional content in favor of comfort as background to our numbing search for gratification from the past.

[3] But anyone scavenging in this cultural boneyard would have bumped into an academic, there since dawn. The thriving intellectual bustle, feeding on Dissanayake’s conclusion about the human need for organization, depends on the past for its relics, too; and now more than ever, intellectuals, seeing the century suddenly closing itself out, are the ones at the clearance sale. We rummage with a fever through piles of opinion and fact, summarizing and encapsulating. Composers borrow Western and non-Western sources in their original form freely, a practice looked upon as heresy in the sixties. Non-Western ritual and communal music is disassociated from its cultural heritage to extract “that sound.” Stricken with retro-speak, we hastily reflect back on a century nearly complete, and feed continually upon sounds that were perhaps too rich to be digested upon their inception, searching frantically for clues to their meaning, lest we find ourselves without the magic keys to the city of the third millennium.

[4] Having been raised on a steady academic diet of continually “new and better” restructuring of the past, I would like to believe that this frantic last-minute inventory serves an important function: to look down and feel the firm earth beneath before we leap. And now that the topic “twentieth-century music” actually means what it says, theorists and musicologists are pick-axing in a gold mine of opportunity. Numerous recent textbooks on the subject by various theorists include three salient ones in the last eight years—texts by Joel Lester,(3) Joseph N. Straus,(4) and J. Kent Williams. And, at least for now, the feeling of the earth beneath is indeed comforting. The view of this article is not from the center of a circle of theorists, but instead the perspective of a composer, performer of contemporary and traditional music, and a teacher of mainly undergraduate students at liberal-arts colleges and state universities for the past 25 years. So let me throw the vultures in my yard a carcass while I focus for a few moments on the pedagogical successes and problems I experienced in the classroom with J. Kent Williams’s text, Theories and Analyses of Twentieth-Century Music.


[5] It is not the purpose of this review to argue with what appear to be small editorial errors that I assume will be reviewed for a future edition or included as a list of errata. I mean instead from a standpoint of personal experience to deal with the larger pedagogical issues of the text: success of practical applications, flow of information, consistency of design among sections, suitability of examples, and concerns experienced at the undergraduate level, which may or may not surface with graduate students. I chose the Williams text over the other two mentioned above primarily, but not exclusively, because of the nature of the course. Several talented students approached me with a request that I teach the course, and therefore motivation to learn these concepts was high. These students had successfully completed two years of undergraduate theory, and in the four-term process, all chapters of the Kostka-Payne Tonal Harmony text.(5) As I designed it, the new course had three objectives: 1) to acquaint students with salient musical examples from the many aesthetic perspectives of this century; 2) to provide them with tools and drills for practicing the disassembling—and, equally important—reassembling of examples in a way that would leave the music intact but better appreciated; and 3) provide them with a resource text that could be used should they find themselves pursuing at a later date (as graduate students or professionals) topics that, due to limited class time, we could not discuss in detail.

[6] So the most important factor in the choice of text, governed by the realities of undergraduate classes, was inclusiveness. The Straus text makes no apologies for being solely pitch-based theory (with the few additions of multi-serial examples at the close), focused on atonal music, both serial and non-serial. The Lester text does include some other elements—rhythm, texture, timbre—but omits Hindemith neotonal models and has only a passing mention of Cage and his disciples.

[7] Williams pays a careful homage to nearly every salient language of this century for which some sort of notation was used at its inception. So popular idioms based primarily on oral tradition do not appear. Considering how inclusive the text is otherwise, it is probably for purely practical reasons of space rather than cultural predisposition that jazz and non-Western traditional musics are not covered. The Williams text is divided into five parts, labeled “Pitch Organization: An Introduction,” “Fundamentals of Set Theory,” “Other Aspects,” “Pitch Organization: A Closer Look,” and “Recent Developments.”

[8] The first section shows the author’s willingness to balance tonality, atonality and neotonality by fronting an example of each for a brief discussion. The author opens the discussion of tonal and neotonal music with a concise definition, but I found the same courtesy curiously missing from the parallel section on atonal music, jumping instead directly to an example. I felt my students were the least comfortable with this music and needed a brief rationale for its sound. The summary that follows the example for each type of organization contains excellent clarifications, so I asked them diplomatically to “read ahead to find the answer.”

[9] The second section introduces students to MIDI and Rahn numbers(6) as continuous pitch codes, and to complete binomial representation including pitch class, name class and octave, a la Alexander Brinkman.(7) Name classes are most useful in analysis of diatonic music, but in this context of set theory and atonal music they seemed superfluous. Williams’s explanation that name class is important in enharmonic circumstances is irrelevant to Part II, since atonal composers and theories tend not to recognize such distinctions. The interjection of name classes so early on, when diatonicism had not yet appeared on the horizon of analysis, led to a brief information overload in our class. Exercise 2-7 (page 43) asks the student to list for a melody the following: pitch (MIDI and Rahn) ordered pitch interval, unordered pitch interval, pitch class, ordered pc interval, unordered pc interval, name class, ordered nc interval, unordered nc interval, MIDI octave, ordered octave interval, and unordered octave interval. This conscientious labeling also affects his discussion of serialism in Part IV, as he insists upon listing both name classes for any “black key” note in row boxes, crowding the page with more information than needed.

[10] Logically this is done so that information is presented in the author’s “spiral organization” pattern by introducing concepts up front and returning in later chapters for greater discussion. But in my class it was not until modality is detailed in chapter 10 that a student raised her head and said “Name classes! Of course!” So the labeling section could lead to pitch-name saturation as the author’s continued inclusion of numerous references demanded that we constantly refer to a single pitch in the manner of always calling a child “Cynthia Marie Sylvia Alicia Jenkins” instead of “Cindy.” This accruing of pitch information is certainly necessary for advanced work in atonal theory, but again seems in keeping with our frantic search for clues in this era, by considering as many horizontal and vertical points of view as possible—simultaneously. Williams does offers brief explanations as to which musical circumstances might prompt the choice of one labeling system (or thread of differing systems) to aid in discovering the meaning of a specific passage. For example, the use of relative rather than absolute representation (page 34) in the Berg “Schliesse mir die Augen beide” presentation from an earlier chapter (pages 12–13) seems logical when F is a constant starting pitch for each row statement. But over-labeling of pitches, perhaps fulfilling the human need for organization expressed above by Dissenayake, can lead away from what some believe is the creative power of serialism, which Anton Ehrenzweig includes in his discussion of “unconscious scanning”:

“Schoenberg’s or Boulez’s critics quite properly complained that it was impossible by ordinary means of appreciation to recognize the submerged order of serialization. Serialization directly attacks all conscious means of continuity. These critics missed the essential point that serialism meant to defeat conscious powers of appreciation. Here is a case of the intellect turning against itself. Hence the composer and listener have to take recourse to undifferentiated (italics mine) visualization which can hold the complex serial structure of the possible permutations in a single glance.”(8)

[11] In Part III, “Other Aspects,” Williams balances the preceding saturation of pitch theory by discussing meter, rhythm, texture, form, process and temporality. Here the thoroughness of the author works in our favor, and one is grateful for an attitude as conscientious with these elements as his approach to pitch. Chapter 7, dealing with rhythm, moves from an example of metric framework in a traditional meter through the various ways composers mutated or attempted to erase this notion in our century. References in the chapter lead us through a generous sampling of the most important analytical work done on rhythm and meter in this century. And in particular, Chapter 9 is one of the best synopses I have seen of time and process. Williams balances the need to find meaningful events and their relationships with a discussion of “process”—in traditional terms, transitions; in contemporary terms anything from background step-progressions to an example of nearly pure process, a fifteen-minute glissando from one vertical sound to another in Kaija Saariaho’s Vers le blanc for electronic tape (page 160). But, another minor interruption of the flow, the discussion of “moment form” contains an inference as to the meaning of the term but no definition. One must look to the chapter summary to find it.

[12] Part IV reinforces the spiral pedagogy above by returning to pitch organization for a greater discussion. Here the author finds room for diatonicism and pentatonicism, symmetrical sets, neotonality, free atonality and serialism. In a book with a lot to swallow to start with, this section is the chewiest. But as before, flow charts pose and answer important questions succinctly, and concise summations place these answers directly in the student’s lap. Drills designed with specific examples in mind build one’s confidence with abstract principles and tether them to an actual work, thus allowing the concept to seek identification in both the general and specific memory. Boxed step-by-step summaries of formulas and procedures provide a reflective breather for most chapters in this section, except the neotonal chapters 12 and 13, and the subsequent atonal chapter, the latter finding most of my students the least confident with the language and therefore in need of such a summary.

[13] A salient pedagogic feature of the chapter on free atonality is a stage-by-stage analysis of two works—Piano Piece, Op. 11, No. 1 by Schoenberg, and Five Pieces for String Quartet, Op. 5, No. 3 by Webern. I was most impressed by Williams’s ability to carry the student through each level of understanding, with helpful suggestions and clues (but not freebies) including, perhaps most important to beginners, an introduction to parsing a score into significant sets, establishing segmentation guidelines based on texture and melodic phrase. Although experienced theorists could always argue with the choices made and the logic involved in the decisions, this kind of active coaching can be an intensely positive model for independent analytical growth with students, undergraduate or graduate, entering this world for the first time.

[14] Part V, “Recent Developments,” is the section which “provide[s] concise introductions to more recent approaches to composition” (Williams, iii). Here the author covers chance and indeterminacy (terms for which he makes a clear distinction) minimalism, eclecticism, and the revival of tonality. The author cites composer prefaces, philosophies and performance notes when appropriate, and provides a piece-by-piece summary of John Cage’s evolution toward 4’33”, which Williams calls “the ultimate realization of Cage’s philosophy” (page 302). A flow chart now appears for phase (process) in Steve Reich’s Piano Phase, as well as examples of how “quote music” is used in George Rochberg’s Carnival Music IV (comparing the original Bach and Brahms sources to their use by Rochberg.) But no musical example of “The New Tonality” is offered. This is a language I consider clearly a more evolved synthesis of current systems, rather than the use of direct quotations from the past. So this is the section of the text that I would hope the author expand in a subsequent edition.

[15] If another edition is forthcoming, I would recommend that any expansion include a recent example by a non-Western composer. Sudanese Hamza el Din’s “Waterwheel,” recorded by the Kronos Quartet is a fine mingling of the ostinato principle on a stable sonority with the bending and slurring of melody tones in the central African vocal tradition.(9) Sparrows (1979) by Joseph Schwantner serves as an example of both “the new tonality” (its quintal harmony is used in two chromatic circle-of-fifth progressions in the first half) and eclecticism (employing Medieval and Baroque styles alongside serial techniques). It is one of the batch of works from the seventies and early eighties to feature his “celestial choir” trademark.

[16] Having taught the text, then, I can reach the following summation: 1) it offers a thoroughly objective look at most current styles, with clear delivery of information; 2) this inclusiveness in a short text compacts the information, demanding careful reading of each sentence and slow digestion; 3) most initial confusion is dispelled by drills, questions for review, and projects; 4) further confidence on the student’s part is gained by providing charts and projects partially completed with correct answers; 5) some chapters, especially the opening one and those on neotonality, would benefit from the same consistent approach with partially-guided drills.

[17] The outcome of my undergraduate twentieth-century theory class was that students who in a traditional theory curricula would not encounter more than a passing look at the music of their own century gained valuable literacy and specific tools for study of nearly every current style. By using the Williams text they acquired a reference guide for future study. Quotations from primary and secondary sources are succinct, to the point, and unencumbered, and suggest directions for many possibilities of continuing with a particular theory. Chapter summaries are clearly-written overviews of the topic’s most critical items. And Williams’s closing of chapters with questions for review and finite analysis projects is especially welcome. Similar to the Lester text, these sections provide hands-on practice, and as the Williams text progresses, provide useful “hints” to prompt the reader in one direction to begin an analysis. The objective approach, though laudable, leaves a bit of the author’s own personality—his bias and bliss—out of the mix. But given the breadth of coverage, this is perhaps a necessary sacrifice in the name of keeping the length under control. In a cynical and often self-serving age, the Williams text offers a refreshing and brave inclusiveness that delivers a balanced and fair treatment of most of the musical languages of this century.

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Larry J. Barnes
Transylvania University
Department of Fine Arts
300 N. Broadway
Lexington, KY 40508

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1. Max Headroom, “Body Banks” episode (ABC-TV, 1989).
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2. Ellen Dissanayake, “What is Art For?” (Seattle: University of Washington Press, 1988).
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3. Joel Lester, Analytical Approaches to Twentieth-Century Music (New York: W.W. Norton and Co., 1989).
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4. Joseph N. Straus, Introduction to Post-tonal Theory (Englewood Cliffs: Prentice-Hall Inc., 1990).
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5. Stephan Kostka and Dorothy Payne, Tonal Harmony with an Introduction to Twentieth-century Music, 3rd ed. (New York: McGraw-Hill, Inc., 1995.)
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6. John Rahn, Basic Atonal Theory (New York: Longman, 1980).
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7. Alexander R. Brinkman, Pascal Programming for Musical Research (Chicago: University of Chicago Press, 1990).
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8. Anton Ehrenzweig, The Hidden Order of Art (Berkeley: University of California Press, 1971).
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9. Kronos Quartet, Pieces of Africa (Compact disc, Elektra Entertainment, 1992).
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Max Headroom, “Body Banks” episode (ABC-TV, 1989).
Ellen Dissanayake, “What is Art For?” (Seattle: University of Washington Press, 1988).
Joel Lester, Analytical Approaches to Twentieth-Century Music (New York: W.W. Norton and Co., 1989).
Joseph N. Straus, Introduction to Post-tonal Theory (Englewood Cliffs: Prentice-Hall Inc., 1990).
Stephan Kostka and Dorothy Payne, Tonal Harmony with an Introduction to Twentieth-century Music, 3rd ed. (New York: McGraw-Hill, Inc., 1995.)
John Rahn, Basic Atonal Theory (New York: Longman, 1980).
Alexander R. Brinkman, Pascal Programming for Musical Research (Chicago: University of Chicago Press, 1990).
Anton Ehrenzweig, The Hidden Order of Art (Berkeley: University of California Press, 1971).
Kronos Quartet, Pieces of Africa (Compact disc, Elektra Entertainment, 1992).
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