Prokofiev’s Symphony no. 2, Yuri Kholopov, and the Theory of Twelve-Tone Chords Christopher Segall NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.18.24.2/mto.18.24.2.segall.php KEYWORDS: Sergei Prokofiev, twelve-tone technique, twelve-tone chord, aggregate chord, Russian music theory, Yuri Kholopov ABSTRACT: A small collection of works, including Prokofiev’s Symphony no. 2 (1924), include chords with all twelve pitch classes. Yuri Kholopov, the foremost late-Soviet theorist, considered twelve-tone chords a branch of twelve-tone technique. Taking Prokofiev and Kholopov as a starting point, and building on prior scholarship by Martina Homma, I assemble a history and theory of twelve-tone chords. The central theoretical problem is that of differentiation: as all twelve-tone chords contain the same twelve pitch classes, there is essentially only one twelve-tone chord. Yet twelve-tone chords can be categorized on the basis of their deployment in pitch space. Twelve-tone chords tend to exhibit three common features: they avoid doublings, they have a range of about 3 to 5.5 octaves, and their vertical interval structure follows some sort of pattern. This article contextualizes twelve-tone chords within the broader early-twentieth-century experimentation with aggregate-based composition. Received May 2017 Volume 24, Number 2, July 2018 Copyright © 2018 Society for Music Theory Introduction [1] This paper bases a history and theory of twelve-tone chords around an unlikely starting point: Sergei Prokofiev, whose Symphony no. 2 (1924) features a chord with all twelve pitch classes.(1) Scholars have developed sophisticated models for various aspects of twelve-tone technique—such as tone-row structure, invariance, hexachordal combinatoriality, and rotation—but with isolated exceptions have not to date examined the phenomenon of twelve-tone verticals. Prokofiev, of course, is not widely associated with twelve-tone technique, and twelve-tone composition has not been a major area of Prokofiev studies. In contextualizing Prokofiev’s twelve-tone chord, this article will investigate the history of twelve-tone chords, the theorists who have described them, and the composers in whose works they have appeared. I draw on the work of Yuri Kholopov (1932–2003) —longtime professor at the Moscow Conservatory, and the foremost Soviet and post-Soviet theorist of his era—whose writings connect Prokofiev to twelve-tone technique in two ways.(2) First, Kholopov viewed Prokofiev’s “twelve-step” chromatic system, with independent harmonic functions on all degrees of the chromatic scale, as the true innovation of twentieth-century ( ) aggregate-based composition.(3) Second, Kholopov argued more generally in several writings for a broad conception of twelve-tone technique that included not only serial dodecaphony (his term for Schoenberg’s practice) but also a variety of other techniques, including twelve-tone chords (dodekakkordï), the topic of this article.(4) Kholopov’s (1983a) chronology of Schoenbergian precursors and parallels includes the twelve-tone chord from Prokofiev’s symphony. In this article, I survey the issues involved in analyzing twelve-tone chords and assemble a theory of twelve-tone chords. I return to Kholopov’s more detailed analysis of Prokofiev’s twelve-tone chord, in order to decipher its contradictions and propose an alternative. Finally, I argue that twelve-tone technique is a construction, rather than a fixed concept, that can be used in various ways by various authors. [2] In considering twelve-tone chords as an independent topic, my paper engages not only with Kholopov, but also with other composers and theorists who have written on twelve-tone chords. Several authors of compositional treatises—namely Alois Hába (1927), Vincent Persichetti (1961), Ctirad Kohoutek (1976), and Eugen Suchoň (1979)—outlined possible forms and uses of twelve- tone chords. Among theorists, Martina Homma (1999, 2001) has most thoroughly investigated the issue, having traced the history of twelve-tone chords and their theoretical explication. Homma has advanced two arguments that will be taken up in the course of this article: first that twelve-tone chords constitute an independent and continuous compositional practice, and second that twelve- tone chords are a vertical analogue to the horizontal technique of twelve-tone rows. In general prior writers have addressed the problem of differentiating twelve-tone chords from one another, given that they all contain the same notes, as well as a variety of additional issues (explored below). As they demonstrate, there is more to consider regarding twelve-tone chords than simply how many notes they contain. [3] The theoretical formulation proposed here draws on a catalogue of twelve-tone chords found in the repertoire. In describing twelve-tone chords as a compositional practice, several writers have referred to specific examples in the repertoire. This study collates all such examples for the purpose of drawing larger conclusions. Although there are exceptions, twelve-tone chords tend to feature the following properties: they avoid doubled pitch classes, they have a range of about 3 to 5.5 octaves, and their internal intervallic structure follows some sort of pattern. These features support the concept of a twelve-tone chord as an intentional compositional object, deliberately structured in such a way as to reinforce its identity as a twelve-tone chord. For this reason, chords containing only 10 or 11 distinct pitch classes are excluded from the study. Twelve-tone chords are special cases of highly chromatic sonorities, as through their purposeful exhaustion of the aggregate they forge a connection to twelve-tone technique more broadly, reinforcing the historically emergent conceit of composing with all twelve pitch classes. [4] Kholopov (2009) offers Prokofiev’s Symphony no. 2 as a case study for analyzing twelve-tone chords, and I address both his analysis and an alternative analysis in this essay. Whereas early sections of the article will focus on ways in which twelve-tone chords can be differentiated from each other, the Prokofiev symphony offers a testing ground to consider how a twelve-tone chord can be analyzed in the context of an individual work, particularly a work that does not otherwise consist of twelve-tone chords. A twelve-tone chord appears in the symphony’s second movement. Kholopov’s attempts to relate the intervallic content of Prokofiev’s twelve-tone chord to other motives in the same movement leads to conflicting interpretations of the same chord. As a twelve- tone chord contains every pitch class, so can it be parsed to contain a variety of motives and intervals. [5] Finally, I’ll propose a perspective of twelve-tone technique as a construction, with a shifting, negotiable definition. What “counts” as twelve-tone technique can change over time and from author to author, and the issue is worth considering from a historiographic standpoint. Specifically, a gambit such as Kholopov’s that broadens the conception of twelve-tone technique beyond serial dodecaphony allows connections to be drawn between the Schoenbergian approach and other aggregate-based practices of the early twentieth century. This perspective is thus historical as well as theoretical. Background [6] Yuri Kholopov, with the title to an article, poses the question: “Who Invented Twelve-Tone Technique?” (1983a).(5) The answer, he assures us at the outset, is Arnold Schoenberg, if by “twelve-tone technique” we mean serial dodecaphony, the technique of composing with transformationally manipulated twelve-tone rows. But he nonetheless outlines a chronology of precursor techniques to Schoenberg’s compositional method, most created independently of Schoenberg and therefore not casting a direct influence on the later method. Composers in the early twentieth century experimented with a number of ideas that seemed to coalesce in the music of Schoenberg and his followers. Kholopov notes early instances of several techniques, including the following: “microserial” technique (a three-note cell in Webern’s String Quartet [1905], a four-note cell in Stravinsky’s Firebird), isolated melodic statements of the aggregate (twelve-tone rows in early Berg and Webern), referential non-twelve-tone vertical sonorities used also for horizontal content (Scriabin’s Mystic Chord, Roslavets’s synthetic chords), and twelve-tone fields in which all twelve pitch classes freely circulate (Nikolai Obukhov, Yefim Golïshev). He also includes the well- known tropes of Josef Matthias Hauer. Through Kholopov’s article, Schoenberg’s technique appears to emerge from a swirling cloud of ideas in the air at the time. Far from presenting Schoenberg as a visionary genius who invented an important method on his own—although Schoenberg, it must be said, is given due credit for the depth of his contribution—Kholopov historicizes Schoenberg, accounting for the way in which he solved problems that composers had been grappling with for decades. [7] In this chronology that leads up to (and slightly past) Schoenberg’s first serial works of 1921–24, we read the following entry: “In the Finale of the Symphony no. 2 (1924) Prokofiev wrote a contrapuntal layer of sonoristic twelve-tone chords” (Kholopov 1983a, 56).(6) (The chords, as will be shown below in Example 1, consist of a single twelve-tone chord transposed via parallel planing.) This is striking, not only because Prokofiev is not typically associated with twelve-tone technique (nor, for that matter, with the sonorism of the later Polish avant-garde), but also because Kholopov himself used Prokofiev as a foil for twelve-tone practices in earlier writings. Kholopov had argued that Prokofiev extended tonal harmony to allow for independent harmonic functions on all twelve degrees of the chromatic scale—what Kholopov called dvenadtsatistupennost’, or the “twelve-step” or “tonal chromatic” system. Thus Prokofiev, with his twentieth-century tonality, had been considered the true innovator of aggregate-based composition.(7) Now Prokofiev is marshaled into service not as an alternative to twelve-tone composition, but rather as a progenitor.