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Music in the Late Twentieth Century


CHAPTER 3 The Apex
Richard Taruskin

While far more lasting than its European counterpart, then, postwar serialism in America has owed its survival to patronage in a society that otherwise functions, in music as in other ways, on the basis of commerce. It has been a closed enclave, a hothouse growth, its cultivators standing with backs resolutely turned to their counterparts in other walks of American musical life. Yet despite the misgivings Babbitt voiced in 1976, many experienced their protected life within the hothouse as a golden age for composition.

And, some would argue, for performance as well: as part of the institutionalization of serial music on American campuses, the Schoenbergian ideal of private performance venues for new music was also established on a broad and well-subsidized scale, with specialized student or professional performing organizations cropping up wherever “Ph.D. music” was composed. Music theory also enjoyed an intense growth phase, with faculty positions proliferating along with professional journals concerned with advanced musical composition and its attendant theory. Eventually, in 1966, a lobbying organization, the American Society of University Composers (ASUC), was formed by a group of Princeton faculty, graduate alumni, current Ph.D. candidates, and more loosely affiliated composers, including Weinberg, Boretz, Donald Martino (b. 1931), Peter Westergaard (b. 1931), and Charles Wuorinen (b. 1938).

The first campus “new music” organization was the Group for Contemporary Music, formed in 1962 at Columbia University (as it happens, one of the few universities where the scholars in the music department refused to sanction a Ph.D. for composition, but where a doctoral program was quickly set up, as if in defiance of the department, by the University's School of the Arts; relations were not happy). Its founders were Wuorinen, an expert pianist, and Harvey Sollberger (b. 1938), a flautist, both then graduate students in composition at Columbia, along with the cellist Joel Krosnick, then an undergraduate, who in 1974 joined the Juilliard String Quartet, a sort of forerunner organization that had been founded in 1946 by William Schuman, then president of the Juilliard School, expressly to give exposure to contemporary works in the medium, beginning with those of Bartók and Schoenberg.

Columbia's Group for Contemporary Music was as widely copied as Princeton's Ph.D. program. Both at Columbia and elsewhere (eventually including music conservatories) the performance rosters expanded to include a wide variety of vocalists and instrumentalists; in particular, a new breed of virtuoso percussionist was spawned. The high premium thus placed on new-music virtuosity led to an ever-increasing preoccupation with extended performance techniques—augmented ranges, novel sounds from traditional instruments (especially the piano), novel cross-fingerings to produce chords or “multiphonics” on woodwinds, and so on—on a par with extended formal techniques of composition.

Of the quasi-scientific journals devoted to academic composition and its theory, the semiannual Perspectives of New Music, produced at Princeton itself, was uniquely authoritative. Its slightly unidiomatic title was the result of its having been named by its patron, Paul Fromm (1906–87), the German-born Chicago wine merchant who had previously funded the Seminar on Advanced Musical Studies mentioned in chapter 1. The editors were Arthur Berger (1912–2003), then a professor at Brandeis University, and Benjamin Boretz (b. 1934), a former pupil of Berger then writing his Ph.D. dissertation under Babbitt. Many of the articles in the first issue, which appeared in fall 1962, had a sharp polemical or factional edge. Their purpose was to stake out what is known in the academy as “turf,” a recognized and respected area of authority.

From this perspective, the most characteristic article in the inaugural issue of Perspectives was not by a composer at all, but rather by John Backus, an acoustician on the physics faculty of the University of Southern California, from whom the editors had commissioned a “scientific evaluation” of the four volumes of Die Reihe (the Cologne-based organ of the “Darmstadt School” described in chapter 1) that had by then appeared in English translation. The aggressive review Backus produced contrasted the bona fide musical science preached and practiced at Princeton with the fraudulent pseudo-science of the European avant-garde in a fashion that easily matched the derision the American serialists felt toward what Wuorinen called “the ‘work’ of John Cage and some of his friends.”41

Backus dismissed the technical language in Stockhausen's writings, for example, as a jargon “designed mostly to impress the reader and to hide the fact that he has only the most meagre knowledge of acoustics.”42 The “pretended display of mathematical erudition” by another, less famous writer is declared to be “pure bluff,” through which “the defenseless reader is being thoroughly swindled.”43 Ligeti's analysis of Boulez's Structures (discussed in chapter 1) is strategically praised for its clarity, but only the better to expose what it described as “a method that is appalling in its arbitrariness,” testifying to “nothing more than a mystical belief in numerology as the fundamental basis for music.”44 The verdict on the composition itself is a little masterpiece of intramural academic invective:

The possibilities are endless; a computer could be programmed to put down notes according to this prescription and in a very short time could turn out enough music to require years for its performance. By using different numerical rules—using a knight's move, for example, rather than a bishop's move along the diagonals—music for centuries to come could be produced.

On the positive side of the ledger, the same inaugural issue of Perspectives also contained a paper by Babbitt laying out his latest extension of twelve-tone technique. Dissatisfied with the incompleteness of his previous operational analogies between pitch and time, Babbitt now proposed a new analogy based on their primary shared property, namely the interval. “Since duration is a measure of distance between time points,” he wrote, and

as interval is a measure of distance between pitch points, we begin by interpreting interval as duration. Then, pitch number is interpretable as the point of initiation of a temporal event, that is, as a time-point number.45

Let us imagine a measure of music, in other words, as containing twelve numbered time-points, each corresponding to a successive pitch-point in the chromatic scale. Thus if we take zero to designate both the first pitch-class in a row (say G) and the time point that initiates the measure, 1 would then represent both the pitch-class G♯A♭ and the second time-point in the measure; 2 would denote the pitch class A and the third time-point, and so on. In effect, Babbitt was adopting Messiaen's old concept of the “chromatic scale of time values,” but was synchronizing it (as Messiaen had not done) with the chromatic scale of pitches. An ascending chromatic scale would thus be conceptually translated (or to put it mathematically, “mapped”) into the twelve elapsing time-points (say sixteenth notes) within a measure in or time.

As Babbitt put it in his article, if the individual “temporal event” or time-point is to retain its identity in the unfolding music,

it is necessary merely to imbed it in a metrical unit, a measure in the usual musical metrical sense, so that a recurrence of succession of time points is achieved, while the notion of meter is made an essential part of the systematic structure. The equivalence relation is statable as “occurring at the same time point with relation to the measure.” The “ascending” ordered “chromatic scale” of twelve time points, then, is a measure divided into twelve equally spaced units of time, with the metrical signature probably determined by the internal structure of the time-point set, and with the measure now corresponding in function to the octave in the pitch-class system. A time-point set, then, is a serial ordering of time points with regard to < [that is, increasing quantity]. At the outset, I do not wish to attempt to avoid the manifest differences between the elements of the pitch system and those of the time-point system, that is, perceptual—not formal—differences. A pitch representative of a pitch-class system is identifiable in isolation; a time-point representative cannot conceivably be, by its purely dispositional character. But an examination of a time-point set will clarify the systematic meanings, and the reasonable musical meanings associated with these new concepts.

Example 3-28 is adapted from the “examination” or demonstration that follows in Babbitt's article. The hypothetical chromatic scale of pitches and time-points is shown in Ex. 3-28a. In Ex. 3-28b, a series of twelve number-pairs is given, in which the first number denotes the order-position within the given series and the second denotes a pitch/time-point position within Ex. 3-28a, the hypothetical chromatic scale. In Ex. 3-28c the second number in each pair is associated with a pitch-class as counted from G (= 0), and in Ex. 3-28d (taken directly from Babbitt's article), the same series is translated into durations by making a similar association of numbers with metrical positions. Numbers that fall within an ascent between 0 and 11 thus find their places within a single measure. Numbers that descend must wait until “the same time point with relation to the measure” comes around again in the next measure. Finally, in Ex. 3-28e, the two interpretations of the number series are combined and distributed into parts for the members of a string quartet.

Life Within the Enclave

ex. 3-28 The “time-point system” as expounded in Milton Babbitt's “Twelve-tone Rhythmic Structure and the Electronic Medium” (Perspectives of New Music, I:1 [fall 1962])

Life Within the Enclave

ex. 3-28b A pitch/time-point series

Life Within the Enclave

ex. 3-28c A pitch/time-point series translated into actual pitches

Life Within the Enclave

ex. 3-28d A pitch/time-point series translated into actual durations

Life Within the Enclave

ex. 3-28e All of the above, combined into a string-quartet texture

In mapping the specific time-point series on to a specific pitch-class series, Babbitt created a means of serializing durations that at last fully solved, at any rate to his own satisfaction, the problem of “appalling arbitrariness” to which John Backus had called attention in his condemnation of Boulez's Structures. Eventually Babbitt built further on the theory that justified the time-point system, eventually coordinating a twelve-fold gradation of loudness — from ppppp to fffff — with the pitches and durations so that aggregates could be completed in yet another dimension and yet another level of “relatedness” could be added to the grid within which each and every “atomic event” in Babbitt's music was located.


(41) Contemporary Composers on Contemporary Music, p. 370.

(42) John Backus, “Die Reihe: A Scientific Evaluation,” Perspectives of New Music I, no. 1 (Fall 1962): 169.

(43) Ibid. p. 170.

(44) Ibid.

(45) Milton Babbitt, “Twelve-Tone Rhythmic Structure and the Electronic Medium,” Perspectives of New Music I, no. 1 (Fall 1962): 63.

Citation (MLA):
Richard Taruskin. "Chapter 3 The Apex." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 21 Jan. 2017. <http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003013.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 3 The Apex. In Oxford University Press, Music in the Late Twentieth Century. New York, USA. Retrieved 21 Jan. 2017, from http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003013.xml
Citation (Chicago):
Richard Taruskin. "Chapter 3 The Apex." In Music in the Late Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 21 Jan. 2017, from http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003013.xml