MUZIKOLOŠKI ZBORNIK — MUSICOLOGICAL ANNUAL X, LJUBLJANA 1974 UDK 781.61 Schönberg STRUCTURE AND PROLONGATION: TONAL AND SERIAL ORGANIZATION IN THE "INTRODUCTION" OF SCHOENBERG'S VARIATIONS FOR ORCHESTRA1 Kenneth L. H i eke n (Lethbridge, Canada) In its broader version this work represents an intensive study of pitch organization in the "Introduction" of Schoenberg's Variations for Orchestra, Op. 31. In keeping with the composer's well-known assertion that his works were "twelve-note compositions, not twelve-note compositions",2 a prime objective of the investigation is "to gain greater insight into Schoenberg's serial music as — music".3 The study concentrates upon three fundamental topics: (1) organization of pitch with reference to tonality; (2) organization of pitch with reference to the twelve-note series; and (3) correlation of serial and tonal organizational modes. Findings may be summarized as follows: (1) Pitch in the Introduction is organized not only serially, but with reference to two simultaneous tonal centers a tritone apart, viz., F and B, in accord with an extension of tonality which the writer terms the principle of "fused bitonality". (2) The Introduction iz susceptible to structure-prolongation analysis (via a generalization of Schenkerian concepts).4 It readily reduces to a "fused-bitonal" Ursatz, and accordingly, may be understood as an elaborate prolongation of this Ursatz. 1 Cf. Kenneth L. Hicken, Structure and Prolongation: Tonal and Serial Organization in the "Introduction" of Schoenberg's Variations for Orchestra (Ph. D. dissertation, Brigham Young University, 1970). 2 Arnold Schoenberg Letters, selected and edited by Erwin Stein, translated by Eithne Wilkins and Ernst Kaiser (New York: St. Martin's Press, 1965), pp. 164—65. Date of letter: July 27, 1932. 3 Hicken, op. cit., p. 1. 4 The writer's point of departure in making this generalization is the thought of Schenker as presented in the " Introduction'' to Heinrich Schenker, Harmony, edited by Oswald Jonas, translated by Elisabeth Mann Borgese (Chicago, University of Chicago Press, 1954; 3rd impression, 1964), pp. XX—XXIV; and as extended by Felix Salzer in his Structural Hearing (New York: Charles Boni, 1952). 27 (3) The Introduction s serial organization is also susceptible to a type of structure-prolongation analysis (via a further adaptation of Schenkerian concepts). The music's series-deployment pattern reduces to a "serial Ursatz", and may thus be viewed as a complex prolongation of this Ursatz. (4) The serial Ursatz may be readily formulated as a prolongation of the fused-bitonal Ursatz. In view of item "4", two very important inferences are drawn: (1) that the fused-bitonal Ursatz exists at a structurally more fundamental level than that of the serial Ursatz; and (2) that fused bitona-lity is therefore a more basic principle of pitch organization in the Introduction of Op. 31 than is the twelve-note technique. Accordingly, it is offered that Schoenberg's "method of composing with twelve tones which are related only with one another",5 as encountered in the Introduction, is indeed a method, "a method used in effecting the unfoldment of the fundamental musical event contained in the fused-bitonal Ursatz".6 Having outlined principal findings, it is now appropriate to to offer a more detailed presentation. The three fundamental topics under consideration, viz., tonal organization, serial organization, and correlation of serial and tonal modes of organization, will now be discussed in greater depth. "TONAL ORGANIZATION"7 As is stated above, pitch in the Introduction of Op. 31 is organized with reference to two simultaneous tonal centers a tritone apart, viz., F and B, in accord with the principle of fused bitonality. Thus, the music manifests concurrently an F-oriented and a B-orien-ted aspect. That element of the music having an F orientation, i. e., the aggregate of pitch-items organized with reference to F, is termed the music's "F component". Similarly, the element organized with reference to B is termed the music's "B component". These components are intimately interfused with each other, many items of one component belonging to the other component also. For this reason, the expression "fused bitonality" is employed. The harmonic content of each component derives primarily from 19th Century chromatic practice, the principal tonal functions being those of the dominant and the tonic. In both components the dominant function is borne by a single six-note augmented-eleventh chord with minor ninth, V*9 Important features of the tonal organization manifested in each example may be outlined as follows:10 (1) In the first example (meas. 18—21),11 the F component contains a highly embellished movement from an inverted Vb9 to a V#n in root position. The B component displays a complex prolongation of V #11 (meas. 18—21), and a resolution from V#n to Mml co-in- ciding with a movement from V#if to V*11 (meas. 20—21). The final #11 verticality of this excerpt is an excellent illustration of a composite of tertian elements from the two components, i.e., a composite of Vbl3 of F (or V*11 of B) and Mml of B. #11 (2) The second example (meas. 24—26) shows two resolutions over the »BACH« motive. The first resolution, involving the motive's » Ibid., pp. 20—37. 9 In this paper, as in the dissertation, all excerpts from the Variations for Orchestra are used by permission of Belmont Music Publishers, Los Angeles, California 90049. 10 Abbreviations used in these examples include the following: "ine" (incomplete); "H" (horizontalized); "h" (partially norizontalized); "Em" (embelishment). A horizontal line separating two chord-symbols means that both chords represented exist essentially concurrently. Thus, for example, the concurrent existence of V #11 and Mml is indicated by y^j. *ii #11 . To signify an inversion of a chord, a numeral representing the chord-member in the bass is placed below the body of the chord symbol. Thus, in V #u, the All is in the bass. #11 11 In this study, measure numbers cited in conjuction with examples may refer to incomplete as well as to complete measures. Thus, only a portion of meas. 18 appears in Example 1. 29 Example 1: Reduction and components 30 S bJ: ^—J- q -p- -_____bar. ^ b}(H' =*^ EziTompžiB^^£i=: M Jä i&___ä^J ftp =^=P2£ =Éë= z^z 3WV»- m a =*= __km. È _^_ qîTTT B : Com p&mrdti M * b*S!r T7 b9 TT* " iŽ£L. C il» -Û& S =T2E =** =#* * S ±Ê ,*1 u#4 ?^9 Em zm X*i__MffiI__ Example 2: Reduction and components first two notes, is from ine V £9 to Mml in F. The second resolution, involving the motive s second two notes, is from V to Mml in B. #11 (3) The third example (meas. 30—33), occurring at the conclusion of the Introduction, presents the penultimate and the final statement of Mml in F, and portrays a terminal dominant-to-tonic progression in B. It also shows the Introduction's concluding vertically, a structure consisting of the roots and fifths of the F and B tonic tetrads. Subsequent to the F and B components' foreground-level presentation in the dissertation, they are reduced, individually, via structure-prolongation analysis until the Ursatz of each is discovered. Then, by combining the two Ursätze, the Introduction's fused-bitonal Ursatz is arrived at, and the fundamental musical event incorporated in that Ursatz is determined. The Ursatz of the F component consists of the harmonic pro« gression V#"9 — Mml in F and of the melodic descent (Urlinie) Bb — Ab. The Ursatz of the B component consists of the harmonic 31 Example 3: Reduction and components 32 progression V*^ — Mml in B and of the melodic descent E — D#. The fused-bitonal Ursatz, as the integration of the F and B Ursätze, consists of (1) the harmonic progression from the six-note composite dominant of F and B (V#£| of F, V*^ of B) to a composite tonic of (plus MI) F and B (Mml of F plus Mml of B) and (2) the two melodic descents Bb — Ab and E — D4j=. This harmonic progression and the concomitant melodic descents constitute the fundamental musical event upon which the Introduction is based. The three Ursätze are represented in Example 4. to oß- F C&mpomvâl et) uf $ Component. &) Fu$eeM*ìtonaJ tfr^iz, É I W~~ »HF 3 SS ^rwz i>XL- st~ li rt- - Ü*- 8-e- -»*«! -.IP Mml ^fr^^^ff T" F:i.r,n 5: X H (pu> y e) Compos lie, konlç ìn F" cyfìd. 'S (pus ys ¦>*$,*«* i« tester 49" (plus bH> •^ ^--------Mn.1—J Example 5: Intermediate-level prolongation of fused-bitonal Ursatz a t i \f\ A', -a u>- W> * Ol R m $ KrKI «- 14- c» s: o o 4» S~«3 & M ft &t 4ssr ad m "M <$JpL [JÇT* op Sn crK Example 6: F and B components of intermediate-level prolongation of fused-bitonal Ursatz Measures: ifc ft 90 da 24. V 29 31 IO Q ^__mmmm - > Mb 7 b a î3aï?a §«m Ha ?a 2b te la ZaXb la J- a i 2 b lOa XL loa I« Iô 10b loa. la loa J iob Tb L ........¦........."....."V............*^ ft ...........,, j if lb cs* V irk ... —N^-..........¦ -¦<¦ »—^v--------, , a- a —Y 101 la la T3C> lob ................"?..... Xab Of J. Example 7: Structure-prolongation analysis of series deployment the over-all pattern according to which the series is deployed in the Introduction divides into two serial components and reduces substantially generalized structure-prolongation analysis to a bi-compo-nential serial Ursatz. The structure-prolongation analysis of the deployment pattern is offered in Example 7. The deployment's serial-duality is demonstrated in Example 8. Ifa Î8 om iS u i— n Bili -----_ ¦ -^s.¥- - -• îk 2b ît -*• la ï* îabl lOa iog îob IOa 4- fc» loa i3* 15a ~$î SOâb io c©mpôii€ht ' J Example 8: Serial duality of series deployment Symbols designating specific forms of the series encountered in the Introduction belong to a system Leibowitz used in his study of the Variations for Orchestra,13 According to this system, the basic set is represented by I,, the retrograde by I, the inversion by 1, and the retrograde inversion by 1. Transposition of I and I are indicated by Roman numerals II—XII surmounted by arrows pointing to the right or to the left, and transpositions of 1 and 1 are indicated by Arabic numerals 2—12, again surmounted by appropriate arrows. Thus, for example, upwards transpositions of I, I, 1, and 1 by one,. two, three, and four semitones, respectively, would be designated II, III, 4, and 5, respectively, etc. The serial "working unit" of the Introduction is the hexachord (i. e., the first or final half of a series-form). Antecedent hexachords are indicated by a suffix "a" (e.g., 10a, the antecedent hexachord of 10); and consequent hexachords, by a suffix "b" (e.g., IVb, the consequent hexachord of IV). In most cases, antecedent and consequent hexachords of a series-form occur simultaneously rather than consecutively. This arrangement is designated by means of both suffixes, one placed above the other (e.g., 7^ ). In the deployment of the series, most of the hexachords are ver- ^-b tically paired (e.g., ^ , 2°, etc.). Such pairs are termed "deploy- 10a 37 ment units". Occasionally, a deployment unit contains more than two hexachords (e. g.,IV ivb ). IValVa Reduction of the series deployment pattern to a serial Ursatz proceeds, as indicated earlier, via a substantial generalization of the structure-prolongational analytical approach. Two assumptions involved in this generalization are the following: (1) that, analogously to the manner in which a group of chords (e. g., I-V-I) bounded by the same chord (i. e., I) may be viewed as a prolongation of that chord, a group of deployment units (e. g., ^^ ^) bounded by the same unit (i. e., ^ ) may be regarded loa 2b 10a 10a as a prolongation of that unit. (2) that, analogously to the manner in which several different positions of a chord (e. g., V7, V65, V43, etc.) may be represented in a general sense by a single position (e. g., V7), a group of deployment units (e.g., VII£ 7a) concluding with an inversion (7a) of the group's initial unit (Vllg ) may be represented, at a structurally more fundamental level, by that initial unit. From Example 7 it may be seen that the serial Ursatz to which —>-the series deployment pattern reduces is _^ (10 being the inversion of I transposed upwards by a major sixth). The deployment pattern's penultimate reduction is -» l!? 2t -> . This reduction may be under- 10a a b lOab J stood as the structurally most fundamental serial prolongation of this Ursatz. —» —> The serial Ursatz, consisting of the two series-forms I and 10, manifests a serial duality which is reflected at the "foreground" level in the deployment pattern itself. As is shown in Example 8, this pattern divides into two components, one of which (termed the "I component") is based upon I, and the other of which (termed the "10 component") is based upon 10. "A SERIAL-TONAL CORRELATION"14 In keeping with the Introduction's susceptibility — both serially and fused-bitonally — to structure-prolongation analysis, it is fitting that correlation of the music's serial and tonal (more appropriately: fused-bitonal) modes of organization should be approached at several lb René Leibowitz, Introduction à la musique de douze sons (Paris: L'Arche, 1949). Explanation of symbols: p. 121. 14 Hicken, op. cit., Chapter IV, pp. 102—178. 38 structural levels. Accordingly, in the dissertation the matter is considered with reference to the foreground and Ursatz levels, and, to a lesser degree, with reference to an intermediate level.15 At the foreground level, correlation takes place essentially as specification of the portions of the F and B components associated with each series-deployment unit. To illustrate, three examples are offered. The first of these, Example 9, is rather complex. The others, Examples 10 and 11, rare relatively simple. F Component: S*«. J fc \mx b4ff:l J _ Example 9: Harmonies deriving from ivb IValva 15 In the dissertation, the matter of the tonal significance of the serial Ursatz's serial duality receives brief attention as well. However, in the present paper, this topic is not discussed. 39 Example 9 (meas. 20—21) shows harmonies in F and in B de- riving from the deployment unit IV^ivab. The harmonic movement in iValVa 7 7 bl3 13 F is from IHbs to III to V Ä1l . That in B is from V_ to a 3 -ffo *ó *u b9 #3 T#ll composite of Mml and #11V . F Component t 1 a • [Y k|dJ:9 i ^7a HÜL^ / a oT imi i-'o 2:|' i/i /^J ir--2 n I H •.• ft -s jzn U /~s r \ , e-» V J p o ^ö) qo ±:5 ^ u ffco) il lu :3 3- l'i (25-) u D Ij6 1 •3T.-3- * li ^ ¥ *.* Il kv ! -L -1 qp \ )' r 1 F ine M» *r 12 B Component; îb- -kM *£ï=m m , b»,i:i3 S Xi5___"t* «^.tt ¦ 9Û *b: E ¦ 1-3 t?» UH -ta ~¥~V\ Hèh É?4 r = a (as) a--? s 231 im: 5:* 3EZ B: rM Fm r#Jf #J/ -!£¦ _^lf- a.-io Mml Example 10: F and B components associated with I ? 2 S a, D Example 10 (meas. 24—25) presents those portions of the F and B components associated with. l£ 2%, a two-unit group supporting the BACH motive. In F, unit I ^provides the progression ine V 40 b9 — Mml, over "BA" (Bb A); and unit 2% supports the progression #11V#n — Mml, over "CH" (Cij). Example 11 (meas. 31—33) portrays sections of the F and B -> —>¦ components deriving from ^ ^, the Introduction's two-unit ter- 10a 10b F Component- inc Vb9 Yh3- k Mm I-------- B C om pone ni% Ta . 10a Ï-H J» } 10b* Hu^aJ-Ljt. Ä iT**- 10:3 SE 1ÏÏ7T- *£- ~ffi^2; 3£ ^ "TÔïT" v3- |^------£^ 1 fam- ine Y" ?b' 32" ZEH I--7 B: hMvnl- —^—ronr r incW Example 11: F and B components associated with Ia Ib 10a 10b 41 minai group. In F, unit ^ supplies an inc V , and an ensuing 10a Mml and a V combined; and ^ permits a continuation of both 10b b9 V and Mml, the latter being partially horizontalized in such a manner that its root and fifth constitute the F component's final harmonic interval. In B, unit ^ provides in ine V , a subsequent 10a Vb9 , and a partial horizontalization of Mml; and ^ permits a con- 10b b9 tinuation of ine V and Mml, the latter being partially horizontalized in such a fashion that its root and fifth constitute the B component's final harmonic interval. Correlation at the Ursatz level proceeds primarily as a comparison of the fused-bitonal and serial Ursätze. This comparison of course has to take place on the basis of grounds common to both. Accordingly, in keeping with the note-order in the series-forms involved, the serial Ursatz is expressed as a fused-bitonal formulation patterned after the Introduction's underlying prolongational design. (See Example 5, above.) That this fused-bitonal formulation is completely compatible with the nature of the harmonic and melodic proclivities harbored within the serial Ursatz may be readily demonstrated via the expression of this Ursatz as two "tonal components", one in F and the other in B, both of which are based upon tonic and dominant harmonies. The serial Ursatz and these two components are presented in Example 12. The fused-bitonal formulation of the serial Ursatz appears in Example 13. Comparison of this formulation with the fused-bitonal Ursatz (which is also present in this example) reveals the former to be a prolongation of the latter. Accordingly, it is concluded that the serial Ursatz exists at a structurally less fundamental level than that of the fused-bitonal Ursatz, and that, in the Introduction, fused bitonality is therefore a more fundamental principle of pitch organization than is the twelve-note technique. Correlation of the Introduction's serial and tonal modes of organization at the intermediate level involves a comparison of the series _*. _^ ^_ _> _v deployment pattern's penultimate reduction, ^ I& 2b ^ ^ (from 10a 10a 10a Example 7, above), and the intermediate-level prolongation of the fused-bitonal Ursatz (presented as Example 5). In this contex, it is found that the serial reduction can be formulated fused-bitonally as a fair approximation of the intermediate-level prolongation. This formulation is offered in Example 14. 42 S eri öl Ut s atz. : tla» *f- Jbi =R= Ho tt" |o ^0 ite: Hfe- zfîz 1 *F*1F B 10o-. Zfepï ho ** H-e- -*m>- 7 ^ ^ "|V*° te ftn F C ompo neht: -b-e^ -f^~6-------&-& JQ •• 3 "tO i.-io »t, cpr:j z£ I:-5 *}----------f-7T5------------^-------©—"S»---------- F: *2 ~\ Q ÎQ'I -^~î^- J?0 IQ:S :M«I ;«cFb9 Mwl 3 Component: r:4tIO:7 lo:g____________,,__ froj.-a #0v fc?P jtrp ioHlI -»»-g?! -*°s.-* #o üai «0^jlî7 B: ¥bS mcMml lncYbB Mwl Example 12: Serial Ursatz and tonal components CONCLUDING REMARKS A prime objective of the dissertational study, as stated earlier in this paper, is to gain greater insight into Schoenberg's serial music as music. As an indication of the degree to which this objective is achieved with regard to the Introduction of Op. 31, the following points are offered: 43 Fused -h\ior\a\ Formu« at ton of Serial u^ui"x F: fì: 7b9 ¥** mc Mm I fpIusblinS) *--------------- Mml fcm ¦V2 :MmI Mml £k* Mml Hml Fused - bihonai Ursatz; m t v, A - If —*> »iTcl ff:7 ZEE iT-© -+5^«- f:7 ( JTQ ) Mug, »tit akve F#)____^% |^q ^): ^ 0) (Auf liiU ahove. C^'i Composite èoY*'ma.flï ih Composite F and 3> fthù N^Äpöl'ifcaH tome ìvt in 3 , and to a lesser Fand S. extent in F. Example 13: Comparison of fused-bitonal formulation of serial Ursatz with fused-bitonal Ursatz (1) The discovery that pitch in the Introduction of Op. 31 is organized with reference to the principle of fused bitonality provides a traditionally oriented basis upon which this excerpt's foreground-level harmonic vocabulary and syntax can be readily described. Accordingly, this music may be understood in terms of recognizable goal-directed harmonic and melodic motions. (2) The discovery of this music's organization with reference to the principle of structure and prolongation affords a view of the 44 P: B: VÎ5- j Mvnl- ¦Tfir S V- ¦Mml: ^ J Example 14: Fused-bitonal formulation of penultimate reduction of series deployment Introduction — both fused-bitonally and serially — as an organic whole whose tonal and serial details have meaning within the context of the whole via their relationship to their respective Ursätze. In particular, the music's foreground-level harmonic and melodic subtleties my be understood as meaningful details in the unf old-ment of the fundamental musical event contained in the fused-bitonal Ursatz. The degree to which this study of the Introduction can increase insight into the musical qualities of the entirety of Schoenberg's serial oeuvre obviously depends upon the extent to which the principal findings of the .study can be found to obtain in these works. Thus, intensive consideration of this music with regard to the findings of the study, and particularly, with reference to fused bitona-lity and to the principle of structure and prolongation, is advocated. In view of the fundamental nature of these findings, it is offered that such consideration may well prove to be emminently rewarding.16 BIBLIOGRAPHY HICKEN, Kenneth L, Structure and Prolongation: Tonal and Serial Organization in the "Introduction" of Schoenberg's Variations for Orchestra. Ph. D. dissertation. Brigham Young University, 1970. 192 p. (Xerox. Microfilm. Ann Arbor, Michigan: Xerox University Microfilms. Order No. 71-8856.)17 LEIBOWITZ, René, Introduction à la musique de douze sons: Les Variations pour orchestre op. 31, d'Arnold Schoenberg. Paris: L'Arche, 1949. 351 p. SALZER, Felix, Structural Hearing: Tonal Coherence in Music. 2 vols. New York: Charles Boni, 1952. 283; 349 p. SCHENKER, Heinrich, Harmony. Edited and annotated by Oswald Jonas. Translated by Elisabeth Mann Borgese. Chicago: University of Chicago Press, 1954. Third impression, 1964. XXXII, 359 p. "Introduction", pp. V—XXIV, contains editor's discussion of concepts of Ursatz and Ur-linie. SCHOENBERG, Arnold, Arnold Schoenberg fetters. Selected and edited by Erwin Stein. Translated by Eithne Wilkins and Ernst Kaiser. New York: St. Martin's Press, 1965. 309 p. —, Style and Idea. Edited by Dika Newlin. New Xork: Philosophical Library, 1950, 224 p. —, Variationen für Orchester, Op. 31. Study score. Vienna: Universal Edition, c 1929. Copyright renewed 1956 by Gertrude Schoenberg. 80 p. 16 To date (March, 1974), the present writer has found the "Theme" of Op. 31 to be organized fused-bitonally at Schenkerian foreground and Ursatz levels and has also discovered fused-bitonal organization at the foreground level in excerpts from the following: Opp. 23 (No. 5); 26; 30; 37; 42; 47; 50b. 17 Xerox and microfilm copies my be obtained from the following sources: 1) Xerox University Microfilms 2) University Microfilms Limited / Dissertation Copies St. Johns's Road P. O. Box 1764 Tylers Green Ann Arbor, Michigan High Wycombe U S.A. 48106 Buckingshamshire England HP 10, 8 HR 46 POVZETEK Osnovni namen razprave je, da poglobi na podlagi temeljite analize tonske organizacije v »Introdukciji« iz Schoenbergovih Variacij za orkester, op. 31, razumevanje skladateljeve serialne glasbe kot glasbe. Avtorjeve ugotovitve lahko formuliramo takole: 1. Tonske višine v »Introdukciji« niso organizirane le serialno, ampak tudi glede na dva tonalna centra, ki sta si oddaljena za zvecano kvarto, torej v smislu razširitve tonalnosti, ki jo oznacujemo kot nacelo »fuzi-onirane bitonalnosti«. Zato lahko omenjeno glasbo razumemo v smislu harmonskega in melodicnega gibanja, ki je spoznavno usmerjeno proti cilju. 2. »Introdukcija« je organizirana po nacelu strukture in prolongacije, zaradi cesar jo je mogoce pojmovati — glede na fuzionirano bitonalnost in serialnost — kot organsko celoto, katere tonski in serijski detajli imajo smisel v kontekstu celote z ozirom na odnos do njihovih jeder. Posebno eminentne harmonske in melodicne finese lahko razumemo kot brezpomembne detajle v razvoju osnovnega glasbenega dogajanja, kot je vsebovano v fuzioniranem bitonalnem jedru. Koliko lahko pricujoce preucevanje »Introdukcije« poglobi razumevanje muzikalnih kvalitet celotnega Schoenbergovega serialnega opusa, je ocitno odvisno od obsega, v katerem bi ugotovitve razprave veljale tudi za druga skladateljeva dela. Zato avtor priporoca intenzivno preucevanje Schoenbergove ustvarjalnosti z vidika fuzionirane bitonalnosti in glede na princip strukture in prolongacije. Sprico dosedanjih ugotovitev je mogoce domnevati, da bi takšno preucevanje koristno rezultiralo. 47