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Music in the Late Twentieth Century


CHAPTER 9 After Everything
Richard Taruskin

The issues can be clarified somewhat by examining Fred Lerdahl's actual composing style, to see how it compares with his unusually explicit and outspoken theorizing. It turns out to be not quite as beholden to “outworn styles” as his theories caused him to worry, or the accusations of his critics might seem to suggest. It is based, rather, on a compromise between, on the one hand, a reinstated (“de-emancipated”) use of consonance and dissonance to effect tension and release, and, on the other, the kind of symmetricalized chromatic pitch relations that had a long history in twentieth-century practice (particularly in Bartók and Berg), but that had only lately achieved comprehensive theoretical formulation in an influential treatise, Twelve-Tone Tonality, by the veteran American composer George Perle (b. 1915), the first edition of which was published in 1977.

In that same year Lerdahl wrote a string quartet in which he first began to apply to contemporary problems of composition the principles that he and Jackendoff were developing for their “listening grammar” of tonal music. It is a “programmatic” work, like many works by theorists in the throes of formulation, in the sense that it sets forth its theoretical orientation as part of the actual musical argument. To put it bluntly, in addition to being a work of art, the quartet provides both an illustration and a practical test of the theory.

The de-emancipation of dissonance is evident from the very start (Ex. 9-6). The consonant dyad G-D is stated in the first measure, repeated in the second, and, in the fourth, established through a cadence as a stable reference point (not to say a tonic). Even though no triads have yet been heard, it is clear that the piece is “tonal,” and that functional (if not necessarily conventional) harmonic closures will play a part in articulating its form. As Lerdahl has put it, “tonality is a psychological condition, not a stylistic one.”77 To put the functional premises of his quartet in terms of a cognitive grammar, one could say that a series of harmonic events unfolds in such a way that the listener is able to group them into discrete (and lengthening) time-spans characterized by fluctuations of harmonic tension. The listener, in short, is enabled (and encouraged) to apply intuitively the four processes held by the generative theory to translate aural stimuli into musical sense.

The fifth chord is distinguished from the others not only statistically, by merely being different, but also qualitatively by being dissonant. Its relationship to the tonic dyad, moreover, is easily specified in terms of function, since every one of its four notes can be interpreted as a leading tone (two converging on G, two on D). Thus measures 3–4 constitute a “departure and return,” the basic form-defining gesture in traditional tonal music, even if the sonorities are not exactly those of traditional tonal music.

Notice now that mm. 3–4 are enclosed within double bars and labeled “III.” They form a unit that takes its place in a series of such units that unfolds over the course of the piece and defines its form. Each begins and ends with the normative consonance, and (once other harmonies are introduced in the third unit) each performs a departure-and-return. Each is also longer than its predecessor. Group I lasts three beats, group II lasts four, III lasts five, IV lasts 7, V lasts 14, VI lasts 19, and so on. The later and longer groups expand in a rough 3:2 proportion, leading the ear to organize ever-greater time spans through prolongational reductions.

One Proposal

ex. 9-6 Fred Lerdahl, String Quartet no. 1, sections I-XIV

The complex of upper and lower leading tones operating in tandem in group III already suggests that harmonic motion is proceeding according to a pair of symmetrical (“equal sum”) interval matrices like the ones deduced by Perle, among others, when investigating Bartók's composing methods. (The difference, of course, is that Bartók's matrices never converged on perfect fifths to produce the kind of consonant reference sonority or functional tonic on which Lerdahl's system here depends.) The impressionis confirmed in group IV, when another chord is interpolated between the initial tonic dyad and the leading-tone complex, and it, too, relates to its companions by mirror-inversion: the first violin's intervallic succession in m. 6, a descending tone and semitone, is mirrored by the second violin's ascent by the same intervals to converge on G (allowing for an octave displacement at the end), while the viola and cello reproduce the same pattern implying convergence on D (allowing for the cello's substitution of the more resonant “root” G at the end).

We have made enough observations to warrant a hypothesis, as set forth in Ex. 9-7a, where complete symmetrical matrices that converge on G and D are superimposed. Every chord in the quartet through m. 12 consists of a superimposed pair of dyads in the same position within their respective matrices. The first chord with more than four pitches in it, in m. 13, adds a dyad from the symmetrical matrix in which the G-D tonic is embedded as a unit (Ex. 9-7b). Having added the third matrix, we can now account for every harmony until the second measure of group VIII (not shown in Ex. 9-6), where the dyad E♭-B♭ (followed eleven beats later by its tritone complement, A-E) invokes the matrix given in Ex. 9-7c.

And so it goes. Successive Roman-numeral groups expand both in terms of the time-span they enclose and in terms of the pitch field on which they draw; in each case we are led from the normative consonance to a progressively further-out point and back again. The process provides for considerable variety (sometimes very dramatically expressed, like a sudden “modulation to E” near the middle of the piece) within a tightly organized and unified pitch system.

One Proposal

ex. 9-7a Fred Lerdahl, String Quartet no. 1, analytical sketches, inversional matrices on D and G superimposed

One Proposal

ex. 9-7b Fred Lerdahl, String Quartet no. 1, analytical sketches, inversional matrix that includes reference dyad G-D

One Proposal

ex. 9-7c Fred Lerdahl, String Quartet no. 1, analytical sketches, matrix that includes E-flat-B-flat and A-E

In the later, lengthier sections, Lerdahl sometimes underscores both the expanding durational plan and the there-and-back trajectory by inserting literal palindromes that open out gradually from motion in eighths to dotted halves and contract back to eighths as the pitches run in reverse (e.g., Ex. 9-8). These help the listener infer the compositional strategy from the musical surface. The consciously constructed compositional grammar is “transparent,” as Lerdahl would say, to the unconscious listening grammar. Or as Steve Reich would put it, the composer knows no secrets of structure that his listener cannot discover.

Although he describes his music as part of what he calls the “postmodern resurgence” of tonality (or more exactly, of hierarchical pitch and metric organization), it is clear that Lerdahl's postmodernism is of a very different character from Rochberg's or Del Tredici's. It entails no consciously formulated expressive or representational purpose, nor any impulse to revive past styles; and, while it certainly takes listeners into account as arbiters of intelligibility, the intended audience seems to be basically the same academic audience that modernist composers address.

One Proposal

ex. 9-8 Fred Lerdahl, String Quartet no. 1, section (C4)

Lerdahl's reputation is far more academically circumscribed than Rochberg's or Del Tredici's, and he writes mainly for campus new-music ensembles. He has even stated, in response to the usual attacks, that “serious composers, myself included, pay more attention to the work than to the audience,”78 and his sole stated theoretical preoccupation has been with devising and validating new techniques of composition. It is possible, ultimately, to regard his work as “progressive” in the “reformist” sense, correcting defects or errors that have deflected the evolution of music from the path of true progress. (The main error, as he puts it, was that of putting “complicatedness”79 —a musical surface densely cluttered with unprocessable information—in place of “complexity,” a depth or richness of structural relations that a listener is able to infer from that surface.) Nevertheless, his is an equally significant manifestation of the postmodernist impulse, precisely because it has taken place within the ivory tower, and within the traditional academic discourses of formalism and even science. Lerdahl's project remains one of research and development, but it is no longer wholly “disinterested.” Innovation can no longer be validated solely on the basis of the old “master narrative.” Innovation must now pass a listener test, and that implies an “esthetic”—that is, a criterion of artistic quality—with a necessary social component. Cold-war purity, “Western”-style, has been breached, perhaps irrevocably.


(77) Fred Lerdahl, musicology colloquium, University of California at Berkeley, February 2001.

(78) Lerdahl, “Composing and Listening,” p. 6.

(79) Lerdahl, “Cognitive Constraints,” p. 255.

Citation (MLA):
Richard Taruskin. "Chapter 9 After Everything." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 18 Jun. 2019. <https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-009011.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 9 After Everything. In Oxford University Press, Music in the Late Twentieth Century. New York, USA. Retrieved 18 Jun. 2019, from https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-009011.xml
Citation (Chicago):
Richard Taruskin. "Chapter 9 After Everything." In Music in the Late Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 18 Jun. 2019, from https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-009011.xml