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Contents

Music in the Early Twentieth Century

GIVING MUSIC AN AXIOMATIC BASIS

Chapter:
CHAPTER 12 In Search of Utopia
Source:
MUSIC IN THE EARLY TWENTIETH CENTURY
Author(s):
Richard Taruskin

The strictness of Schoenberg’s adherence to the ordered twelve-note series in his compositional practice, and the consequent pervasiveness with which the series informed the musical substance thus created, elevated the series in Schoenberg’s usage to the status of a Grundgestalt, the “basic shape” or intervallic constellation that informs an entire composition down to its smallest details and gives it its “organic” motivic consistency. Indeed, the use of an exhaustive twelve-note series makes the Grundgestalt function, and the organic unity thus guaranteed, virtually automatic. And that, of course, was the great breakthrough, the “principle capable of serving as a rule,” which allowed the composition of large-scale, abstract, and autonomous atonal music of constant and at-all-times-demonstrable motivic coherence despite its renunciation of predefined tonal hierarchies, and despite its frequent “athematicism.”

But beware! As soon as any musical characteristic becomes the automatic result of a method, it stops being a compositional achievement. As long as Schoenberg’s atonal music was based on “working with the tones of a motive,” meaning an unordered collection of intervals, the kind of tightly controlled motivic organization visible (to cite one especially rich instance) at the beginning of the first piece in op. 23, composed in July 1920, is an impressive compositional tour de force (Ex. 12-4).

Giving Music An Axiomatic Basis

ex. 12-4 Arnold Schoenberg, Op. 23, no. 1 (Sehr langsam), mm. 1–5

The strict three-part contrapuntal texture is supersaturated with versions of the intervallic Grundgestalt (or basic cell, to use an “organicist” metaphor) first expressed as the opening harmony (F♯ A♭ A), which contains a major second, a minor second, and a minor third. The first three notes in the middle voice (A♭ G B♭) are a “linearization” of the same cell, immediately echoed by the top voice in m. 2 (E♭ D F). Meanwhile, the first three notes in the bottom voice (A C B) present a variant of the same linearization, in which the same intervals occur in the opposite order and with the contour reversed (a “retrograde inversion”). The bass B in the second measure is a pivot linking two sequential statements of this manner of presenting the basic cell. In m. 3 the middle voice repeats the three-note beginning of the bass in diminution at the octave, while in mm. 4–5, the bass reciprocates with a transposition of the middle voice’s opening cell (B♭ A C), with the final interval inverted from a rising minor third to a falling major sixth.

(Note, incidentally, the “hairpins” in m. 5 over a single note, A. They are obviously impossible to perform on the piano, as Schoenberg surely knew perfectly well. The expressive swell on a single note, typical of vocal and string music, is part of the “idea” of the piece, rather than its sound — and so, it might be argued, is the motivic consistency we are now accounting for, which is far more likely to reveal itself fully to the analytical eye than to the listening ear. Again we see the composer characteristically preoccupied with “poietics” over “esthesics,” with input over output, manufacture over effect.)

Meanwhile, another variant of the basic cell, in which the minor third and the minor second go in the same direction, covering a major third’s total distance, has been enjoying a similar “developing variation.” The first three notes in the top voice (F♯ E♭ D) are its first presentation, echoed in the middle voice in m. 3 (C B G♯). It, too, gets a “harmonic” presentation, on the downbeat of m. 4. But even before the middle voice has echoed it, the top voice reverses it (D♯ E G in mm. 2–3), and that reversal is also echoed in the middle voice (G♯ A C in m. 4). Both the initial statement of this variant in the top voice and its echo in the middle voice overlap with presentations of the variant previously described. Thus the first four notes of the “soprano” (F♯ Eb D F) and the four sixteenth notes in the “tenor” in m. 3 (A C B G♯) each present the two variants of the basic cell (but in opposite order) with the middle pair of notes doing double duty.

The head swims, not only at the thought of such motivic density (which the foregoing description has by no means fully accounted for) but also at the thought of the mental labor it must have required to contrive it. One can easily sympathize with the wish to find the kind of labor-saving device Schoenberg adopted in the final waltz from the same set of pieces, even if the lessened labor can seem to lessen the intellectual accomplishment. In any case, from 1921 on, virtually every one of Schoenberg’s atonal compositions would adopt a chromatically exhaustive twelve-note series like the one in the waltz (or in Hauer’s 1919 Nomos) as its basis.

Schoenberg called such a series a Tonreihe, using a German word for series, Reihe, that has “row” as its English cognate; hence the term “tone row” has become standard in British and American usage. At first he called the method on which he now relied Reihenkomposition, “composition with rows” or “serial composition.” English usage in this case has favored Hauer’s term Zwölftontechnik, “twelve-tone technique.” (More pretentious writers sometimes call it “dodecaphony” from the Greek for twelve.) Eventually Schoenberg also came round to using this nomenclature, calling his method “composition with twelve tones related only to one another” (rather than to a predefined tonic).

And yet the term “twelve-tone”, although we are certainly stuck with it, remains something of a misnomer; for what gives a tone row its distinction is not its pitch content (for every tone row has that in common with every other tone row) but its ordered interval content. That is what enables a row, like any basic cell or Grundgestalt, to maintain its identity when transposed. Indeed, it was transposition, as an outgrowth of his earlier Grundgestalt or “developing variation” technique, that now became Schoenberg’s primary technical preoccupation: more specifically, the question of how transpositions (and precisely which transpositions) may help realize the form-defining or harmony-defining properties of particular tone rows. That is where Schoenberg will henceforth engineer his tours de force of compositional planning and motivic saturation.

The first major work of Schoenberg’s that was written using twelve-tone row technique throughout was a five-movement Suite for Piano, published as opus 25 in 1925. The pieces in it—Präludium, Gavotte and Musette, Intermezzo, Menuett, Gigue—had accumulated over an eighteen-month period between July 1921 and March 1923, during which Schoenberg was also working on other compositions, but all were based on a single twelve-tone row, albeit treated with a bit more variety than Schoenberg had allowed in the waltz, the first twelve-tone piece to be published.

There, as we recall, Schoenberg had contented himself (partly as a technical challenge, partly in an effort to outdo Hauer) with a single “row form” until the end, when he ran it backwards a couple of times. The row was never even transposed, so that in this case it was indeed literally a row of tones as well as intervals. The technical challenge, of course, was to disguise the fact that the piece consisted of what in less sophisticated hands might have sounded like a relentless melodic ostinato. The suite was based on a complex consisting of a row, its inversion, and the transposition of each by a tritone (Ex. 12-5). Inverting a row, like inverting any motive or Grundgestalt, maintains the same intervallic sequence as if seen in a mirror. Transposition, of course, has no effect at all on intervallic sequence. So the four rows in Ex. 12-5 are merely four ways of representing a single intervallic succession (i.e., a single Grundgestalt).

Giving Music An Axiomatic Basis

ex. 12-5 Row complex from Arnold Schoenberg, Suite, Op. 25

NB: In analyzing twelve-tone compositions, row transpositions are often counted by semitones. Thus the four row forms in Ex. 12-5 are labeled P (for “prime,” the form heard first), I (“inversion”), P6 (prime transposed up six semitones) and I6 (inversion transposed up six semitones). For extra clarity, untransposed row forms are usually designated as having been transposed by “zero” semitones, thus: Po and Io. In the diagram, the arrows running right to left are a reminder that rows can be freely reversed for additional variety within the same interval-determined unity.

Even before looking at or listening to the music, the row complex gives us a foretaste of its harmonic world. The row has been deliberately constructed so as to create close relationships between exactly these four forms, so as to produce an even more pervasive unity than a single row form could achieve. In other words, the row has been constructed with its role as a Grundgestalt in mind, and the character of the composition will be to a significant degree determined by the relationships that have been built into the structure of the row. And what are these relationships? By now they will seem very familiar, having appeared in the work of so many of the “maximalist” composers of the early twentieth century, including Schoenberg himself along with Stravinsky, Bartók, Webern, and Berg. But here they have been sublimated or abstracted into a formal and methodical context that accords with the cool ironic mood of postwar modernism.

It will take no more than a glance at the beginnings and ends of all the row forms in Ex. 12-5 to establish harmonic symmetry based on the “invariance” properties of the tritone as the principle Schoenberg’s rows have been designed to exploit. The first and last notes in the untransposed prime form of the row are a tritone apart. Since the tritone reproduces itself when inverted, and since the only transposition invoked in Ex. 12-5 is that of the tritone itself, E and B♭ are the invariant framing pitches of every row form employed in the Suite. That is already a giant step toward defining a consistent (if contextual) “tonality” for the piece.

But there is more. Since any tritone can be embedded in a circle of minor thirds that shares its invariance properties (reproducing itself when inverted or when transposed by its generating interval), the notes G and D♭ will have the same invariance properties within this row complex as do the notes E and B♭. And that is the reason why Schoenberg made sure that those two notes would occupy adjacent positions in the untransposed prime form. They occupy order positions 3 and 4 in every form shown in Ex. 12-5, and hence will also function as an invariant pair within the actual music of the Suite. (When reversed forms of the row are employed, of course, the G and D♭ will just as invariably occupy positions 9 and 10.) In addition, the first pair of notes in each row form in Ex. 12-5 has a counterpart in one of the reversed forms: EF begins both Po and RI6; EE♭, Io and R6; B♭B, P6 and RIo; B♭A, I6 and Ro. And ending pairs coincide similarly, as they must. These, too, are invariance relationships, the invariant pairs linking not only forward and backward row forms, but also transposed and untransposed ones.

By seeking out abstract invariance relationships like these within the row forms, it is easy to create concrete musical relationships in which some aspect of a musical configuration changes while some other aspect remains the same. That is the essence of the “developing variation” technique that Schoenberg had long insisted was implicit in Brahms’s motivic textures. And that is one of the features of twelve-tone composition, as Schoenberg practiced it, which allowed him to claim that this method, no less than his earlier “atonal” style, was a “natural” (or even an inevitable) evolution of “classical” or “mainstream” techniques rather than a break with them, despite its rejection of the most salient — indeed, the defining—feature of “tonal” music. Indeed, twelve-tone techniques, by rationalizing the composition of atonal music and making it more orderly and “plannable,” significantly strengthened the bonds that connected atonal music with the formal methods of the “classical mainstream.” In this sense, it too was a “neoclassical” move, another response to the postwar “call to order.”

Citation (MLA):
Richard Taruskin. "Chapter 12 In Search of Utopia." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 10 Dec. 2018. <http://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-012004.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 12 In Search of Utopia. In Oxford University Press, Music in the Early Twentieth Century. New York, USA. Retrieved 10 Dec. 2018, from http://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-012004.xml
Citation (Chicago):
Richard Taruskin. "Chapter 12 In Search of Utopia." In Music in the Early Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 10 Dec. 2018, from http://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-012004.xml