“On the System of Stravinsky’s Harmony” by Yuri Kholopov: Translation and Commentary

[1] Introduction

[1.1] Yuri Kholopov (1932–2003) is generally regarded as the foremost Russian music theorist in the latter half of the twentieth century. He taught Music Theory at the Moscow Conservatory for much of his career, and he was instrumental in reforming theory curricula after the famous “struggle with formalism” that so pervaded the arts in the Soviet Union and that prohibited, to a large extent, simple analysis of music outside of its political and social context. He published over 600 items throughout his distinguished career; he wrote on figures as diverse as Aristoxenus, Boethius, Monteverdi, and Beethoven, and on topics as diverse as modal theory, form, Schenkerian analysis, medieval chant, and tuning and temperament. But he was happiest when discussing twentieth-century concepts; it was to this end that he devoted a large part of his life’s work. And Kholopov was a music theorist first and foremost—his magnum opus, Garmoniia (Harmony; [1988] 2003), attests to this fact.^(**) The present article is from 1997, six years before Kholopov died.

[1.2] Kholopov’s observations about Stravinsky’s music, in the article translated here, may be of particular interest. First, he links a quotation from Stravinsky to Sergei Taneev’s Podvizhnoǐ kontrapunkt strogogo pis’ma (Invertible Counterpoint in the Strict Style; [1909] 1959), thus suggesting that the Petersburg-based Stravinsky was influenced by the Moscow-based Taneev (1856–1915). This speaks to a possible Russian influence on Stravinsky aside from Rimsky-Korsakov, whose influence on Stravinsky is not in doubt. Second, Kholopov posits that there exists a new fundamental “neotonality” in Stravinsky’s music, which exhibits a “central element” (CE) to which all other tones gravitate. Intrinsic to Kholopov’s neotonality is a neomodality based on the ideas of Boleslav Yavorsky (1877–1942); herein lies another possible Russian influence on Stravinsky. (The modes of neomodality are a subset of Kholopov’s version of neotonality.) Third, Kholopov’s work situates octatonicism within a broader framework of Stravinsky’s compositional practices. Octatonicism is not emphasized as a fundamental structural element in Stravinsky’s music, as it is in writings by Arthur Berger (1963), Pieter van den Toorn (1983), and Richard Taruskin (1996 and 2011), for example. Fourth, Kholopov posits that when Stravinsky uses the term “polarity” in relation to his music, he may have meant to say “stability,” which was a term from the writings of Yavorsky that most Russian musicians knew in the early twentieth century. The reinterpretation of polarity sheds new light on this most important concept in Stravinsky studies. Lastly, there is the idea that Stravinsky was, in fact, a serial composer for his entire life. Of course, Stravinsky famously claimed so himself late in life. Kholopov solidifies this claim, traces the evolution of Stravinsky’s serial works, and finds an intriguing four-note series in Firebird.

[1.3] Immediately following this Introduction is the translation, in which I have included minimal editorial remarks. (Such remarks are placed in square brackets followed by my initials, “PE”.) Further commentary, which addresses small corrections and changes made for clarification, is provided in a separate Editorial Notes section; links to these notes are provided with the marker “[ed].” The translation is formatted exactly as it is in the Russian, with the same headings, footnote numbers, example numbers, and paragraph breaks.^(***) I discuss the six main headings in the article (harmony, tonality, modality, polarity, serialism, and historical context) in a section of commentary, after the translation.

[1.4] Kholopov’s quotations from and about Stravinsky come from four sources: (1) Stravinsky [1963] 2005; (2) Stravinsky 1971; (3) D’iachkova 1973a; and (4) Varunts 1988. The first, Khronika moeǐ zhizni (Chronicle of My Life) is the original translation from French to Russian of Chroniques de ma vie. The second, Igor Stravinsky: Dialogi (Igor Stravinsky: Dialogues) is a compilation of the first four books of conversations between Stravinsky and Robert Craft (Stravinsky 1959, 1960, 1962, and 1963). Insofar as these conversations were originally in English, I found the original quotations and used those, rather than translate back into English. Further, I indicate the sources for these quotations in editorial comments in the footnotes.^(****) The third is a book entitled I. F. Stravinsky: Stat’i i materialy (I. F. Stravinsky: Articles and Materials). All of the quotations that Kholopov uses from this source are from the section of this book from Stravinsky’s Musical Poetics (1959). Finally, Kholopov’s fourth source is I. Stravinsky: Publitsist i sobesednik (I. Stravinsky: Publicist and Conversationalist). This is a fascinating chronological compilation of Stravinsky’s spoken and written words—many never before published in English—from 1912 until his death. Here again, original sources are provided in editorial comments in the footnotes. I kept Kholopov’s formatting in the footnotes, using only the titles of these four works in abbreviated form as he did—Khronika, Dialogi, Stat’i i materialy, and Publitsist i sobesednik.

[2] Translation

[2.1] It is unfortunate that Stravinsky, having spoken and written a vast amount of prose over the course of a long lifetime, never got around to writing a treatise about his own compositional technique. Not only are his compositions characterized by polished skill and striking precision (the mark of a great master with a consistent style), but his extant music-theoretical formulations—though not always adequately passed on by his interviewers and translators—are also distinguished by forethought and sophistication. In contrast to, say, Shostakovich, who avoided formulating the musical principles behind his compositional style, Stravinsky told us a lot about his own compositions and, in particular, his system of harmony. Therefore, it makes sense to use the terms and ideas formulated by Stravinsky himself.

[2.2] By “harmonic system” we mean those fundamental principles, the totality of which encompasses the composer’s entire harmonic thinking in its most important forms. Clearly, under such a formulation there is no need to present a complete list of harmonic techniques. The question is, what are these fundamental forms and what is their organic connection with each other? Here we will lay them out in a series of principal theoretical problems.

[2.3] These problems fall under several headings:

• The Concept of Harmony
• Tonality
• Modality
• Polarity
• Serialism
• Historical Context

[2.4] These are the main headings of the article. The Concept of Harmony is a fundamental aesthetic problem; in relation to this concept, the following four headings prove to be constituent parts. Historical Context presupposes the connections of the principles of Stravinsky’s harmonic thinking with other analogous cases in twentieth-century music.

The Concept of Harmony

[2.5] About this concept, the composer, clearly expressing his thoughts, uttered the following well-known statement: “Harmony, a doctrine dealing with chords and chord relations, has had a brilliant but short history.”⁽¹⁾ What are we to do if the composer completely discarded harmony like that! As early as 1924, in an interview entitled “On My Most Recent Compositions” which, one could say, is a manifesto of neoclassicism, the future composer of Oedipus and the Symphony of Psalms proclaimed:

It seems to me that pure counterpoint is the only material from which it is possible to hammer out strong and stable musical forms . . . . Forms built on a modulating development or on harmonic transitory passages are unstable and always have an incoherent and vague character . . . . Not harmony—a fluid and unstable thing—but counterpoint represents the true constructive material.⁽²⁾

Stravinsky explains the “short history” of harmony thus: “chords gradually abandoned their direct function of harmonic guidance and began to seduce with the individual splendors of their harmonic effects.”⁽³⁾ Incidentally, this idea is an obvious borrowing from the Introduction of Taneev’s Invertible Counterpoint in the Strict Style. And from the preceding quotation we see that Stravinsky’s ideas are a clear continuation of Taneev’s ideas. Stravinsky continues, “The contemporary ear demands a completely different approach to music.” Finally, in 1969, recalling how composers were taught in his time, he also mentions lessons in harmony and immediately notes parenthetically: “consult a dictionary”—you’ll find this old-fashioned science there! Stravinsky even precisely dates the historical period when harmony existed—between the middle of the seventeenth and the middle of the nineteenth centuries.⁽⁴⁾ Moreover, he adds, “before Bach no one wrote harmonically.”⁽⁵⁾

[2.6] But the question is more complicated than this. Stravinsky has also made contrasting statements that cast his understanding of harmony in a completely different light. It would seem that, if in the second half of the nineteenth century (even before Stravinsky’s birth) harmony ended, then that would reinforce dodecaphonic-serial music as the domain of the twentieth century, that is, a century without harmony! Meanwhile, with respect to his own serial music Stravinsky affirms: “I hear harmonically, of course.”⁽⁶⁾ In connection with his Abraham and Isaac (1963), he writes: “The sound of harmonies or, as I like to call them, serial verticalities,”⁽⁷⁾ as such, the verticalized segments of a dodecaphonic series are easily called harmonies, as if they were simple tonal chords. In 1963, after a large number of serial compositions had been written, Stravinsky said: “In the distant [ed] past I wrote many compositions harmonically.”⁽⁸⁾ So, apparently harmony did exist for Stravinsky in the twentieth century, as if to say [ed]: “The king is dead; long live the king!” With respect to early music, Stravinsky offhandedly suggests the splendid and theoretically precise term “polyphonic harmony.”⁽⁹⁾ Yet there was already polyphony in the thirteenth century.

[2.7] What should we believe? Does Stravinsky maintain no clear position?

[2.8] Not in the least. All of Stravinsky’s statements outline a clear non-contradictory and perfectly accurate historical understanding of both the essence of harmony and its evolution. For brevity’s sake we will leave out the details and the proof and, instead, will formulate only the general result and the position of Stravinsky the music theorist.

[2.9] Harmony as a basis for composition—a basis associated with the contrast of tonal functions as well as the contrast-conditioned gravitational pull of all pitches to a tonic—belongs to the period from the middle of the seventeenth to the middle of the nineteenth centuries, that is, a period situated somewhere between Monteverdi on the one hand and Mussorgsky and Liszt on the other. Further achievements in music are connected with other techniques: coloristic effects, special modes (neomodality), self-contained dissonant complexes (functional inversion [ed]), and so on. Of course, the phenomenon of gravitation to the center of a harmonic system is retained and, in particular, so is the traditional resolution to a tonic triad. But this is no longer the essence of the system; the “brilliant” history of the classical tonal system had ended.

[2.10] Yet new late-Romantic harmony is also harmony, though it is no longer possible to grasp it merely with the tonal designators T, D, and S. And Stravinsky’s new harmony (which negates late-romantic harmony), as in The Rite of Spring, is also harmony though, again, in a completely different sense. And his serial harmony, with its verticalized segments of the row—a harmony that negates the outdated chordal-modal harmony of The Rite of Spring—is also harmony, although in a far-removed sense.

[2.11] Let us listen anew to a quotation from late Stravinsky, from his serial period: “When I say that I still compose ‘harmonically,’ I mean to use the word in a special sense and without reference to chord relations.”⁽¹⁰⁾

[2.12] Up until what moment, then, can we speak of harmony? It is entirely clear—as long as the musical whole was still organized melodically and harmonically (and also stereophonically [ed]) so that under any breakdown of compositional order the music suffered and began to sound bad. That is, as long as harmony was still a pledge of beauty in music. Stravinsky never allowed even the slightest deviation from his scores. Is it necessary to explain why? Because we clearly hear Stravinsky’s artistic world in all of his compositions as a result. In other words, the world of Stravinsky’s harmony: up until 1963, and beyond.

Tonality

[2.13] In all books it is written that Stravinsky is a tonal composer. That he “stands against” (though not completely) “atonal” composers. Let us look at an example from Stravinsky’s early period (Example 1 [ed]):

[2.14] Where is the tonality? It is neither B major nor C major, and it seems as if there is no tonic. Nor is there any gravitation or diatonicism. As Monsieur Voland said in Bulgakov’s Master and Margarita, “What’s going on here? Whatever I ask for, you don’t have [ed].” Further along, in the neoclassical period, good old key signatures are frequent (see the Violin Concerto), as are diatonic scales. On the other hand, everything from the 1950s is written using the serial technique.

[2.15] However, with respect to a harmony as in “The Drake,” there is a magic wand—“polytonality,” which means that on top we have B major and below C major, and they are “synthesized.” A modal synthesis transforms into a tonal synthesis. And in terms of his serial music, there is a convincing answer: in it, there is “atonality.”

[2.16] What does Stravinsky himself say? Concerning harmony, his answer, on the whole, includes an explanation regarding tonality. To summarize his words in one statement: strictly speaking tonality is a musical property occurring from the middle of the seventeenth century to the middle of the nineteenth century. Subsequently, new harmonic tendencies and properties were of interest. In order to understand these new tendencies and properties, a different complex of categories is necessary. In other words one should not apply the same names, such as “C major” or “C♯ minor,” to structures that are altered in their composition (since these categories of functional harmony in their well-known classical form had a terminal “short history”) but, rather, one should try to find new concepts, suitable to their subject matter. (Even for late-Romantic harmony the current term “new harmonic techniques” is necessary.)

[2.17] For the very same reason, the two favorite evasions of traditionalists—“polytonality” and “atonality”—are useless. The limitations of classical harmony and the absence of a suitable new theory can make us detect a combination of old structures in the tonality of the New Music rather than new harmonic structures (which may be unknown) [ed]. And thus, the infamous “polytonality” is born. How this is done is well known. Referring back to Example 1, the top layer is B major and the bottom layer is C major and together—their synthesis—is the “polytonality” B-major/C-major.

[2.18] The untenability of “polytonality” has always been evident. First, there is an elementary substitution of concepts. In harmonies such as those in Example 1, not one of the layers contains a tonality: in the upper layer there is a chord and not a tonality or key of B major; in the lower layer there is a dyad and not a tonality or key of C major. The confusion is typical. A scale or chord is mistakenly considered a “tonality.” But their combination is a polymode, a polychord (as in Example 1), or a combination of one or the other. More generally, their designation is a polyharmony, and not a polytonality. Stravinsky (1926) says the following about this: “I consider polytonality complete nonsense. Those who use polytonality want none other than to learn the laws of chaos—it is madness.”⁽¹¹⁾ You cannot say it better than that.

[2.19] In this case, what are these polystructures that are so frequent in Stravinsky’s music? One famous example is the Petrushka theme (which we won’t cite here since it is so well known). It is a single polychord, F♯ + C, which in a horizontal melodic unfolding also forms the symmetrical duplex-major mode (Boleslav Yavorsky’s term). Its formulation in semitones is: F♯^1.3.2, that is, the scale F♯–G♮–A♯–C–C♯–E. That this is not “polytonality” is easy to check. If F♯ and C were tonalities then the transition from one tonality to another would be a modulation, which is completely absent in an aural sense. Moreover, two major keys should give a joyous shade of mode, yet we hear in its place “Petrushka’s despair.”⁽¹²⁾

[2.20] Just as fruitless is the term “atonality,” another conclusion from a limited and ahistorical theory. It is even simpler: we don’t hear any type of C major or E♭ minor and, in this sense, there is no tonality whatsoever. And thus appears “atonality.” Stravinsky condemns the tinge of indifference in the prefix “a” and says as early as 1930: “My music is not atonal—there is as little atonality in it as there is the devil.”⁽¹³⁾ We can also find such a sentiment in his serial period: “I don’t accept the term ‘atonality,’ that is, without tonality. I prefer the term ‘antitonality.’”⁽¹⁴⁾ And about serial music itself: “When they say that serial music is ‘atonal,’ that is not the correct word; serial music is antitonal or contratonal.”⁽¹⁵⁾

[2.21] In 1917 Stravinsky entered in his journal nothing less than the following deadly characterization of “atonality,” which we want to associate at the same time with “polytonality”: “I’ve noticed that those who speak most of all about atonality have a very poor understanding of tonality itself, and of the tonal system.”⁽¹⁶⁾

[2.22] However, polytonality and atonality represent that which is not there. What, then, is there?

[2.23] Consistent with an authentic musician’s hearing, which persistently maintains that Stravinsky is a tonal composer, we can elaborate on the understanding of tonality in the New Music of the twentieth century. It is neotonality, that is, a centralized system with new elements [ed]. By “centralization” we mean a relatedness of harmonies with one, single, central element, and by “new elements” we mean those that are new with respect to the old centralized system, which consists of consonant triads and harmonies derived from them. Thus, the new elements in Example 1 are the polychords C–D + B–D♯–F♯–G♯ and C–G + A–D♯–B, neither of which can be found in the harmony of Bach, Mozart, or Tchaikovsky. The system is centralized because the second of these chords is derived from the first [in the sense that C–G is derived from C–D, both with a centric pitch C, and B–D♯–A is derived from B–D♯–F♯–G♯, both with a centric pitch B if we take B to be the root of a dominant seventh and of a major triad with added sixth. –PE]: this process plays out further along in the piece.

[2.24] Stravinsky developed, theoretically speaking, certain structural laws of neotonality—see the headings below on “Polarity” and “Serialism.”

[2.25] If we bear in mind the substitution of the system’s elements, then it is possible to capture the entire evolution of Stravinsky’s harmony with the sole concept of neotonality: the turbulent ascent to the new harmonic thinking of roughly 1910 to 1912, the partial retreat and the compromise with old tonality in the neoclassical period, and the transition to a new centralization in the “atonal” serial-dodecaphonic period. Did Stravinsky speak of any tonal components of his serialism? It turns out that he did: “The intervals in my series gravitate toward tonality; I compose vertically, and this means, at least in one sense, that I compose tonally.”⁽¹⁷⁾

[2.26] It looks like this (Example 2a and 2b) [ed]:

[2.27] The examples show exactly how the intervals of certain series gravitate toward tonality: they form diatonic fields. Stravinsky was an inveterate diatonicist, and remained so even in his dodecaphonic music.

[2.28] The centralization itself, in its conception, merges the general idea of harmony, in its orderly formation, with a certain architecture of tones. It is interesting that Stravinsky himself spoke about this in one of his conversations from 1930.⁽¹⁸⁾ There the maestro, in passing, let slip a curious metaphorical term, “architect-tonality,” having joined the harmonic ideas of two art forms.

Modality

[2.29] When speaking of the historical evolution of the highest principles of musical composition, Stravinsky places three of them on equal footing:⁽¹⁹⁾

[2.30] Thank god we don’t have to justify or summarize anything with the term “modality.” We’ll simply clarify that modality is that harmonic principle which emanates from a horizontal-melodic row of tones and not from a triad or series. This group is usually called a modal scale. There are two types of modality: (1) natural modes (the Western church, ancient Greek, Byzantine, Russian chant, and folk modes), and (2) symmetrical modes based on an equal division of the twelve semitones (diminished [in particular octatonic], hexatonic, wholetone, and various tritone-based modes; and, correspondingly, various complementary hemitonic segments [ed].

[2.31] Actually, Stravinsky’s modality blooms with a splendid blossom. Here are examples of natural (Example 3a) and symmetrical (Example 3b) modes:

[2.32] At the beginning of Petrushka there is a rare incomplete pentatonic scale D–E–G–A, unfolding at first vertically, and then melodically. It is curious that the traditional key signature does not relate to the mode of the quoted section, insofar as the scale lacks not only $\hat{6}$ (B♭) but also $\hat{3}$ (F). Indeed, this mode is beyond the limits of major and minor tonality.

[2.33] In the main theme of the first movement of the Symphony of Psalms, the choir sings a stern “Phrygian” melody. In the accompaniment there is a pure octatonicism, the semitone-wholetone mode. More precisely, this is, of course, the mode of Rimsky-Korsakov, Stravinsky’s teacher. Both the Russian tradition and its renewal are undoubtedly at play here. If in the nineteenth century symmetrical modes conveyed, for the most part, fantastical otherworldly images, then for Stravinsky it was a calm, specific modal-harmonic color, with the salient sonority of the diminished-seventh chord (in this case, F–G♯–B–D).

[2.34] The theoretical development of the following fundamental category of his harmonic thought, worked out by Stravinsky himself, is of particular interest. Stravinsky called it “Polarity.”

Polarity

[2.35] Stravinsky specifically includes the technique of the “sonic pole” with tonality and modality in the abovementioned classification.⁽²⁰⁾

[2.36] Stravinsky gives his first description of the polar technique in Chronicle of My Life, from 1935–36. Regarding the Serenade in A, he writes: “Having called my composition the ‘Serenade in A,’ I was pursuing a particular goal: here the matter lies not in the definition of tonality but, rather, how I compel all the music to gravitate toward one sonic pole, which in the given instance is the tone A.”⁽²¹⁾ Undoubtedly, the author has the following types of harmonies in mind (Examples 4 and 5 [ed]):

[2.37] Why is this not tonality in the usual sense? In Example 4 the chord, of and by itself, has the root tone F (and the quality of F major), and not A (and the quality of A minor), yet the composer is indeed making the music gravitate toward A and not F. In Example 5 the E–G–A–C♯–E chord seems to outline the tonality of D major but, in reality, the dissonant A-major turns out to be the center of gravitational pull [ed]. Neither one thing nor the other fits into the traditional notions of A minor or A major and, of course, the (new) tonality would be more properly designated as “in a/A.”

[2.38] However, Stravinsky’s term “pole” raises doubts. He gives the following more explicit explanation of the term: “So our chief concern is not so much what is known as tonality [that is, A minor or A major in relation to our Examples 4 and 5. –Yuri Kholopov] as what one might term the polar attraction of sound, of an interval, or even of a complex of tones. The sounding tone constitutes in a way the essential axis of music. Musical form would be unimaginable in the absence of elements of attraction which make up every musical organism and which are bound up with its psychology.”⁽²²⁾ “A system of tonal or polar centers is given to us solely for the purpose of achieving a certain order, that is to say more definitively, form, the form in which the creative effort culminates.”⁽²³⁾ “Diatonic tonality is only one means of orienting music toward these poles. The function of tonality is completely subordinated to the force of attraction of the pole of sonority.” The pole is “the center upon which the series of sounds involved in my undertaking should converge.”⁽²⁴⁾

[2.39] That which Stravinsky describes does not exactly correspond with the term “pole.” The author always speaks about a certain center of attraction on which the pitch structure is based. Indeed, the concept “pole”—coming from the Greek “pólos” (meaning the tip or end of an axis, or the Arctic or Antarctic pole)—essentially presupposes not one but two antagonistic centers; polarity is the opposition of one thing to another. Stravinsky never mentions any type of counterpole. In essence, something like a classical tonic is implied, but without the necessity of its specific pitch configuration (a consonant triad). The breadth of the generalization does not allow for the use of the term “tonic,” thus Stravinsky uses the term “pole” instead.

[2.40] Here are several examples of Stravinsky’s “poles,” insofar as we can understand what he meant (Example 6 [ed]):

[2.41] The six-note polychord in Example 1 is a typical “pole” as well. This polychord is the central element of an individual mode that is derived from the properties of the main sonority, in exactly the same fashion that a classical C-major tonality grows out of the properties of the C-major triad. In none of the examples is there a counterpole and, moreover, there are no signs indicating what “counterpole” could mean.

[2.42] Regarding Stravinsky’s term “pole,” one analogy with Russian terminology comes to mind, though this time it is hardly possible to speak of the Russian tradition or any kind of Russian music-theoretical influence. Notably, the term “pole” [polius. –PE] precisely corresponds to the notion of “stability” [ustoǐ. –PE] that was formulated in the theories of Boleslav Yavorsky. And its breadth, its irreducibility to the traits of the classic tonic, and its structure—as one tone, an interval, a chord, a group of intervals or chords, or even a row like a series in its basic pitch position—all precisely match the contemporary idea of “stability.” At any rate, it is better than the concept “pole.”

[2.43] Unfortunately, it is unknown whether Stravinsky heard of the term “stability” from other Russian musicians; therefore, we are speaking of an analogy. But the far-reaching similarities of the meanings of the term “pole” with one of the basic concepts of Russian music theory make it possible to connect them together. Let this be, then, a parallel line in the development of music theory in Russia.

[2.44] I will take the liberty of expressing yet another supposition. When a Russian theoretical text is translated into a foreign language, it often turns out that certain concepts are practically untranslatable, let us say, the following terms into German: lad, intonatsionnyǐ kompleks, ustoǐ, neustoǐchivost’, or predykt [mode, intonational complex, stability, instability, or retransition. –PE]. In this case, it is necessary to translate ustoǐchivyǐ and neustoǐchivyǐ [stable and unstable. –PE] as fest and locker in German (from Webern’s theory of structure). The supposition lies in the following: the term “stability” (or its concept) was known to Stravinsky, and he wanted to express it in French and English, but couldn’t. Perhaps, because of this difficulty, he chose the word “pole”? At any rate, when Stravinsky says “pole” it is always possible to replace it with the word “stability” and, thus, the sense is made even simpler and clearer [ed].

Serialism

[2.45] For decades it was possible to perceive an antagonism between Stravinsky’s “tonal-modal” model and the “atonal-serial” model of the Second Viennese School. “I’m not an atonal composer, of course. For me, atonality simply doesn’t exist,” Stravinsky observed about himself in 1963.⁽²⁵⁾ Granted, at the end of his life Stravinsky apparently betrayed himself and accepted the dodecaphonic faith.

[2.46] And then, as is often the case, Stravinsky offers us something unexpected: “I’ve always been a bit of a serialist, in all of my music,” Stravinsky said in 1963, in the twilight of his career (the text actually reads “total serialist,” and not “serialist”). “The series has the same legal rights as a harmony!”⁽²⁶⁾

[2.47] It turns out that Stravinsky wanted to separate the twelve-tone technique and serialism (in classical dodecaphony they are connected). “Schoenberg’s twelve-tone system interests me much less than the series.” “The use of all twelve tones of the octave is, in my opinion, not necessary. I personally am not a dodecaphonist, but a serialist, that is, I consider it possible to use not all twelve notes.” Stating his ideas about serialism, Stravinsky mentions a row of five notes—C–E–F–G–G♯—as an example of a series.⁽²⁷⁾

[2.48] Though they are scattered here and there, Stravinsky expresses completely clear ideas. Two different types of serialism exist:

• Serialism (a construction of musical fabric from one chosen group of pitches, which can be of a varied quantity: from 4–5 to 11–12)
• Twelve-tone Technique (the sequential use of all twelve tones, both with and without the repetition of tones)

[2.49] Accordingly, various combinations of one with the other are possible and, consequently, applicable. Logically, the four following possibilities result (a plus sign means that the property exists and a minus sign means that it does not):

1. Serialism (–) and Twelve-tone Technique (–)

   For example: Prokofiev’s Sixth Piano Sonata or Hindemith’s Mathis der Maler

2. Serialism (+) and Twelve-tone Technique (–)

   For example: Webern’s 1905 String Quartet (Introduction), or Stravinsky’s Three Songs from William Shakespeare, No. 1

3. Serialism (–) and Twelve-tone Technique (+)

   For example: Shostakovich’s Symphony No. 14 or Alemdar Karamanov’s Prologue, Thought, Epilogue for solo piano

4. Serialism (+) and Twelve-tone Technique (+)

   For example: Webern’s Op. 21 Symphony or Boulez’s Third Piano Sonata

[2.50] In this classification, the points of maximal concentration of properties under the combination of Serialism and Twelve-tone Technique are shown. Yet a variety of forms also belong to this classification system, while the artistic merits of the music, as well as the historical significance of the composition, do not depend on the classification system. In his well-known article published in the journal Anbruch in 1924, in a demonstration of Schoenberg’s new “Grundgestalt” method (“basic shape”—Schoenberg’s term [ed]), which was subsequently called “dodecaphony,” Erwin Stein uses Schoenberg’s op. 23, no. 3, as the main example in which the serial principle is conducted sequentially in a pure twelve-tone context (that is, without signs of diatonicism). Yet in the series of this piece there are not twelve pitches, but only five: B♭4–D4–E4–B3–C♯4. The technique itself is a genuine serial technique, and the musical sound is practically not at all different from a piece with a twelve-tone series (as in, for example, the same opus, from the final “Waltz”).

[2.51] It turns out that Stravinsky has the same type of serialism. The inspired score of Firebird was a powerful breakthrough into the magical empire of the New Music. Serialism was also among the range of the composer’s discoveries—truly, “an art form of a completely different dimension than harmonic or modal music.”⁽²⁸⁾ In Example 7a, what seems to be at first glance “harmonic” music turns out to be, in reality, clearly serial music as well. The density of textures of the “Grundgestalt” (in relation to the whole, this is still just a “Nebengestalt”—an additional constructive element) is just as great as in the Introduction of the eighth song from Schoenberg’s Pierrot Lunaire. In Example 7b a fragment from Firebird’s “Supplication of the Firebird” is presented [ed]. This fragment is completely composed in the serial technique. The four-note leitmotiv of the heroine, the Firebird, is the series.

[2.52] Here we are using the concept of the series in the abovementioned sense, consistent with Stravinsky’s theory.⁽²⁹⁾

[2.53] But the series (and consequently, serialism) has not only “legitimate rights” on par with harmony. Stravinsky feels that “serialism in music constitutes, in a sense, a tonal foundation for a composition.”⁽³⁰⁾ The commonality of the series and the tonic as a tonal (“architectonal”) foundation of music can be revealed in the more general idea that stands above the level of concrete pitch properties of one or another pitch complex—they are both different forms of a Central Element (CE) of a Pitch System. The principle—with which the major/minor tonal system, as well as the individualized system in each serial composition, complies—can be stated uniformly: the formation of a system of relationships on the basis of properties of the system’s central element. In earlier tonality, from a Mozart quartet to a Rachmaninov concerto, the CE was predetermined. In neotonality the CE is chosen and freely constructed by the composer. By the same token neotonality links up with serialism, where the CE-series, according to the principle of the composition, is composed by the composer individually for each piece, or even for a separate movement. Refer back, for instance, to the piece by Stravinsky in Example 1.

[2.54] Also, the thirteen CE–poles shown in Example 6 demonstrate the panorama of those pitch structures that lie at the heart of those pieces or passages thereof. This is also tonality (that is, neotonality). And it is also serialism, in Stravinsky’s understanding, that is, without the twelve-tone technique, though it can also be part of the structure (see Examples 6j, 6l, and 6m).

[2.55] As a matter of fact, it turns out that:

• Stravinsky was, in a certain sense, a “serialist” for his whole life;
• this serialism actually constitutes a (neo)tonal basis for his compositions;
• the neotonal-serial principle of Stravinsky's composition, for all intents and purposes, yields an “art of new dimensions,” particularly in combination with his rhythmic language and new syntax.

[2.56] Taking into account the underlying connection between the “polarity” and (in the sense given by Stravinsky) the “series,” it is now possible to state Stravinsky’s historical ternary complex, from roughly 1942, differently:

Stravinsky’s Harmony in Historical Context

[2.57] But of what historical context exactly? As an artistic figure, Stravinsky made his mark as far back as 1907, with his song “Spring (the Cloister),” op. 6. From 1909–1910 onward he enjoyed worldwide fame; Firebird’s dazzling shine has not faded at all, even until today. The mystical springtime of twentieth-century art arrived in 1913 with his Rite of Spring. Whereas the charming serial trifle “The Owl and the Pussycat,” dedicated “to Vera,”⁽³¹⁾ dates from 1965–1966.

[2.58] During a period of the rise of a newly empowered avant-garde, Stravinsky’s transformation to dodecaphony in the 1950s and an interest in the new artistic world of Webern nicely placed the “great Igor” into this period as well. However, in essence, Stravinsky kept his distance from the ideas of the post-war avant-garde, which came under the banner of sonorism, multi-parameter composition, stereophonic spatiality, and the “new sound” (Webern’s term). The avant-garde—Stockhausen, Boulez, Nono, and Cage, for instance—liberated the subatomic energy of sound (in particular, they emancipated timbre and rhythm). The avant-garde also changed the relationship between man and time (in which the criteria of classical song forms became specific examples in a range of rhythms of micro-time and macro-time), and the relationship between the space of the artist-performer and the space of the consumer (= participant)-listener, unlocking artistic time (plainsong, Guillaume de Machaut, and Gesualdo became our senior contemporaries). Lastly, the avant-garde expanded the geopolitical space of music (Gagaku and Raga ceased to be exotic, and African-American jazz evolved into worldwide folklore).

[2.59] But Stravinsky (as well as his harmony) belongs to different spheres of the art of sounds. Despite Stravinsky's “1001 styles,” all Stravinsky emanates from two currents [ed]: Russian music (he once called it “great Russian art”⁽³²⁾) and Western Renaissance polyphony (as if realizing the legacy of late Glinka). Stravinsky was a great musician of the first half of the twentieth century, and his harmony antedates sonorousness. This harmony relies on the interval (and not sonorities or timbral composition). The nucleus of Stravinsky’s harmonic structure is always the “series” or “Grundgestalt” as a combination of intervals with a strict rhythmic formula. Stravinsky (despite being carried away by Webern’s skill), like the Neoclassicists, conceived of harmony, chiefly, as coplanar notes, and not as notes that are stratified stereophonically. The harmonic structure uses (imitates) the properties of chosen material, yet in its own syntax and rhythmic language. Counterpoint is the basic harmonic fabric and, accordingly, the counterpoint is in a contoured two-part writing. (Prokofiev, once answering a question on the principles of his own compositional method, said, “Stravinsky and I both write in two-voice counterpoint.” [ed])

[2.60] “Dodecaphonists” strove to infuse individuality in each composition by means of an individual intervallic order in the selected series. Stravinsky the “serialist,” in an analogous fashion, attained an individual distinctiveness for each composition (which was derided as “1001 styles”) by choosing an individual method, a unique “mode,” in an expanded sense, for each composition. In a way he anticipated the total-global-temporal ideas of the second half of the twentieth century, having dressed up his own compositional language—which was always of one and the same structure—in such motley attire. The “series”-material (including harmonic) chosen by Stravinsky is always new. Let’s compare:

• the thirds of Kashchei and the Firebird mode (4.1.1), as if taken from Rimsky-Korsakov;
• the duplex-major mode of Petrushka and the Shrovetide Fair songs;
• the enigmatic chords of “Zvez–do–li–ki”;
• the polychord E major + E♭7 from the “Dance of the Adolescents” from the Rite of Spring;
• the peasant modality of the lullaby “Oh, Tomcat Tomcat,” from the Cat’s Cradle Songs;
• the forest polyharmony of the “Bear’s Little Song” from Three Children’s Tales;
• the folk-polyphonic voice-leading of the Russian traditional folksong “In Our Savior’s Parish at Chigasi,” from Four Russian Folk Songs for women’s chorus;
• the squeaky high-pitched sounds of the violin and the drumbeat patterns in A Soldier’s Tale;
• the poignant banality of the African-American Piano-Rag-Music;
• a variety of materials from Pergolesi;
• the incomplete diatonicism (oligotonicism) of the five fingers, Do–Re–Mi–Fa–Sol;
• the Russian “Italianateness” from the times of Fedor Dubianskii and Aleksandr Dargomyzhskii;
• and so on, through a “series” of materials from the early classics, J. S. Bach, “The King’s 24 Strings,” Tchaikovsky, Carl Maria von Weber, Handel, Rachmaninov’s Vespers, Russian municipal folk songs, the jazz of Woody Herman and, finally, the 4-, 5-, and 12-note series in a strict sense (and in a strict style—see Example 2 above), in the manner of Webern, Schoenberg, and Hauer, but in the style of Stravinsky. And, in a sign from above, the last thing that the great master—a lover of strange models—wrote was an instrumentation of two sacred songs by Hugo Wolf for voice and five wind and five string instruments (1968). [ed]

[2.61] Great styles result in an explosive development of musical-biological “niches,” which then reveal themselves to composers. Stravinsky’s style is great because of the creative development of its “niche.” Its distinctiveness lies in the focus and accumulation of a few key ideas of the epoch, the first half of the twentieth century. A great style summarizes great ideas. As we have seen, Stravinsky absorbed the most important ideas of his antipode, the Second Viennese School. And Stockhausen’s favorite principle from recent years, formula composition, is also “serialism” in some free non-Schoenbergian sense.

[2.62] In contrast to Bartók, Berg, Webern, Prokofiev, Hindemith, Schoenberg, and Shostakovich, Stravinsky developed a new rhythmic language, which, as is well known, existed “at the beginning” [ed]. The serialists (Boulez, for example) remarked on and appreciated the creative meaning of this rhythmic language.

[2.63] And in contrast to those same composers (with the exception of Webern) and a throng of other composers of the same period, Stravinsky produced a syntax of musical speech from his new rhythmic language, a syntax that allowed him to deviate from the metrical framework of classical song forms and other traditional structural types.

[2.64] This new syntax and rhythmic language provided a new temporal dimension and, correspondingly, a new life of harmonic functionality for Stravinsky’s harmony. This functionality was no longer bound, then, to traverse a pre-required path of an inevitable thickening of harmonic connections, which were already approaching some limit or “sound barrier” (as in aviation).

[2.65] If, traditionally, the possibility of further advancement required a most complicated internal reorganization or serialism (Webern found a more radical solution—counterpoint and harmonic parametral stereophonics), then model-series were sufficient for Stravinsky, that is, the selection of well-defined CE-nucleus-models, also including, as it were, a “foreign” type of model (“as it were” because the breathing of music—rhythm—cannot be borrowed, despite the occasional borrowing of rhythmic figures). Stravinsky’s model-series in Petrushka is the “breathing in-and-out” figure of the Shrovetide-fair harmonica, which became the CE of the ballet’s entire musical form; in “The Fairy’s Kiss” it was Tchaikovsky’s melody with Stravinsky’s music; and so on.

[2.66] How does Stravinsky appear in Historical Context at the end of the twentieth century? The avant-garde, having begun in 1950 (the “zero hour” of the New Music) or in 1945, emerged from Webern’s discoveries in pitch organization and harmony and from Stravinsky’s in rhythm and time. This avant-garde flourished magnificently in the 1950s and 1960s, stagnated magnificently (as still water stagnates) in the late 1960s and into the 1970s, and further decomposed, gradually becoming commonplace. And indeed Stravinsky, with his model-series and his redemption in rhythm, from the “serialist” within, turned to dodecaphony in 1957–1958 (with his Threni: id est Lamentationes Jeremiae prophetae).

[2.67] The impression is such that all of these methods fizzled out, having reached the summit and transferred the impulsive energy to others. In 1964 Stravinsky accurately criticized the former, orthodox “dodecaphonists”: “At one time the series or row was used sequentially as the basis of a composition, yet now it rarely serves as anything larger than a point of departure”⁽³³⁾ (among new composers this relates to Edison Denisov, for example).

[2.68] In the context of today’s rear-guard nadir, Stravinsky’s harmony not only seems non-anachronistic but, against the backdrop of avant-garde imitators, is heard as something original and creative, and not at all worn out by the waves of time.

[3] Commentary

The Concept of Harmony

[3.1] In Russia, aside from simply meaning “a harmony” (such as a C-major harmony), the term harmony (garmoniia) represents an important discipline within a core curriculum of music study. In this sense “harmony” means “music theory.” Aside from being a discipline, garmoniia can mean “pitch structure” or “pitch organization.” The title of Kholopov’s article, then, might be “On the System of Stravinsky’s Pitch Organization.” Notably, garmoniia, in this usage, is broader than “pitch organization”: it might include other musical parameters, such as rhythm, meter, or scansion, for instance. It is quite possible to render “pitch structure” or “pitch organization” in Russian (vysotnaia struktura or vysotnaia organizatsiia) and, to be sure, writers use these terms; it is also common, however, to include them under the umbrella term of garmoniia.

[3.2] But the matter is more complicated than this. While in the West the notion of “harmony,” so often linked with “tonal harmony,” gave way to post-tonal ideas, Kholopov embraces it to encompass a unifying notion from the ancient Greeks to the present day. In his Garmoniia he goes to great lengths to expand the notion of harmony to include neotonality and neomodality (among other concepts), which in turn account for common pitch structures in the music of Stravinsky, Bartók, Prokofiev, Shostakovich, and others. This expansion of harmony to include music beyond what we often term in the United States “functional tonal harmony” should be considered a hallmark of Kholopov’s work. In fact, his treatise might more accurately be called “The Theory of Harmony.”

[3.3] In his section on “The Concept of Harmony,” Kholopov evaluates and contextualizes several of Stravinsky’s observations. One intriguing link he makes is that between Stravinsky and Sergei Taneev, suggesting that Stravinsky borrowed from the Introduction to Taneev’s Podvizhnoǐ kontrapunkt strogogo pis’ma (Invertible Counterpoint in the Strict Style) ([1909] 1959). Taneev was a Moscow-based figure, so his interaction with the Petersburger Stravinsky was limited. After briefly mentioning this Moscow/Petersburg divide, Stravinsky reminisced about Taneev and acknowledged the influence of his book on counterpoint: “Taneyev was a good teacher, and his treatise on counterpoint—one of the best books of its kind—was highly valued by me in my youth” (Stravinsky 1960, 60). (Importantly, Kholopov hears a strong harmonic foundation in Stravinsky and others even though Stravinsky himself spoke out against harmony in favor of counterpoint.)

[3.4] The material in the Introduction to Taneev’s work is strikingly similar to the sentiments that Stravinsky expressed regarding the importance of counterpoint and the end of harmony. It is worth citing the relevant passage from Taneev’s work in its entirety, to stress the impact that these words had on Stravinsky and his harmonic thinking:

The tonal system that replaced the church modes is, in turn, being reborn into a new system that seeks to destroy tonality and substitute the diatonic basis of harmony with chromaticism. And the destruction of tonality leads to a disintegration of musical form. The consistent realization of the principle in which any chord can follow any other chord in a chromatic framework deprives harmony of tonal connections and excludes those elements that separate compositions into distinct parts, group smaller parts into larger ones, and bond everything into one organic whole. The harmony of strict counterpoint, in which any chord can follow any other chord (though in a diatonic framework) did not yet have the forming element of tonality. New harmony [of the late nineteenth and early twentieth centuries], in the form to which it is now adapted and which Fétis calls “omnitonality,” once again excludes this element. The only difference is that the diatonic basis of strict counterpoint was replaced with a chromatic basis. At the same time omnitonal harmony, enriched with new combinations, deprives itself of those strong methods of influence connected with tonal functions. A stable area in one key in contrast to a more or less quick change in modulations, the juxtaposition of contrasting forms, a gradual or sudden transition to a new key, or the prepared return to the main theme: all of these methods—which make large sections of a composition prominent and which facilitate the listener’s perception of its form—are disappearing from contemporary music little by little. And from here lies the disintegration of the formation of separate movements and the decay of general composition. Whole musical compositions, durably held together, are becoming more and more rare. Large-scale compositions are being created not as well-shaped organisms but as formless masses of mechanically connected particles, which can, at the discretion of the composer, be rearranged and replaced by others.

For contemporary music, in which harmony is gradually losing its tonal connection, the connecting force of contrapuntal forms shall be particularly valuable. In his late compositions, Beethoven, turning to the technical devices of the old contrapuntalists, showed the best path for subsequent music. Contemporary music is predominantly contrapuntal. Not only expanded orchestral compositions, in which an abundance of independent voices often lead to complications and ambiguity, or operas based on contrapuntally worked-out leitmotivs, but even works of a smaller size rarely manage without counterpoint. Therefore, the study of free counterpoint constitutes a necessary condition of the technical preparation for contemporary composers. But in light of the extreme melodic and harmonic complexity of this counterpoint, one should not begin one’s study with free counterpoint. The study of strict counterpoint—more accessible for learning in light of the simplicity of its elements—should serve as a preparatory step. (Taneev [1909] 1959, 9–10)

[3.5] The parallels with Stravinsky are obvious: “It seems to me that pure counterpoint is the only material from which it is possible to hammer out strong and stable musical forms,” “Not harmony—a fluid an unstable thing—but counterpoint represents the true constructive material,” “Chords gradually abandoned their direct function of harmonic guidance and began to seduce with the individual splendors of their harmonic effects” (see Kholopov’s paragraph 2.5 above). It is clear that Taneev’s book had a significant impact on Stravinsky. Ultimately, Kholopov goes to great pains to insist that, whatever vagaries may exist in Stravinsky’s compositional output, they can still be subsumed under the rubric “harmony.”

Tonality

[3.6] Kholopov begins this section by building up the concepts of “polytonality” and “atonality,” only to knock them down as he proceeds.⁽³⁴⁾ In paragraph 23 Kholopov makes first mention of “neotonality,” which became a constant theme in his writings later in life. The magnitude of this concept relative to Stravinsky’s music is revealed in paragraph 2.25: “it is possible to capture the entire evolution of Stravinsky’s harmony with the sole concept of neotonality.” Kholopov’s thinking was influenced by Mikhail Tarakanov’s work on neotonality.⁽³⁵⁾

[3.7] Kholopov elaborates on these ideas in his article on neotonality (Kholopov [1988] 2003). He defines the concept thus:

Twentieth-century Neotonality is qualitatively a different phenomenon in comparison with classical tonality, since neotonality relies mainly on dissonance (a dissonant chord, that is, any group of notes expediently collected by the composer) and on a 12-note structure . . . that doesn’t have a directly sensed gravitation to a central complex at every moment. Neotonality is structurally diverse and individualized. At the same time, as with classical tonality, it represents a logical, well-formed, hierarchically ordered system of functional pitch connections—in other words, a mode. The pitch situation of motives and chords in neotonality is aesthetically regulated (and not “atonally” indifferent). (Kholopov 1991, 548–49)

Of course the idea of neotonality is nothing new in the analysis of twentieth-century music. Ultimately Kholopov was interested in finding new theoretical systems to understand twentieth-century music, and he added many new ideas to the general notion of neotonality. In the quotation above, the crucial role of “mode” is apparent, which is key to understanding Stravinsky’s music.

Modality

[3.8] It is difficult to convey the importance of the term “modality” in Russian, and in Russia. Ellon Carpenter says, “In Russian music theory, the concept of mode forms one of the major and most important tenets upon which that theory is based. In its broadest interpretation, the Russian concept of mode has no exact equivalent in western music theory” (1995, 76–77). Kholopov focuses on the second type of modality listed in paragraph 2.30, “symmetrical modes based on an equal division of the twelve semitones.” These symmetrical modes are based in large part on Yavorsky’s “Theory of Modal Rhythm,” which was first explicated in his Stroenie muzykal’noǐ rechi (The Structure of Musical Speech; 1908). Indeed, much late-chromatic and twentieth-century music can be understood though Yavorsky’s theory, and Kholopov draws heavily on it when dealing with Stravinsky.

[3.9] In paragraph 2.30 Kholopov mentions the term “octatonic.” The original Russian read oktatonika (English octatonicism). As is well known, the octatonic scale in Russia is called the “Rimsky-Korsakov” scale, and music that is often considered octatonic in North America is considered to be in either the duplex-chain mode or the diminished mode in Russia (see Ewell 2012). Kholopov tried, unsuccessfully, to promulgate the Americanized term oktatonika in Russia later in life; he was well aware of the octatonic debates going on in North America, in general and in relation to Stravinsky’s music, and he wished to use a new term for this diminished-mode music. In paragraph 2.33, however, we see how he reverted to calling this octatonicism the “semitone-wholetone” and “Rimsky-Korsakov” mode (Russian lad) and not scale (Russian gamma). Given its rich modal theory, it is not surprising that the term oktatonika has not caught on in Russia. Kholopov and other theorists in Russia have known about octatonicism in Stravinsky’s music for a long time, and do not consider it to be that important with respect to pitch structure in his music.

Polarity

[3.10] The most significant part of this section is the link Kholopov makes between Stravinsky’s “pole” and Yavorsky’s “stability.” It would be difficult to show that Yavorsky and his theories had a direct influence on Stravinsky. Yavorsky’s work was first published in 1908. Further, Yavorsky was from Ukraine and, when he was not studying or working in Kiev, he did so in Moscow. That is to say he was simply not part of Stravinsky’s St. Petersburg. Still, it is not out of the question that Yavorsky’s work impacted Stravinsky, even if only in some small way. For his part, Yavorsky did not think highly of Stravinsky’s music. In a letter to Anatoly Lunacharsky from 1927, Yavorsky wrote, “Stravinsky makes a mockery of his listeners” (Varunts 2003, 3:264). Were Stravinsky cognizant of such a sentiment, his reluctance to cite Yavorsky as an inspiration would make even more sense.

[3.11] The concept of a pole or axis is nothing new in Stravinsky studies.⁽³⁶⁾ Though Stravinsky’s most famous quotations on polarity come from his lectures at Harvard in 1947, the composer Nikolai Nabokov gives an interesting account of Stravinsky’s thinking two decades earlier, in the late 1920s. Nabokov quotes his friend Stravinsky as saying, “Art—in my case musical composition—is the control of order, the invention of well-ordered pitch structures in well-ordered time and space. What’s important to me is the root tone of the chord—or the root tone itself—as a pole of attraction. Call it what you will—tonality, modality, chordality. Only the ear should distinguish it in every syntagm, in every phrase” (cited in Stravinsky [1963] 2005, 284). So, it seems that Stravinsky was thinking about polarity long before his lectures at Harvard.

[3.12] Often, with Stravinsky’s triadic music, there is a duality at play, which could be related to the polar aspect of this music. Kholopov’s Examples 4 and 5 demonstrate this duality. He implies that the chord in Example 4 exhibits qualities of the root tone “F” (of F major), and not “A” (of A minor). Indeed, the musical example shows that, despite the F-major triad in first inversion, there is a pull toward the pitch “A” (with a feeling of A minor).⁽³⁷⁾ Kholopov conveys the idea of “axis” in Example 6—each of these examples represents an axis, generally, which becomes a “center of intersection” for the given piece.⁽³⁸⁾

[3.13] Stravinsky’s numerous quotations on polarity have interested scholars for decades.⁽³⁹⁾ Kholopov touches on some of these in the section on poles; see paragraph 2.38. A longer quote on poles, from Stravinsky’s Poetics, reads:

Having reached this point, it is no less indispensable to obey, not new idols, but the eternal necessity of affirming the axis of our music and to recognize the existence of certain poles of attraction. Diatonic tonality is only one means of orienting music toward these poles. The function of tonality is completely subordinated to the force of attraction of the pole of sonority . . .

So our chief concern is not so much what is known as tonality as what one might term the polar attraction of sound, of an interval, or even of a complex of tones. The sounding tone constitutes in a way the essential axis of music . . .

In view of the fact that our poles of attraction are no longer within the closed system which was the diatonic system, we can bring the poles together without being compelled to conform to the exigencies of tonality. For we no longer believe in the absolute value of the major-minor system based on the entity which musicologists call the C-scale. (Stravinsky 1959, 37–38)

So, it seems that Kholopov’s broad understanding of “pole” is fitting, given Stravinsky’s idea that such a polar attraction could be a sound (read here “note”), interval, or complex of tones (read here “group of notes”). Kholopov raises three worthwhile points with respect to Stravinsky’s usage. First, a pole implies a counterpole (paragraph 2.39). Second, “pole,” in Stravinsky’s usage, corresponds with the term “stability” in a Yavorskian sense (paragraph 2.42). Finally, and most important, it may be that Stravinsky actually meant to say “stability” in place of “pole” (paragraph 2.44). This last point is striking and, to be sure, substituting one with the other does make sense when looking at Stravinsky’s words and matching them to his music. In this reading, then, one need not look for counterpoles; one can be content simply thinking of the stability or “central element” that holds Stravinsky’s music together.

[3.14] Finally, it is worth mentioning the polar views of another significant Russian composer and Stravinsky contemporary, Alexander Scriabin, inasmuch as these views may have influenced Stravinsky and how he viewed polarity. Scriabin, who famously claimed that in his music “melody becomes harmony and harmony becomes melody—for me they are one in the same” (Sabaneev [1925] 2000, 54), saw a logical evolution from classical tonality to his own, from one type of polarity to another. Scriabin said:

After all, why in classical music could there be a harmony that is different from melody? Because there, with harmony, there was a polarity between tonic and dominant: with the dominant, the dominant harmony gravitated toward the tonic . . . But in my Prometheus there is already a different system; my polarity is not between tonic and dominant but, rather, the polarity is of these sonorities [two Mystic chords], located at the distance of a diminished fifth . . . It is completely analogous to the tonic-dominant succession and cadence in the classical system, only on a different plane, a level higher. (Sabaneev [1925] 2000, 260)

This is a remarkably telling quotation with regard to Scriabin’s music and, more generally, how composers at the beginning of the twentieth century began to think of new ways to expand tonality. Scriabin’s usage of two Mystic Chords whose roots were a tritone apart or his utterances on this subject may have affected Stravinsky’s understanding of polarity. There is a clear distinction between the two, however: while Scriabin’s use of poles exhibited the duality inherent in the term since he dealt with “two chords a tritone apart,” Stravinsky’s use is far closer to Yavorsky’s “stability” since there is generally no counterpole to speak of in the system, and only one “complex of tones.”

Serialism

[3.15] In the section on serialism Kholopov reveals serial elements in an early work by Stravinsky, Firebird (Example 7). His conclusion to this section says it all (paragraph 2.55): Stravinsky was always a serialist in a certain sense, serialism represents a neotonal basis for his works, and this “serial-neotonal” method of composition was in fact a new form of musical art. Significantly, and spurred on by the same quotation from Stravinsky that some poor Ph.D. student may be forced to find serial tendencies in his early works, Kholopov locates exactly the same four-note motive that Richard Taruskin finds in Firebird, though at different sections of the piece (Taruskin 1996, 596–99). Both authors acknowledge that this is not serialism in any strict sense of the term. Stravinsky was wrong: not a Ph.D. student, but two of the most preeminent Russian-music scholars of our time found serial precedents in one of his early works.⁽⁴⁰⁾

[3.16] Kholopov distinguishes between Serialism writ large (Russian sereǐnost’) and the Twelve-tone Technique (dvenatsatitonovost’), since Stravinsky fits into the former category and not in the latter (paragraphs 2.48–2.49). There are two instances in which Kholopov changes the wording of an original quotation, with acknowledgement, so that he can fit Stravinsky into the correct type of serialism. In paragraph 2.46 Kholopov mentions that “the text actually reads ‘total serialist’ (Russian serialist) and not ‘serialist’ (Russian sereǐnnik).” That is to say that in Russian, a sereǐnnik is a serial composer or one with serial tendencies (and in this case, Stravinsky), and a serialist is a total-serial composer (not Stravinsky). And then, in footnote 29, Kholopov changed the meaning ever so slightly. The original was rendered as “serial’nye tendentsii,” i.e., “serial tendencies.” Kholopov changed this to “seriǐnye tendentsii,” also “serial tendencies.” Insofar as the first Russian term refers to total serialism whereas the second term refers to pitch serialism, Kholopov made this change in the translated version and noted the change parenthetically.⁽⁴¹⁾

[3.17] In paragraph 2.53 Kholopov first makes mention of the “central element” (CE). Along with neotonality, the CE is axiomatic for him in the analysis of twentieth-century music. In many ways it is analogous to Yavorsky’s stability, though it is broader in scope. For example, the open noteheads in all of the excerpts in Example 6 can be considered CEs. He further refined this idea by speaking of central tones and central sonorities (CTs and CSs), all of which were part of the neotonal framework by which Kholopov understood most twentieth-century music. For Kholopov, “the formation of a system of relationships on the basis of properties of the system’s central element” (paragraph 2.53) was the key to understanding Stravinsky’s harmony.

Historical Context

[3.18] In this section Kholopov touches on many of the most important factors that set Stravinsky apart from other twentieth-century figures. Kholopov introduces the concept of the avant-garde in music, one of his favorite topics. Most notable are his words about Stravinsky’s new rhythmic language and new syntax, and how they created a new temporal dimension in music.

[3.19] With respect to Stravinsky’s rhythm and syntax, Kholopov makes yet another intriguing suggestion in a different publication (2006, 11). In the same way that Kholopov posits that Taneev influenced Stravinsky’s early views on counterpoint, Kholopov suggests that both Georgiǐ Konius (1924) and Alekseǐ Losev (1927) had an impact on Stravinsky’s new rhythm and syntax. Again, Konius and Losev were Moscow figures, so the direct influence on Stravinsky is hard to prove. Still, Stravinsky had undoubtedly heard of these figures and their work, and it is entirely plausible that they influenced Stravinsky’s new musical language.

[4] Conclusion

[4.1] There is, at times, an unfortunate insularity in the academic study of music in North America, a neglect of ideas from other scholarly communities, including those closely connected to a given topic. I believe this is the case with Stravinsky studies in America. For all of his voluminous and admirable work on Stravinsky, Taruskin offers little more than a connection to Rimsky-Korsakov and the octatonic scale when dealing with pitch structure in Stravinsky’s music. (See, most recently, Taruskin 2011, along with eight responses in the same issue of Music Theory Spectrum.) With the present work and a previous article in this journal (Ewell 2012) I wish to point out other possible viewpoints on Stravinsky’s pitch organization.

[4.2] Not surprisingly, Kholopov’s views on Stravinsky mirror those of many authors in North America. Kholopov also offers many new and intriguing ideas, however. The possible influences of Taneev or Yavorsky (or even Konius and Losev), are intriguing. Taneev’s counterpoint text had a clear influence on Stravinsky, and the link between Stravinsky and Yavorsky deserves further examination. Because Stravinsky is considered a modal composer in Russia, there is a natural link with Yavorsky’s theories. If, as Kholopov suggests, Stravinsky meant “stability” when he said “polarity,” this could motivate a move away from octatonic interpretations. (Berger viewed this polar attraction as that of the tritone, which is central to octatonicism; see footnote 39 above and Berger 1963, 25.) Octatonicism then becomes but one of many tools in Stravinsky’s toolbox. Neotonality, and the neomodality thereof, represents another solid addition by Kholopov to Stravinsky studies. The central element of the system, to which all pitch elements gravitate, is a hallmark of this neotonality. It is in fact useful to view much of Stravinsky’s music in terms of Yavorsky’s modes, and the gravitations of the system provide an able account of voice leading in his music, which is absent in the work of van den Toorn.⁽⁴²⁾ Lastly, there is the idea that Stravinsky was, in fact, a serial composer for his entire life. Kholopov solidifies this claim, tracing the evolution of Stravinsky’s serial works.

[4.3] Yuri Kholopov was a consummate scholar whose impact on present-day music theory in Russia is hard to overstate. Aside from presenting Kholopov’s and other Russian views on Stravinsky to a North American audience, it is my hope that this translation-commentary might serve as a starting point for further study of Stravinsky’s harmonic language.

Philip A. Ewell
Hunter College and CUNY Graduate Center
Department of Music
695 Park Ave.
New York, NY 10065
pewell@hunter.cuny.edu

Editorial Notes

(2.5) Footnote 3: Kholopov wrote “ibid.” for this quotation, implying that it could be found in Publitsist, the preceding source. The actual quotation is in Dialogi however, so I made the necessary change.
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(2.6) I added the word “distant” in the quotation summarized in footnote 8. In that sentence the original Russian read, “In the past (sic!—Yuri Kholopov)...,” with “sic” written with Latin letters. “Sic” is occasionally used in Russian, and it often has the same meaning as in English. Here, however, it has the added meaning of simply emphasizing the point that was made immediately preceded, in this case, “In the ‘distant’ past.” There were no misspellings or strange usages in the original Russian, “V proshlom,” hence, I added the word “distant.”
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(2.6) I added, “as if to say.”
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(2.9) “Functional inversion” refers to the motion, common in late-nineteenth-century chromatic harmony, of harmonies not to consonances or stabilities such as the tonic, but to dissonances and instabilities other than the tonic.
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(2.12) Kholopov used the term “stereophonic” (stereofonicheskiǐ) in a new sense with respect to post-tonal music. He claimed that this new music, starting with Webern, acquired a new, third dimension of “depth” (glubina), in addition to the first two dimensions of music, “pitch” (vysota) and “the horizontal” (gorizontal’). If music is stereophonic, there are certain layers of depth to the notes—some will seem quite close, others somewhat farther away, and still others quite far away, in the “depth” of the piece. This layering of depth is a “stereophonic” effect in Kholopov’s usage. See Kholopova and Kholopov 1984, 262–65, for more on this topic. I am indebted to Tatiana Kiuregian for this citation.
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(2.13) Example 1: I added, “from Four Russian Songs (1918), measures 1–3.”
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(2.14) I added, “in Bulgakov’s Master and Margarita” in this paragraph.
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(2.17) Kholopov first makes mention of the “New Music” in this paragraph. When he writes this phrase, “Novaia muzyka,” with a capital “N,” he is making reference to Webern’s use of the term. I therefore use “New Music” in these instances in the translation.
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(2.18) Footnote 11: This quotation does not appear on p. 18 of Publitsist. I was unable to find where it does appear.
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(2.19) Footnote 12: I added “from Petrushka, Third Tableau” in this footnote.
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(2.23) The Russian for “neotonality” is “novaia tonal’nost’,” a direct translation of which would be “new tonality.” I have chosen to use the Greek prefix and conflate the Russian into the one-word “neotonality,” a rather common term in English. It would be possible, in Russian, to use one word as well, “novotonal’nost’.”
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(2.26) The series in Example 2a is an inversion of the generally accepted prime form of the series. See Straus 2001, 197n28 and 201.
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(2.28) Footnote 18: Kholopov wrote that this material was on p. 199 of Publitsist, but in fact it is on p. 99.
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(2.30) Hemitonic segments are groups of three or four notes that contains at least one semitone.
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(2.36) Footnote 21: The page number that Kholopov cited in his article was incorrect. He said “p. 311” and it is on page 185. The quotation also appears in the 2005 reprint of this book, on page 275.
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(2.36) In Example 5, Kholopov wrote an F♯ in the fourth measure of the excerpt, and the correct note is F♮.
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(2.37) Kholopov uses upper and lowercase letters to designate major and minor keys—I have used all uppercase letters with “major” or “minor.”
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(2.38) Footnote 24: Kholopov actually paraphrased the second quotation to which this footnote refers. He had, “tsentr, k kotoromu vse skhoditsia,” when in fact the original Russian was, “Eto privodit k poiskam tsentra, k kotoromu dolzhna skhodit’sia seriia zvukov.” I located and used the original English in the translation.
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(2.40) Kholopov had the wrong rehearsal number for the Ebony Concerto in Example 6i; he had said “5” and it should be one bar before Rehearsal “6.” Also, he has omitted the Alto and Tenor Sax parts from this “pole.” In Example 6f I added “Part 1, Scene 2, measure 3.”
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(2.44) At the end of this paragraph there were page numbers in which Kholopov cross-references the usages of “poles” in his article. I omitted these page numbers since they will not be the same in the present work.
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(2.50) Kholopov had mistakenly written that “Grundgestalt” was Webern’s term and not Schoenberg’s. I made the correction in the text.
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(2.51) Example 7b: The G–A♭ upbeat figure in the bottom treble clef of the three-stave system does not occur in the score. Rather, it occurs in the second bar of Rehearsal 24, in the violas, with similar music as at 24 but with a slightly denser texture.
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(2.59) It was Olivier Messaien who claimed that Stravinsky had “1001 styles.”
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(2.59) Footnote 32: the year of publication for Taruskin’s work in Kholopov’s article, 1966, is incorrect. I put the correct year of publication, 1996, in the translation.
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(2.59) Kholopov does not cite the quotation at the end of this paragraph.
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(2.60) I added, “from the ‘Dance of the Adolescents’ from the Rite of Spring,” “from the Cat’s Cradle Songs,” “from Three Children’s Tales,” and “from Four Russian Folk Songs for women’s chorus” to this paragraph. There was a misspelling by Kholopov, as well as a repeat of Stravinsky’s misspelling, in the title of “In Our Saviour’s Parish at Chigasi.” Kholopov wrote “U Spasa v Chibisakh,” and the last word should be “Chigasakh” (i.e., “g” and not “b”). And with respect to Stravinsky’s misspelling, see Taruskin 1996, 1139.
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(2.62) Kholopov writes “at the beginning” in quotation marks in this sentence in a nod to Hans von Bülow’s famous aphorism, “Im Anfang war der Rhythmus” (in the beginning there was rhythm).
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Works Cited

Berger, Arthur. 1963. “Problems of Pitch Organization in Stravinsky.” Perspectives of New Music 2, no. 1: 11–42.

Cairns, Zachary. 2012. “Svetlana Kurbatskaya on Serial Music: Twelve Categories of ‘Twelve-Toneness.’” Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic 5, no. 1.

Carpenter, Ellon. 1995. “Russian Theorists on Modality in Shostakovich's Music.” In Shostakovich Studies, ed. David Fanning, 76–112. Cambridge: Cambridge University Press.

D’iachkova, L. S., ed. 1973a. I.F. Stravinsky: Stat’i i materialy (I. F. Stravinsky: Articles and Materials). Moscow: Sovetskiǐ Kompozitor.

—————. 1973b. “O glavnom printsipe tonal’no-garmonicheskoǐ sistemy Stravinskogo (sistema poliusov)” (On the Main Principle of Stravinsky’s Tonal-Harmonic System [the System of Poles]). In I. F. Stravinsky: Stat’i i materialy (I. F. Stravinsky: Articles and Materials), ed. L. S. D’iachkova, 301–22. Moscow: Sovetskiǐ Kompozitor.

Ewell, Philip. 2002. “Scriabin’s Seventh Piano Sonata: Three Analytical Approaches.” Indiana Theory Review 23: 23–67.

—————. 2007. “Scriabin and the Harmony of the 20th Century.” Annotated translation of article by Yuri Kholopov. Journal of the Scriabin Society of America 11, no. 1: 12–27.

—————. 2012. “Rethinking Octatonicism: Views from Stravinsky’s Homeland.” Music Theory Online 18, no. 4.

Kholopov, Yuri. (1975) 2008. “Symmetrische Leitern in der Russischen Musik” (Symmetrical Modes in Russian Music). In Die Musikforschung 28, 379–407. Reprinted as “Simmetrichnye lady v russkoǐ muzyke” in Idei Iu. N. Kholopova v XXI veke, 114–45. Moscow: Muzizdat.

—————. (1981) 2008. “Problema novoǐ tonal’nosti v russkom i sovietskom teoreticheskom muzykoznanii” (The Problem of New Tonality in Russian and Soviet Musicology). In Voprosy metodologii sovietskogo muzykoznaniia (Questions of Methodology in Soviet Musicology). Moscow: Moscow State Conservatory, 100–26. Reprinted in Idei Iu. N. Kholopova v XXI veke (The Ideas of Yuri Kholopov in the Twenty-First Century), 199–219. Moscow: Muzizdat.

—————. 1982. “Modal’naia garmoniia: Modal’nost’ kak tip garmonicheskoǐ struktury” (Modal Harmony: Modality as a Type of Harmonic Structure). In Muzykal’noe iskusstvo. Obshchie voprosy teorii i estetiki muzyki (Musical Art. General Questions of Music Theory and Esthetics). Tashkent: Guliam Publisher of Literature and Art, 16–31.

—————. (1988) 2003. Garmoniia (Harmony). Moscow: Muzyka. Reprint, Moscow: Lan’. Citations are to the Lan’ edition.

—————. 1991. “Tonal’nost’” (Tonality). In Muzykal’nyǐ entsiklopedicheskiǐ slovar’. Moscow: Sovetskaia Entsiklopediia.

—————. 1997. “O sisteme garmonii Stravinskogo” (On the System of Stravinsky’s Harmony). In I. F. Stravinsky: Sbornik Stateǐ (I. F. Stravinsky: Collected Articles). Moscow: Moscow State Conservatory, 28–46.

—————. 2006. “Stravinsky i puti novatorstva v muzyke XX veka” (Stravinsky and the Ways of Innovation in 20th-Century Music). In Stravinsky v kontekste vremeni i mesta (Stravinsky in the Context of Time and Place). Moscow: Moscow State Conservatory, 7–14.

Kholopova, Valentina, and Yuri Kholopov. 1984. Anton Vebern: zhizn’ i tvorchestvo (Anton Webern: Life and Work). Moscow: Kompozitor.

Konius, Gregoriǐ. 1924. “Metrotektonicheskoe razreshenie problemy muzykal’noǐ formy” (The Metrotechtonic Solution to the Problem of Musical Form). In Muzykal’naia kultura (Musical Culture), 36–41. Moscow.

Losev, Alekseǐ. 1927. Muzyka kak predmet logiki (Music as a Subject of Logic). Moscow.

McQuere, Gordon D. (1983) 2009. “The Theories of Boleslav Yavorsky.” In Russian Theoretical Thought in Music. Edited by Gordon D. McQuere. Ann Arbor: UMI Research Press. Reprint, Rochester: University of Rochester Press. Citations are to the Rochester edition.

Plotitsa, E., ed. 2008. B. Yavorsky: Izbrannoe: Pis’ma, vospominaniia (B. Yavorsky: Collected Letters and Recollections). Moscow: Kompozitor.

Sabaneev, Leonid. (1925) 2000. Vospominaniia o Skriabine (Recollections of Scriabin). Moscow: Muzyka. Reprint, Moscow: Klassika XXI. Citations are to the Klassika edition.

Savenko, Svetlana. 2011. Email correspondence with the author.

Straus, Joseph. 1982. “Stravinsky’s Tonal Axis.” Journal of Music Theory 26, no. 2: 261–90.

—————. 1984. Review of The Music of Igor Stravinsky, by Pieter van den Toorn. Journal of Music Theory 28, no. 1: 129–34.

—————. 2001. Stravinsky’s Late Music. Cambridge: Cambridge University Press.

Stravinsky, Igor. (1947) 1959. Poetics of Music in the Form of Six Lessons. Cambridge, MA: Harvard University Press. Reprint, New York: Vintage Books. Citations refer to the Vintage edition.

—————. 1959. Conversations with Igor Stravinsky. Garden City, NY: Doubleday.

—————. 1960. Memories and Commentaries. Garden City, NY: Doubleday.

—————. 1962. Expositions and Developments. Garden City, NY: Doubleday.

—————. 1963. Dialogues and a Diary. London: Faber and Faber.

—————. (1963) 2005. Khronika moeǐ zhizni (Chronicle of My Life). Leningrad: Gos. Muz. Izdatel’stvo. Reprint, Moscow: Kompozitor.

—————. 1971. Dialogi: vospominaniia, razmyshchleniia, kommentarii (Dialogues: Recollections, Reflections, Commentaries). Leningrad: Muzyka.

Taneev, Sergei. (1909) 1959. Podvizhnoǐ kontrapunkt strogogo pis’ma (Invertible Counterpoint in the Strict Style). Leipzig and Moscow. Reprint, Moscow: Gos. Muz. Izdatel’stvo. Citation is to the 1959 edition.

Tarakanov, Mikhail. 1972. “Novaia tonal’nost’ v muzyke XX veka” (Neotonality in 20th-Century Music). In Problemy muzykal’noǐ nauki (Problems in Music Theory), Installment 1. Moscow.

Taruskin, Richard. 1996. Stravinsky and the Russian Traditions: a Biography of the Works through Mavra. Berkeley: University of California Press.

—————. 2011. “Catching Up with Rimsky-Korsakov.” Music Theory Spectrum 33, no. 2: 169–85.

Van den Toorn, Pieter. 1983. The Music of Igor Stravinsky. New Haven: Yale University Press.

Varunts, Viktor, ed. 1988. Igor Stravinsky: Publitsist i sobesednik (Igor Stravinsky: Publicist and Conversationalist). Moscow: Sovetskiǐ Kompozitor.

—————, ed. 2003. I. F. Stravinsky: Perepiska s russkimi korrespondentami (I. F. Stravinsky: Communications with Russian Correspondents). 3 vols. Moscow: Kompozitor.

Webern, Anton. 1975. Put’ k novoi muzyke: lektsii o muzyke, pis’ma (The Path to the New Music: Lectures on Music, Letters). Moscow.

Yavorsky, Boleslav. 1908. Stroenie muzykal’noǐ rechi: Materialy i zametki (The Structure of Musical Speech: Materials and Notes). Moscow.

—————. 1929. “Konstruktsiia melodicheskogo protsessa” (Construction of the Melodic Process). In Struktura melodii (The Structure of Melody). Moscow.

Footnotes

*. With thanks to Olga “Ellen” Bakulina, Valentina Kholopova, Tatiana Kiuregian, John Licari, Yonatan Malin, Andrew Pau, Anton Rovner, Svetlana Savenko, and Joe Straus, all of whom helped in one way or another with this translation-commentary. I also thank the two anonymous reviewers of this journal for their helpful suggestions. I would like to dedicate this work to the memory of Yuri Kholopov.
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**. Though Kholopov calls Garmoniia a textbook in the Preface, it is, for all intents and purposes, a treatise on harmony.
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***. All translations from Russian into English are my own. I have used the Library of Congress transliteration scheme in this work, which can be found in the Chicago Manual of Style (16th ed.), on page 568 as Table 11.3. (Though typical anglicized names—Prokofiev, Stravinsky, and Tchaikovsky, or Moscow and St. Petersburg, for example—appear throughout.) Further, all titles of Stravinsky’s works, which usually have three versions (English, French, and Russian), are rendered in English. At times I added some titular information that was not in the Russian, for the sake of clarity. For example, where Kholopov simply wrote “The Drake,” I wrote “The Drake, from Four Russian Songs (1918), measures 1–3.” Longer additions (as with “The Drake”) are noted in the Editorial Notes section.
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****. Dialogi takes the four English-language works mentioned above and regroups all the material into three headings: Stravinsky’s recollections on his life; Stravinsky on his own music; and Stravinsky on music in general. This made it difficult to locate the original quotation since all of the material was out of the original order. In two instances I could not find the original English quotation, in which case I simply translated the Russian back into English and noted the book from which the material came, without page reference.
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1. Dialogi, 237. [This quotation appears in Stravinsky 1959, 121. –PE]
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2. Publitsist i sobesednik, 45. [From 1924, translated from a newspaper article in Polish into Russian after a concert tour by Stravinsky to Poland, among other places. –PE]
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3. Dialogi, 238 [ed]. [From Stravinsky 1959, 121. –PE]
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4. From Muzykal’naia Poetika (Musical Poetics), cited in Stat’i i materialy, 30. [From Stravinsky (1947) 1959, 40. –PE]
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5. Publitsist i sobesednik, 210. [From 1963, from an interview in New Mexico with K. J. Mak-Nespi. –PE] It is possible that this idea also speaks of Stravinsky’s connection to the Russian tradition. In Yuri Tiulin’s retelling, I once heard of Glazunov’s account of how several musicians, including Rimsky-Korsakov, once met and played through Bach’s Chorales and everyone concluded that “No, Bach still did not understand harmony.” Stravinsky’s words sound somewhat different, but the idea is similar. It is not out of the question that a certain exchange of words from Rimsky-Korsakov to Stravinsky is illuminated through this quotation.
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6. Dialogi, 242. [From Stravinsky 1960. –PE]
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7. Publitsist i sobesednik, 420. [From 1964–66, from program notes to Abraham and Isaac. –PE]
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8. Publitsist i sobesednik, 210. [From 1963, from an interview in Zagreb, Croatia, at a music festival. –PE]
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9. Publitsist i sobesednik, 326. [From 1968, from Stravinsky’s Introduction to Glenn Watkins’s Gesualdo: The Man and His Music (London: 1973). –PE]
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10. Dialogi, 238. [From Stravinsky 1959, 121. –PE]
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11. Publitsist i sobesednik, 18 [ed]. [From 1913, from an interview with A. Postel du Mas. –PE]
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12. It is a different matter when we sometimes see a combination of two musics simultaneously, each in its own tonality, that is, having its own stabilities and instabilities and having at least two different functioning elements. In order for them to be perceived independently, different factors for their detachment—register, timbre, meter—are necessary. As an example see “The Ballerina and the Moor” from Petrushka, Third Tableau, Rehearsal 73 [ed].
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13. Publitsist i sobesednik, 100. [From 1930, translated from a German newspaper article into Russian, from a conversation with Stravinsky. –PE]
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14. Publitsist i sobesednik, 199. [From 1962, from an impromptu conversation in Leningrad after an open rehearsal of the Leningrad Philharmonic. Published in Publitsist for the first time. –PE]
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15. Publitsist i sobesednik, 205. [From 1963, first published in the journal Sovetskaia Muzyka 1 (1963): 123–25. –PE]
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16. Publitsist i sobesednik, 401. [From 1917, from Stravinsky’s diary. –PE]
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17. Dialogi, 242. [From Stravinsky 1960. –PE]
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18. Publitsist i sobesednik, 99 [ed]. [From 1930, from an interview with P. Verri published in Brussels. –PE]
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19. Stat’i i materialy, 31. [From Musical Poetics. –PE]
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20. L. S. D’iachkova’s article “O glavnom printsipe tonal’no-garmonicheskoǐ sistemy Stravinskogo (sistema poliusov)” [On the Main Principle of Stravinsky’s Tonal-Harmonic System (the system of poles); 1973b. –PE] gives a theoretical account of the problem of Stravinsky’s “polar attraction.” See Stat’i i materialy, 301–22.
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21. Khronika, 185 [ed].
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22. Stat’i i materialy, 29. [From Stravinsky (1947) 1959, 38. –PE]
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23. Stat’i i materialy, 32. [From Stravinsky (1947) 1959, 44. –PE]
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24. Stat’i i materialy, 29 and 30 [ed]. [From Stravinsky (1947) 1959, 37 and 39. –PE]
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25. Publitsist i sobesednik, 209. [From 1963, from an interview in Zagreb, Croatia, at a music festival. –PE]
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26. Publitsist i sobesednik, 210. [From 1963, from an interview in Zagreb, Croatia, at a music festival. –PE]
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27. Publitsist i sobesednik, 209, 199, and 200. [Page 209 is from a 1963 interview in Zagreb, Croatia, at a music festival, while pages 199 and 200 are from 1962, from an impromptu conversation in Leningrad after an open rehearsal of the Leningrad Philharmonic. The row C–E–F–G–G♯ was given only as an example and does not appear in any work by Stravinsky. –PE] Edison Denisov offers a similar broad and free treatment of the concept of the “series” with respect to Bartók’s compositional technique.
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28. Publitsist i sobesednik, 199. [From 1962, from an impromptu conversation in Leningrad after an open rehearsal of the Leningrad Philharmonic. Published in Publitsist for the first time. –PE]
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29. Curiously enough, the author knew about serialism in Firebird. With his characteristic humor Stravinsky wrote: “When some poor PhD candidate [this is Stravinsky speaking about us. –Yuri Kholopov] is obliged to sift my early works for their ‘serial tendencies,’ this sort of thing will, I suppose, rate as an Ur-example” (Dialogi; version of the translation by the present author), 142. [From Stravinsky 1962, 151. –PE]
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30. Publitsist i sobesednik, 197. [From 1963, from a Polish publication. –PE] Anton Webern had a similar thought: “The series, in its original form and pitch structure, plays the same role as the ‘home key’ did earlier; the recapitulation naturally returns to it. We cadence ‘on the same tone’!” (Webern 1975, 79).
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31. On April 2, 1971, that is, four days before his death, Stravinsky was supposed to sign a short note in Russian, but he wrote with Latin letters. Vera Stravinsky then asked him to write with Russian letters. Seeing that she was observing him, Stravinsky wrote in Russian, however, not his name but “Oh, how I love you!” See Publitsist i sobesednik, 435. [From 1971, from Robert Craft’s Stravinsky: Chronicle of a Friendship. –PE]
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32. Publitsist i sobesednik, 195. [From 1962, from interviews with E. Lidin and S. Razgonov published in Moskovskaia Pravda. –PE] The growth of Stravinsky’s music in the bosom of Russian art is shown in Richard Taruskin’s phenomenal work Stravinsky and the Russian Traditions (Taruskin 1996), which is 1757 (!) pages in length [ed].
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33. Publitsist i sobesednik, 235. [From 1964, from an article in the New York Times. –PE]
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34. He was clearly influenced by Yavorsky in doing so. Later in his career, in a work on the structure of melody, Yavorsky wrote: “Neither atonality nor polytonality can be accepted as scientific terms, and they signify a corresponding fundamental flaw in the literature” (Yavorsky 1929, 21). Significantly, as an exception Kholopov mentions the existence of polytonality in footnote 12, where he cites Rehearsal 73 of Petrushka. This music is quite audibly in two keys in a relative relationship: B major and G♯ minor (as the orchestra plays B major at Rehearsal 72, nine bars later the cellos, basses, English horn, and contrabassoon play a G♯-minor melody as the orchestra continues in B major).
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35. And in particular, Tarakanov’s article from 1972, an admirable piece that draws on theorists such as Paul Collaer, George Perle, Taneev, and Yuri Tiulin (among others) and composers such as Schoenberg, Bartók, Stravinsky, Prokofiev, Shostakovich, and Berg.
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36. One well-known example of this method of analysis is Joseph Straus’s “tonal axis” (Straus 1982), which Kholopov would certainly call a “pole” in a general sense.
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37. About Examples 4 and 5, Stravinsky scholar Svetlana Savenko says, “Here Kholopov is speaking about the duality of appearances with ‘tonality–polarity,’ insofar as on the surface this is tonal music with a major or minor inclination but, in fact, the music is subordinated to modal (i.e., melodic) logic” (2011). The original Russian of this quotation read: “Iu. N. i govorit o dvoǐstvennosti iavleniǐ tonal’nost’ – polius, poskol’ku vneshne eto tonal’naia muzyka s minornym ili mazhornym nakloneniem, no na samom dele ona podchinena modal’noǐ (melodicheskoǐ) logike.” Used with permission.
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38. Tarakanov acknowledged the general idea of an axis in his study on neotonality: “Periodically one or another note acquires the meaning of tonal ‘axis,’ becoming in a sense the ‘center of intersection’” (1972, 35).
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39. Perhaps the most famous speculation on Stravinsky’s use of this term comes from Arthur Berger: “It is tempting to speculate on whether Stravinsky’s choice of ‘polarity,’ a word which cannot accurately be applied (as he applies it) to one thing without its opposite, either had implications that escaped the intermediary who transcribed his thoughts, or—which seems more likely—reflected an awareness, if only on a subverbal level where it was difficult to articulate, of the special properties of the tritone which make it possible for pitches at 0 and 6 (capable of graphic representation as ‘poles’ in a circle of fifths...), by virtue of similitude or equal and thus independent weight, to remain in equilibrium or—to the end that a tone center is asserted by neither—to stand in a certain opposition. This speculation might easily take flight in a direction which would establish, as a necessary condition of ‘polarity,’ the denial of priority to a single pitch class precisely for the purpose of not deflecting from the priority of a whole complex of tones” (1963, 25). As is well known, Berger was making a case for octatonicism in Stravinsky’s work, and that is why he is bound to the tritone as the operative “pole” in Stravinsky’s work.
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40. It is worth noting that Kholopov found this four-note series more than twenty years before Taruskin. Kholopov first published this finding in 1975, in a German publication ([1975] 2008). Each author cites different four-note segments, which happen frequently throughout Firebird, yet the segments are quite similar. They both speak of the possible serial aspect of these segments, prompted by the same quotation about the Ph.D. student cited above.
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41. The concept of serialism, as understood in Russia, is dealt with extensively in Cairns 2012.
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42. Joseph Straus (1984) makes this point in his review of Van den Toorn 1983.
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