Locanto - Stravinsky's Late Technique

DOI: 10.1111/j.1468-2249.2011.00302.x

 

‘C T    T

 I’: I





L S

musa_302

S  S

221..266

C J

The use of intervals as the basic material of musical construction consistently served as an important and deeply personal characteristic of Stravinsky’s compositional process. In his final serial compositions, however, this aspect assumed a more decisive role and underwent significant changes. Stravinsky’s late writings, composed in collaboration with Robert Craft, reflect this renewed interest in intervallic construction. In them, the composer repeatedly describes the first stages sta ges of the cre creati ative ve pro proces cesss as ‘work ‘work wit with h int interva ervals’ ls’ and ev even en pro projec jects ts thi thiss practice backwards to cover the entirety of his musical output. Stravinsky thus emphas emp hasise ises, s, per perhap hapss exc excess essiv ively ely,, the con contin tinuit uity y of his thi thinki nking ng des despit pite e the 1 evident changes that took place throughout his compositional career. The new and more important role occupied by the intervallic component in Stra St ravi vins nsky ky’s ’s se seria riall co comp mpos osit itio ions ns is is,, to a lar large ge ex exte tent nt,, a co cons nseq eque uenc nce e of th the e gradual abandonment of pitch collections (octatonic, whole-tone, diatonic, and so on),2 which had played such a decisive role in his earlier music, in favour of a growing tendency to make systematic use of twelve-note aggregates – a tendency de ncy ac acce cent ntua uate ted d pa parti rticu cular larly ly in th the e co comp mpos osit itio ions ns wh whic ich h fo follo llow w Threni .3 Althou Alt hough gh Str Strav avins insky ky con contin tinued ued to pre prefer fer the sam same e pc set setss (pa (particu rticular larly ly tet tetrarachords) which in his earlier compositions were derived from diatonic or octatonic collec col lectio tions, ns, the ske sketch tches es for his las lastt com compos positi itions ons see seem m to ind indica icate te tha thatt the creative process has moved from specific intervals to larger combinations (and not vice versa), thereby producing harmonic environments which can appear variously diatonic, octatonic or chromatic. By freeing the treatment of intervals from a broader system of pitch organisation,4 Stravinsky seems to have followed a path which presents some similarities to – but also some profound differences from – the predominantly motivic pathway followed by Schoenberg and his pupils in their gradual departure from traditional tonality. Although all of these composers treated the intervallic compone po nent nt in di diff ffer eren entt wa ways ys,, it be beca came me for th them em th the e fo foun unda dati tion onal al as aspe pect ct of a ‘motivic’ technique – that is, one based on the use of a restricted number of intervallic configurations which serve a basic unifying function within a musical work. wor k. Yet the specific way in which Stravinsky Stravinsky used interva intervallic llic motiv motives es emerg emerges es through a study of his many unpublished versions of pieces, and these must be evaluated in relation to the peculiarities of his aesthetic. Music Analysis Analysis,, 28/ii-iii (2009) © 2011 The Author. Author. Music Analysis © 2011 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA

2 21

222

 

All of this raises an interesting issue: although in so-called atonal music the (presumable) absence of a hierarchy among the sounds allows the composer to employ all twelve pitch classes as he pleases (considering them exclusively in terms of their intervallic relationships), 5 with the adoption of serial procedures a new constructive order is imposed. Now, while in the work of other composers one cou could ld sa say y tha thatt thi thiss new con constru structi ctive ve ord order er enc encomp ompass asses es and ess essent entiall ially y identifies with motivic-intervallic syntax, in Stravinsky the result of such identification is instead rather problematic, because these two aspects operate according to slightly – but significantly – different criteria. In the following pages, I will atte attempt mpt to demon demonstra strate te how how,, particularly in the compositions compositions from Agon onward onw ards, s, thi thiss app approa roach ch pro provid vided ed Str Strav avins insky ky wit with h a sti stimul mulus, us, rather rather tha than n an obstacle, to composition. I will also attempt to interpret some characteristics of Stravinsky’s creative process and serial technique which are by now well known but whose deeper motivations still require further investigation. Motivic-Intervallic Syntax: General Characteristics Even if it is ev Even evid iden entt th tha at th the e us use e of in inte terv rval alss as th the e ba basi sic c ma mate teri rial al of th the e compositional process constitutes a central feature of Stravinsky’s late musical thou th ough ght, t, th the e sp spec ecifi ific c te tech chni nica call me mean anss em empl ploy oyed ed le lend nd th them emse selv lves es to be bein ing g 6 described in rather different ways. Stravinsky never specified exactly what he meant by the expression ‘composing with intervals’, nor does the study of his sketches offer any definitive answers. answers. A great deal of his work with pitch material, in fact, took place at the keyboard, in a phase prior to that documented in the earliest sketches, which in actuality record a stage in the creative process that is already quite advanced. 7 Given this this modus operandi one can easily imagine that Stravinsky’s interval-based procedures were not codified according to any kind of systematic approach.This, however, does not exclude the possibility that such procedures can be described retrospectively in theoretical terms. To this end, I will use as a brief first example the original twelve-note row of A Sermon, a Narrative, and a Pray Prayer er (Ex. (Ex. 1).The row can be subdivided into four distinct trichords, three of which – the first, second and fourth – belong to set clas cl asss [0 [014 14]. ]. Se Segm gmen ents ts 2 an and d 4 ar are e or orde dere red d as <0, 1, 4>, while segment 1 is ordere ord ered d as <1, 0, 4>.8 Fr From om an in inte terva rvalli llic c po poin intt of vi view ew,, if we co cons nsid ider er th the e intervals interva ls apart from their melodic direction direction (ascending (ascending or descending descending), ), that is, as unordered unord ered pitch-class pitch-class interva intervals ls (inte (interval rval class classes), es), all three segments segments conta contain in a

Ex. 1 Stravinsky, A Stravinsky, A Sermon, a Narrative, Narrative, and a Prayer Prayer : subset structure of the original twelve-note row 3

1

4

4 [014]

1

4

3 [014]

© 2011 The Author. Author. Music Analysis © 2011 Blackwell Publishing Ltd

1 [015]

3 [014]

Music Analysis Analysis,, 28/ii-iii (2009)

222

 

All of this raises an interesting issue: although in so-called atonal music the (presumable) absence of a hierarchy among the sounds allows the composer to employ all twelve pitch classes as he pleases (considering them exclusively in terms of their intervallic relationships), 5 with the adoption of serial procedures a new constructive order is imposed. Now, while in the work of other composers one cou could ld sa say y tha thatt thi thiss new con constru structi ctive ve ord order er enc encomp ompass asses es and ess essent entiall ially y identifies with motivic-intervallic syntax, in Stravinsky the result of such identification is instead rather problematic, because these two aspects operate according to slightly – but significantly – different criteria. In the following pages, I will atte attempt mpt to demon demonstra strate te how how,, particularly in the compositions compositions from Agon onward onw ards, s, thi thiss app approa roach ch pro provid vided ed Str Strav avins insky ky wit with h a sti stimul mulus, us, rather rather tha than n an obstacle, to composition. I will also attempt to interpret some characteristics of Stravinsky’s creative process and serial technique which are by now well known but whose deeper motivations still require further investigation. Motivic-Intervallic Syntax: General Characteristics Even if it is ev Even evid iden entt th tha at th the e us use e of in inte terv rval alss as th the e ba basi sic c ma mate teri rial al of th the e compositional process constitutes a central feature of Stravinsky’s late musical thou th ough ght, t, th the e sp spec ecifi ific c te tech chni nica call me mean anss em empl ploy oyed ed le lend nd th them emse selv lves es to be bein ing g 6 described in rather different ways. Stravinsky never specified exactly what he meant by the expression ‘composing with intervals’, nor does the study of his sketches offer any definitive answers. answers. A great deal of his work with pitch material, in fact, took place at the keyboard, in a phase prior to that documented in the earliest sketches, which in actuality record a stage in the creative process that is already quite advanced. 7 Given this this modus operandi one can easily imagine that Stravinsky’s interval-based procedures were not codified according to any kind of systematic approach.This, however, does not exclude the possibility that such procedures can be described retrospectively in theoretical terms. To this end, I will use as a brief first example the original twelve-note row of A Sermon, a Narrative, and a Pray Prayer er (Ex. (Ex. 1).The row can be subdivided into four distinct trichords, three of which – the first, second and fourth – belong to set clas cl asss [0 [014 14]. ]. Se Segm gmen ents ts 2 an and d 4 ar are e or orde dere red d as <0, 1, 4>, while segment 1 is ordere ord ered d as <1, 0, 4>.8 Fr From om an in inte terva rvalli llic c po poin intt of vi view ew,, if we co cons nsid ider er th the e intervals interva ls apart from their melodic direction direction (ascending (ascending or descending descending), ), that is, as unordered unord ered pitch-class pitch-class interva intervals ls (inte (interval rval class classes), es), all three segments segments conta contain in a

Ex. 1 Stravinsky, A Stravinsky, A Sermon, a Narrative, Narrative, and a Prayer Prayer : subset structure of the original twelve-note row 3

1

4

4 [014]

1

4

3 [014]

© 2011 The Author. Author. Music Analysis © 2011 Blackwell Publishing Ltd

1 [015]

3 [014]


‘C  I’

2 23

Ex. 2a Ex. 2a Sc Scho hoen enbe berg, rg, St Strin ring g Qu Quart artet et No No.. 4: su subs bset et st struc ructu ture re of th the e fu funda ndame ment ntal al twelve-note row [015]

[015]

[015]

[015]

Ex. 2b Be Ex. Berg, rg, Lyric Lyric Sui Suite te:: su subs bset et st struc ructu ture re of th the e tw twel elv vee-no note te ro row w of th the e th thir ird d movement [0126]

[0126]

[0126]

[0126]

semitone (ic1), a minor third (ic3) and a major third (ic4). 9 In consequence, we could describe describe the three segments segments as three statement statements, s, differ differently ently ordered, ordered, of the same group of three interval classes, or equally well as three statements, differently ordered, of the same set class [014]. Cons Co nside iderin ring g th the e se segm gmen ents ts of th the e ro row w as un unor orde dere red d se sets ts co corre rresp spon onds ds to a constructive logic which, far from being exclusive to Stravinsky, seems deeply rooted roo ted in mos mostt tw twelv elve-n e-note ote and seri serial al mus music ic in gen genera erall and is cert certain ainly ly ve very ry familiar from the published literature on serialism. Many of the basic operations which whi ch con concern cern the sub subset set structure structure of the tw twelv elve-n e-note ote ro row w are bas based ed on thi thiss logic. In Schoenberg, Schoenberg, Berg and Webern, the rows are often organised organised in such a way as to maximise certain segments which, if considered apart from the order of th the e pi pitc tche hes, s, be belo long ng to th the e sa same me se sett cl clas asss. To To me ment ntio ion n on only ly a co coup uple le of examples, exam ples, one could could cite the the row of Schoenb Schoenberg’s erg’s String String Quartet No No. 4, in which one can identify four segments of three notes as belonging to set class [015] (Ex. 2a),10 or the row employed in the twelve-note section of the third movement Suite, which contains of Berg’s Lyric Berg’s Lyric Suite, contains four segments segments belonging to the class [0126] 11 (Ex. 2b). Furthermore, Furthermo re, in man many y twel twelveve-note note compositions compositions the idea of considering some segm se gmen ents ts of th the e ro row w as un unor orde dere red d se sets ts co cons nsti titu tute tess an es esse sent ntia iall pr prem emis ise e fo forr establishin esta blishing g variou variouss types of formal relationship relationships. s. The internal structure of the row, in fact, allows some of its subsets to preserve the same global pitch content even after the typical transformational operations (transposition, retrograde and inversion) inv ersion) are applied.This gives rise to a netw network ork of rela relations tions among the various forms of the row employed in a composition. 12 The very notion of hexachordal combinatoriality,13 which plays a fundamental role in Schoenberg’s twelve-note music, is based on the possibility of conceiving the hexachords as unordered collections. The global intervalli intervallic c con conten tentt of the these se seri serial al seg segmen ments ts of cou course rse pla plays ys an impo im porta rtant nt ro role le in en enab ablin ling g th this is ty type pe of re rela lati tion on fr from om th the e mo mome ment nt th that at ea each ch Music Analysis Analysis,, 28/ii-iii (2009)

© 201 2011 1 The Auth Author. or. Music Analysis © 2011 Blackwell Publishing Ltd

224

 

Ex. 3 Webern, Cantata Cantata No. 1, Op. 29: subset and interva intervallic llic structure of the original twelve-note row [014]

[014] 1

O

[014] 3

[014] 1

RI

segment can be considered either as an unordered set of pitch classes or as an unordered unord ered set of interva intervall class classes. es. Partic Particular ular attention attention to interva intervallic llic content forms the basis of Webe ebern’s rn’s pra practi ctice ce of deri derivin ving g a ro row w fro from m the reitera reiteratio tion n of a sin single gle basic cell. To ment mention ion only one well-known well-known examp example: le: in Canta Cantata ta No. 1, Op. 29 14 (Ex. 3), the four discrete trichords of the row are all members of the same set class cla ss [01 [014]. 4]. The importanc importance e of the global global int interva ervallic llic content content of set class [014] (semitone, minor third and major third) is underlined by the presence of the semito sem itone ne bet betwe ween en the first and sec second ond seg segmen ments ts and bet betwe ween en the third and fourth segments, and by that of the minor third between the second and third segments. To summarise: the idea of globally considering the pitches and/or intervals contained in some serial segments typically constitutes one of the basic constructi stru ctive ve crit criteria eria of tw twelv elve-n e-note ote ser seriali ialism. sm. Nev Neverth erthele eless, ss, thi thiss crit criterio erion n corr correespon sp onds ds on only ly in pa part rt to th the e co conc ncep eptt of in inte terv rval alli lic c mo moti tiv ve wh whic ich h I ho hope pe to illumin illu minat ate e in the mus music ic of Str Strav avins insky ky.. Gen Genera erally lly,, the con consti stitue tuent nt pit pitche chess of a 15 motive can be used in either a harmonic or a melodic sense, and compared in any order. Nevertheless, Stravinsky, working with the orientation of single intervals, va ls, rad radica ically lly mod modifie ifiess the ph physi ysiogn ognom omy y of his mot motive ives, s, whi which ch can the thereb reby y assume forms corresponding to different set classes. From this point of view, then, an intervallic motive no longer corresponds, in any sense, to a class of unordered unord ered pc sets. Rath Rather, er, Stra Stravinsky vinsky’s ’s operations operations act more on the leve levell of single intervals than on the level of the global configurations within which these single intervals are included. The difference becomes clear if we return to the third segment of the row of (see again Ex. 1). This segment segment belongs not A Sermon, a Narrative, and a Praye Prayer r (see to set class [014], but rather to the class [015]. As a consequence, its global interva int ervallic llic con conten tentt is dif differ ferent ent.. Ho Howe weve ver, r, thi thiss seg segmen mentt sha shares res wit with h the oth other er segmen seg ments ts tw two o of its thr three ee int interva ervals ls (ic (ic1 1 and ic4), which are mer merely ely arra arrange nged d differently (Ex. 4): in the third segment they are joined in the same direction, thereby ther eby producing producing an ic5; in the first, secon second d and fourth segments they they are joined in opposed direction directions, s, there thereby by producing producing an ic3 (Ex. 4).16 In short, consid considered ered as as unordered pc sets, only three of the four segments of the row of Ex. 1 turn out to belong to the same class; considered, however, as intervallic motives formed through the combination – in varying directions – of two intervals, they turn out to all be members of the same motive class (Ex. 5): the semitone and the major third conjoined, expressed symbolically as 1–4. 17 © 2011 The Author. Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

225

Ex. 4 Intervallic motive class 1–4 in the two forms of set class [015] and [014] 1–4 motive 5 4

ic4

ic3 1

ic1

(ic5)

1 ic1

0

(ic4)

0

Ex. 5 Stravinsky, A Sermon, a Narrative, and a Prayer : motivic-intervallic structure of the original twelve-note row 3

1

4

4

1

[014] E 4 C

4

3

E (3)

4 B

1

[015]

D

1

1

5

[014]

4

D (3)

[014]

B

1

A

4 (5) G 1

3

4 F

1 A (3)

1–4 motive

F

This simple alteration in intervallic direction constitutes a precious compositional resource in Stravinsky’s hands. Joining various forms of a single (or at most two) motivic class(es), he creates twelve-note rows – as in the previous example – as well as smaller or larger successions of pitches to be employed either melodically or harmonically in a musical passage. For instance, in Ex. 6 we can observe the succession of pitches which serves as the basis for three episodes (bars 7–22) included in the first section (up to the prima volta) of the first of the five Movements. This passage conceals a closely woven fabric of overlapping motives of the semitone-tone (1–2) and semitone-tritone (1–6) types (indicated by square brackets). Depending on the orientation assumed by the two intervals, the first motive (1–2) produces sets of three pitches belonging to set classes [012] and [013]. The second motive (1–6), on the other hand, produces collections belonging to set class [016] regardless of the orientation assumed by the two intervals.18 It should be apparent that, in defining this type of intervallic syntax as motivic, the term ‘motive’ is being used with some degree of latitude. In the Formenlehre tradition, for example, a motive is typically conceived as a structural nexus of rhythm and intervals.19 In Stravinsky’s music, however, a motive is essentially an abstract configuration of intervals: pitch components and rhythm are treated as initially distinct and separate dimensions which can subsequently be related. 20 As suggested above, in spite of some apparent similarities, this conception of inter Music Analysis, 28/ii-iii (2009)

© 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd

226

 

Ex. 6 Stravinsky, Movements, i: motivic-intervallic structure of the succession of pitches contained in each of the three solo episodes of bars 7–22 [012] [012]

[016] [016]

[013]

[016]

[016] [016]

[012]

[013] [012]

[016]

[016] [016]

[016]

1–2 motive

2 1

6

[012]

(5)

[012] [016]

[013]

1 [012]

6

[7] = 5

2 1

[013]

[016]

[016] [016]

1–6 motive

(1) (3)

[012] [012] [016]

1 [016]

[016]

vallic motive also differs radically from that familiarly applied to the post-tonal music of Schoenberg, Berg and Webern. For these composers, the concept of motivic elaboration which guaranteed coherence in tonal music was gradually replaced by a constructive principle based on the use of fundamental intervallic constellations which operate at a more basic level. According to Martina Sichardt, this reduction of the various Gestalten within a passage to its most elementary intervallic basis – a tendency Schoenberg himself had consciously put into practice in his own analytical formulations – represented a fundamental premise for the elaboration of the twelve-note method. 21 In this respect, it is interesting to note that most of the basic intervallic constellations which form the expressive vocabulary of melodic gestures in Schoenberg’s compositions consist merely of the union of two or three intervals – one of which is usually the semitone – disposed in a particular arrangement. 22 An interesting analogy with Stravinsky’s practice can nonetheless be glimpsed wherever Schoenberg subjects these basic combinations of intervals to a process of variation. Jack Boss, for example, has demonstrated that the majority of the intervallic motives in the first of Schoenberg’s Vier Lieder , Op. 22, could be derived by applying three types of modification to a motive formed from the combination of one ic1 and one ic3.23 Boss considers all of the possible arrangements of these two intervals (that is, <+1, +3>, <+1, -3>, <-1, +3>, <-1, -3>, <+3, +1>, <+3, -1>, <-3, +1> and <-3, -1>) as variants belonging to the same motivic category. Moreover, each of these forms can undergo in its turn three fundamental types of variation, two of which involve octave complementation and pitch reordering. All of this corresponds exactly to my definition of motive class 1–3. However, despite this similarity, a profound discrepancy remains regarding the very concept of motive. Schoenberg’s procedures, as described by Boss, ‘effectively identify motive as an entity which may be subjected to a wide range of transformations while remaining largely recognisable’. According to Boss, for example, the third basic category of variation employed by © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd

Music Analysis, 28/ii-iii (2009)

‘C  I’

227

Schoenberg involves the expansion of intervals. 24 In this respect, the Schoenbergian concept of variation implies a decisively greater quantity and variety of forms derivable from a single motive than those which occur in Stravinsky. Still more important is the fact that the Schoenbergian concept of variation implies a broader process, one which involves the entire plan of the musical form. Indeed, in Schoenberg, the variation of a motive cannot be dissociated from the concept, central to the Austro-German tradition, of motivic elaboration, understood as a means of conferring coherence and organic unity on a composition.25 All of this is foreign to Stravinsky’s musical thought, in which the manipulation of intervallic motives is understood as a procedure for generating primary compositional material capable of being employed as a point of creative departure. The idea – developed in particular through the work of George Perle 26 – that a ‘basic cell’ or ‘referential sonority’ can be presented even in a vertical sense could be considered another point of contact between Stravinsky’s motivicintervallic syntax and the post-tonal harmonic language of Schoenberg, Berg and Webern. However, unlike the notion of the Stravinskian intervallic motive, the concept of the basic cell consists of a fixed configuration of intervals and corresponds therefore to a single set class.27 The most decisive difference, however, concerns the contrasting aesthetic-musical aspects within which a motive unit is taken to function: in the music of Schoenberg, Berg and Webern an intervallic configuration disposed vertically always maintains a motivic character – from which, in fact, the idea of ‘chord as motive’ arises – even in a dynamic sense. The nature of this element is expressed by the Schoenbergian concept of unrest: What is a motive? A motive is something that gives rise to motion. A motion is that change in a state of rest, which turns it into its opposite. Thus, one can compare a motive with a driving force ... . What causes motion is a motor . One must distinguish between motor and motive ... . A thing is termed a motive if it is already subject to the effect of a driving force, has already received its impulse, and is on the verge of reacting to it ... . The smallest musical event can become a motive if it is permitted to have an effect; even an individual tone can carry consequences. (Schoenberg 1995, p. 386; emphases in original)

In the music of Schoenberg, the simultaneous presentation of pitches produced by an intervallic configuration can be considered the result of an extreme concentration in time of an event whose essence is decidedly dynamic – tied, that is, to the movement of time. Therefore, if Schoenberg’s motivic conception is essentially temporal – the very idea of a suppression of temporality associated with the Schoenbergian ‘law’ of the unity of musical space implies in actuality the concept of time – the Stravinskian approach conversely returns to a conception we may define as ‘spatial’ or ‘plastic-visual’: the motive is understood as a configuration of intervals which can be arranged in two dimensions, as in visual space. Music Analysis, 28/ii-iii (2009)


228

 

Theoretical Aspects Before examining some specific examples, a number of purely theoretical considerations are worth reviewing in greater detail. As mentioned earlier, the possibility of freely orienting any intervallic configuration ensures that a single motivic class corresponds to more than one set class. With respect to the motives formed from two different intervals (the model Stravinsky most frequently employs), each of the fifteen possible combinations generally produces two different set classes, depending on the orientation of the two intervals conjoined. Only those motives containing the tritone produce a unique set class regardless of intervallic orientation (see the left-hand side of Table 1). 28 The right-hand side of Table 1, however, shows the motives which are capable of producing a particular set class of three pitches. For example: the set class [013] can be obtained by uniting one ic1 and one ic2 in the same direction (motive 1–2), or by uniting a single ic2 and a single ic3 in opposite directions (motive 2–3). As can be seen, according to the global intervallic content, 29 each set class can be produced by a variable number of up to three intervallic motives. Only set class [048], which contains three identical intervals (three ic4s), cannot be produced by any motive formed from two different intervals. The motives formed through the union of three different interval classes do not constitute an analytically relevant object since too many different set classes are generated. For example, a motive which combines a semitone, tone and minor third in whatever order and direction would produce ten different set classes containing either three or four distinct pitch classes: 30

Table 1 Motives formed by two different conjoined intervals Motivicintervallic class

Set class(es) produced

1–2.............................................(012) (013) 1–3............................................ (013) (014) 1–4.............................................(014) (015) 1–5.............................................(015) (016) 1–6 .............................................(016) 2–3.............................................(013) (025) 2–4.............................................(024) (026) 2–5.............................................(025) (027) 2–6 .............................................(026) 3–4.............................................(014) (037) 3–5.............................................(025) (037) 3–6............................................ (036) 4–5.............................................(015) (037) 4–6 .............................................(026) 5–6 .............................................(016)


Set class

Associated motivic-intervallic class(es)

(012) ............................1–2 (013) ............................1–2 (014) ............................1–3 (015) ............................1–4 (016) ............................1–5 (024) ............................2–4 (025) ............................2–3 (026) ............................2–4 (027) ............................2–5 (036) ............................3–6 (037) ............................3–4 (048) ............................—

1–3 1–4 1–5 1–6

2–3 3–4 4–5 5–6

2–5 2–6

3–5 4–6

3–5

4–5


‘C  I’

229

Table 2 Motives formed by two different intervals, with one of them repeated once Motivicintervallic class

Set class(es) produced

1–2–1............................(012) (0123) (0134) 2–1–2............................(0123) (0235) 1–5–1 ............................(0145) (0156) (0167) 5–1–5 ............................(0156) (0167) (0158)

Set class

Associated motivic-intervallic class(es)

(012)..............................1–2–1 (0123) ............................1–2–1 2–1–2 (0134)............................1–2–1 (0145)............................1–5–1 (0156)............................1–5–1 5–1–5 (0158)............................5–1–5 (0167)............................1–5–1 5–1–5 (0235)............................2–1–2

1–2–3: [013][023][0123][0124][0125][0134][0135][0136][0146][0236] Moreover, the majority of these ten set classes can be derived from other motives covering three different intervals. Thus every set class can be associated with an excessively broad number of motives and vice versa. However, motives that may be realised using only two interval classes, one of which repeats once (for example, 1–2–1) to form a set of four pitches, are relatively common. In Stravinsky’s case, motives of this type are typically those which employ the semitone in conjunction with the whole tone or perfect fifth (1–2–1, 2–1–2, 1–5–1 and 5–1–5). As can be seen on the left-hand side of Table 2, these motives produce only two or three different set classes, according to the orientation assumed by the intervals. The right-hand side of the same table, on the other hand, show how two different motives of this type can, at times, produce the same set class. For example, the set class [0123] is obtained by both 1–2–1 and 2–1–2. Intervallic Syntax and Serial Technique The major discrepancy between the motivic-intervallic syntax described so far and serial technique – as conceived by Stravinsky himself – consists in the fact that while the first operates predominantly on the level of single intervals, the second acts essentially on the level of pitch-class sets, understood as the units of primary structural value. 31 Different orientations of the single intervals of a motive can produce forms which belong to different set classes; by contrast, neither the retrograde, nor the inversion, nor the retrograde inversion, nor any type of permutation of the order of a particular pc set is capable of generating a different set class. From the point of view of musical perception, one could even say that motivic-intervallic syntax attributes to the quality of single intervals an importance superior to the globalising tendency of pc sets. Put simply, intervallic logic tends towards disintegration, serial technique towards unification. Music Analysis, 28/ii-iii (2009)


230

 

Despite these discrepancies, in Stravinsky’s compositional thought the two aspects seem to aim towards the same end. In order to clarify how this occurs, consider Ex. 7, which reproduces the three choral statements at the beginning, in the middle and towards the end of the ‘Dies irae’ of the Requiem Canticles. These three fragments constitute an autonomous formal layer which interacts with the surrounding layers of contrasting musical material (omitted from the example). The first choral statement (bars 82–83) divides into two parts: in the first part the chorus (doubled by the brass) intones the words ‘Dies irae’ on a forte chord repeated in a dotted rhythm; in the second, the single word ‘irae’ (chorus and horns con sordini ) is repeated as an echo to a piano chord which bears a certain affinity with the preceding harmony. The second statement (bar 86) is limited instead to a repetition of the forte chord on ‘dies illa’, and without the echo response. The third statement (bar 97 onwards) is essentially a recapitulation of the first, although it presents a slight harmonic departure.Thus, the entire layer assumes a type of ABA′ form. My analytic symbols placed below the score in Ex. 7 show the motivicintervallic construction of this layer. The two chords of the first statement (bars 82–83) correspond to the two forms – [015] and [016] – of the motivic class 1–5. Moreover, notice that these forms share the pitches E  and A, which together form ic5. The impression that the first chord is echoed by the second (come eco) therefore derives not only from the presence of two common tones, but also from the intrinsic motivic-intervallic affinity of the two harmonic simultaneities. The second choral statement (bar 86) opens onto a symmetrical sonority, a member of set class [0156] containing two ic1s and two ic5s. This sonority is obtained through the sum of the two 1–5 motives appearing in the two chords of the first statement: E –F –A [015] + E –A –B [016] = E –F –A –B [0156]. This time the chord is not simply repeated: in the middle of the bar, the lowest voice moves a semitone from B to B , thereby giving rise to a sonority containing an ic1 (F–F ) and two conjoined ic5s (A –E –B). The recapitulation (bar 97) is practically identical to the first statement; nevertheless, in the first part (the forte chord on ‘Dies irae’), the bass moves a semitone from F  to G. Finally, notice that the perfect fifth A –E is a constant presence throughout the layer in its entirety, thus forming a kind of operative tonal axis. The sketches transcribed in Ex. 8a and 8b concern the composition of the same formal layer. Ex. 8a reproduces a strip of paper containing an early version of the first statement (bars 82–83), preceded by the pre-emptive instrumental gesture which introduces it (bar 81). 32 Note that in this version the harmony of the choral part includes a move of a semitone from F  to G in the bass voice, a solution which Stravinsky will subsequently adopt for the varied recapitulation (compare Ex. 8a with Ex. 7).33 Ex. 8b reproduces a little sheet containing two different versions – in the upper and lower systems respectively – of the first and the second statements, worked out as an unbroken succession. Here the second statement adumbrates the echo response, which in the final version Stravinsky uses only for the first statement (and for the recapitulation). In the first version © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’ o c e e m o c

,

i d

231

o c e e m o c

] 6 E 1 0 [

B A

,

1

, e a r

5

G 1

i

F

s e

n o i t c u r t s n o c c i l l a v r e t n i c i v i t o m : 8 9 – 7 9 d n a 6 8 , 3 8 – 1 8 s r a b , ’ e a r i s e i D ‘ , s

A

7 9

] 5 E 1 0 [

5

{

I I . . I . n e n t b r T

I I . I . r T

I I I . I

. d . r o r o s C n o c

. . S A

V I . I I

O R O C

. . T B

] 5 1 0 [ + ] 6 1 0 [ = E ] 6 5 1 0 [

, a l

B

l i

1

s e

F

B A

6 8

i d

1

5

{


I I . I . r T

. . S A

O R O C

. . T B

] 6 E 1 0 [

B A , e a r

1

5

1

F

i

A

o c e e m o c

] 5 E 1 0 [

5

{ , e a r

e l c i t n a C m e i u 2 q 8 e R

, y k s n i v a r t S 7 . x E

i D

{

1

i s e i D

{

) 8 6 =

I I . I . r T


I I

E A ( R I 6 S 3 1 E I = D


. d . r o r o s C n o c

3

V I . I I I

. . S A

O R O C

. . T B

i n a p m i T

o n a i P


232

 

Ex. 8a Stravinsky, sketches for Requiem Canticles, ‘Dies irae’ (compare bars 81–83 of the printed score) (Paul Sacher Foundation, Igor Stravinsky Collection) II Inv.

Tmp

3

3

eco S A 3 3

Di

es

i

rae

i

- [i ll eg ib le ]

3

T B 3

of the passage (the upper system), the chord of the second statement is a series of three conjoined perfect fifths (B–F  –C –G). In the second version (the lower system) the B is modified to a B . The alteration forms set class [0157], which contains two conjoined ic5s (F –C –G) along with an ic1 between B and C. In the final version, Stravinsky preferred a sonority containing two ic1s and two ic5s, as we have already seen. In the event, all of the variants in the sketches, like the final version, can be interpreted from the point of view of a systematic use of combinations of ic1 and ic5. The only serial symbols discernible in the sketches are on the page transcribed in Ex. 8b and refer to the second of the two fundamental twelve-note rows employed in the Requiem Canticles,34 or, more precisely, to the two ‘rotational arrays’ generated respectively by the first hexachord of series I (I a) and the first hexachord of series RI (RI a) of Ex. 8c.35 Without going into detail on the various properties of this type of table and the ways of using it, 36 I will briefly describe its construction. The pitches of the original hexachord are first made to rotate systematically from right to the left: the first rotation begins with the second pitch of the original hexachord, through which the first pitch moves into the final position; the second rotation begins with the second pitch of the first rotation (the third pitch of the original), and so on for five iterations (after which it returns to the original form). The five rotated forms thus obtained are transposed successively so that they all begin on the same pitch as the original hexachord (in the specific case of Ex. 8c, F for the forms generated by hexachord Ia; G for the forms generated by hexachord RIa). Each of the five rotatedtransposed forms thus obtained contains the same succession of intervals © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

233

Ex. 8b–d (b) Stravinsky, sketches for Requiem Canticles, ‘Dies irae’ (cf. bars 81–83, 86 and 97–98 of the printed score) (Paul Sacher Foundation, Igor Stravinsky Collection); (c) rotational arrays of the hexachord a of the inversion (left-hand column) and retrograde inversion (right-hand column) of twelve-note row II, with encircled serial segments employed in the upper sketch (the circles and connecting arrows are not part of Stravinsky’s original autograph); (d) motive 1–5, in the forms of sets [016] and [015] (b)

R inv.α 1 (4 & 5) S A Di

es

i

rae

(ir

rae)

di

es illa

a[ sic])

(ill

T B

R inv.α 1 (5 & 6) S A Di

es

i

rae,

(irae)

{

Di

es illa

{

illa

T B

II inv. α 1st 1 & 2 2nd

1&2

3 & 2 [T11]

1st

1&3

1st

2&3

Row II – hexachord Iα

1

Row II – hexachord RIα

1

(c)

(d) 2

2

F 5 3

3

4

4

5

5

6

6

5 C

1

D B A

1

B

[016]

[015]

globally – each time beginning at a different point within the succession – but different pitch classes. 37 The symbols on the sketch shown in Ex. 8b clearly indicate that the chords of the choral part result from the combination of dyads freely selected from the two Music Analysis, 28/ii-iii (2009)


234

 

rotational arrays (Ex. 8c). 38 In general, the dyads derive from segments of two consecutive notes within a line of the tables. In one case, they even derive from two non-consecutive notes (‘1st, 1 & 3’= the first and third note of the first line). In another case, the dyad derived from the third and second note of the second line (‘2nd, 3 & 2’ = G –F) is transposed down a semitone (T 11), so as to become G–E. As can be seen, Stravinsky does not seem to have selected the dyads on the basis of a pre-established criterion or precise order within the table. Rather, it seems that his only intention was to ensure the production of numerous ic1 and ic5 relations.These intervals attain a certain importance within the original form of hexachord a , where they form two motives of class 1–5, in the forms [016] and [015], respectively (also shown in Ex. 8d). Moreover, given the structure of the tables, these intervallic motives also appear in the rotated(-transposed) forms. This justifies Stravinsky’s recourse to the rotational arrays, but it does not explain his reason for extrapolating only dyadic segments, rather than complete hexachordal units. Nevertheless, it is evident that, by operating in this manner, Stravinsky hoped to obtain a denser and more cohesive motivic construction than could be achieved using the hexachords in their entirety. Note, for example, that the two 1–5 motives interlaced to form the symmetrical set [0156] in the second choral statement derive from neither hexachord a nor from its rotated(-transposed) form. This demonstrates that from Stravinsky’s point of view serial technique is not essential per se, but instead functions only as a means to an end with regard to motivic-intervallic syntax. The use of complete serial forms does not, as a matter of fact, represent a restriction: if necessary, their use can pass into the background in favour of a more immediate and direct engagement with single intervals. From Intervallic Motives to Rows The problem of the interaction between intervallic-motivic logic and serial technique becomes central in the compositions following Agon, which are systematically based on the use of ordered pc sets (tetrachords, hexachords, twelvenote rows, and so on). This interaction can be observed in two distinct conceptual stages of the creative process: (1) the initial definition of a row of pitches and (2) the transformation of the ‘abstract’ row into concrete musical contexts. In either of these stages, motivic-intervallic logic can take on a role of greater or lesser importance. In the first stage, such logic can determine the physiognomy of the pc sets to be used as primary series. In the second stage, it can determine the manner in which the rows are manifested musically. The implicit motivic-intervallic relations in the abstract formulation of the row, in fact, can be revealed through a variety of devices.These devices can occasionally elucidate different motivic-intervallic aspects latent in the row, which is then subjected to a process of continual motivic interpretation. In each composition, motivic-intervallic logic may be present in one rather than the other of these two conceptual stages of the creative process. In Agon, for © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

235

Ex. 9 Motive 1–2–1 in [0134] form, reordered as tetrachord <0, 1, 4, 3> 1

2

1

1–2–1 motive in <0134> form

the same reordered as <0143>

example, this logic seems to have characterised the pre-compositional stage (that is, the initial definition of a tone row). Indeed, the majority of the rows employed in the work demonstrate a very clear and definite motive-intervallic design. Elsewhere, I have tried to show how the overwhelming majority of rows (ranging from four to twelve pitches) which in recent studies of the compositional process have been identified throughout the ballet,39 from the Triple Pas-de-Quatre forwards, can be traced back to motivic-intervallic combinations of ic1 and ic2. 40 Consider, for example, the ordered tetrachord <0 , 1 , 4 , 3>, which appears for the first time in the Pas-de-Deux: it can be generated by a 1–2–1 motive, with the intervals oriented in the same direction to form set class [0134], by simply ordering the sounds according to the succession <0, 1, 4, 3> in which the whole tone is found between the second and fourth notes and the two semitones on either side. The central position is then occupied by a (non-structural) major third (Ex. 9). The majority of the rows (from six to thirteen pitches) employed in the succeeding movements of the ballet are obtained by combining different statements of this characteristic tetrachord. 41 Consequently, the 1–2–1 motive becomes the generating nucleus for the remainder of the work. Other rows not based on the <0, 1, 4, 3> tetrachord can still be traced back to a particular combination of ic1 and ic2.The first five notes of the hexachord stated in canon at the beginning of the Bransle Simple (Ex. 10a), for instance, are formed by a succession of alternating tones and semitones, interpretable as two 1–2 motives united by a common pitch class. In this case, the particular design of the intervals – the first motive is in the form [013], with the intervals oriented in the same direction; the second is in the form [012], with the intervals in opposite directions – guarantees that between the highest pitch, D, and the lowest, G, an ic5 is formed, the same interval as that produced by the concluding B (the only note which lies outside the 1–2 pattern) and the preceding F . This results in a symmetrical structure, with two ic5s (D–G and B–F) at the distance of a semitone. The twelve-note row employed in the coda of the first Pas-de-Trois (presented for the first time in bars 185–189) is entirely formed from a chain of 1–2 motives in the two forms [012] and [013] (Ex. 10b). In Agon, the intervallic motives containing the tone and semitone, aside from generating the majority of the fundamental rows, perform an important role even in the movements not based on serial technique. 42 Thus their presence imposes coherence on the work in its entirety, despite the different compositional techniques employed.43 The passage for the first violin (doubled by the cello) at bars Music Analysis, 28/ii-iii (2009)


236

 

Ex. 10a Stravinsky, Agon, Bransle Simple (opening): motivic construction [012] 2

5

2

1

1

5

[013]

Ex. 10b Stravinsky, Agon, twelve-note row of the coda of the first Pas-de-Trois: motivic construction [013] [012] 2

[013] [012]

[013] 1

2

2

1

2

1

1

2

1

5

Ex. 11 Stravinsky, Agon, Triple Pas-de-Quatre: motivic construction of bars 97–102 = 2–1–2 motive

[0123]

(C. ni)

[0123] [0123]

[0123]

[0123] [0123]

[0123] [0235]

[0123]

[0123] [0235]

[0123]

[0123] [0123]

[0123] [0123]

[0123] [0123]

[0123] [0123]

[0123] [0123]

[0123] [0123]

[0123] [0123]

[0123]

[0123]

[0123] [0123]

97–102 of the Triple Pas-de-Quatre, for example, derives from a dense chain of overlapping 2–1–2 motives (Ex. 11).The intervallic orientation of the motives is almost always a zigzag, forming the chromatic set class [0123], but at times (see the circled motives in Ex. 11) the intervals are oriented in the same direction, thus forming the set class [0235] (see again Table 2). 44 By comparison with the rows used in Agon, the motivic structure of the twelve-note rows employed in the compositions which succeed it chronologically appear to be less well defined. Beginning with Movements, Stravinsky seems to have derived many of his twelve-note rows from a reading of a concrete musical idea – most often a brief polyphonic passage.This procedure guarantees that the intervallic motives contained in the initial musical idea are less evident in the related twelve-note row, in which the structural intervals can be found between non-adjacent pitches. This creates a sort of circularity between the two stages into which I have conceptually subdivided the creative process: from a concrete musical idea comes an abstract row of pitches, and on the basis of this row, new



‘C  I’

237

and different concrete musical passages are realised. In effect, Stravinsky appears to open up a wider field of compositional possibilities: if indeed the motivicintervallic structure of the resultant row is more ambiguous, the row more easily presents various musical realisations capable of illuminating different motivicintervallic aspects that are implicit within it. In his last works, Stravinsky hinted at different cases in which the formulation of a twelve-note row could derive from an initial concrete musical idea. 45 Consider for example the following declaration concerning the composition of Epitaphium: I began the Epitaphium with flute-clarinet duet (which I had originally thought of as a duet for two flutes, and which can be played by two flutes ... ). In the manner I have described in our previous conversations, I heard and composed a melodic-harmonic phrase. I certainly did not (and never do) begin with a purely serial idea, and, in fact, when I began I did not know, or care, whether all twelve notes would be used. After I had written about half the first phrase I saw its serial pattern, however, and ... began to work toward that pattern. The constructive problem that first attracted me in the two-part counterpoint of the first phrase was the harmonic one of minor seconds. The flute-clarinet responses are mostly seconds, and so are the harp responses, though the harp part is sometimes complicated by the addition of third, fourth and fifth harmonic voices. (Stravinsky and Craft 1960, pp. 99–100)

Assertions of this sort often find confirmation in the sketches of the compositions from Movements onwards, where one encounters some melodic or contrapuntal annotations which probably served as the model for the formulation of the rows.46 A circumstance of this kind probably explains the origin of the two twelve-note rows employed in the Requiem Canticles, which Stravinsky explicitly attributed to ‘some intervallic designs which I expanded into contrapuntal forms’.47 The ‘intervallic designs’ to which this quotation alludes can be found among the sketches for the instrumental Interlude – which in actuality was the first movement in chronological order of composition. 48 The amount of preparatory material which survives for the Interlude is uncommonly large, considering the Stravinskian standard: more than twenty small sheets and strips of paper of different sizes, forms and typologies for a passage lasting only 67 bars.49 Some sketches contain only one or two brief musical phrases, mostly corresponding to the exposition of a single form of row I or row II (or of one of their constituent hexachords). Other pages assemble their content from various earlier sketches. The final form of the passage thus results from a sort of montage of single ideas which had been elaborated individually in the first stages of composition. Comparison of these versions, together with analysis of the various written materials employed and the autograph dates placed by Stravinsky on some pages, allows for chronological reconstruction of the sketches for the Interlude with a good degree of certainty. 50 One of the very first ideas notated by Stravinsky is reproduced in Ex. 12a. It is formed Music Analysis, 28/ii-iii (2009)


238

 

Ex. 12a Stravinsky, sketches for Requiem Canticles, Interlude (Paul Sacher Foundation, Igor Stravinsky Collection) I 0 3

[ ]

II 0

Ex. 12b Motivic analysis of the musical ideas contained in the sketches of Ex. 12a 3

F 5

C 1

5

D 5

A

B

A

[016]

[015]

1

5 5

D G C F

G 1

F

2

E [013]

G

1

F

1

E

1

F

2 1

[013]

C 2

E D [013]

2

B

D

1

C

1

2

C 1

[012]

A 2

G

1

A

B [013]

[012]

from the union of two brief contrapuntal phrases based on the two original rows employed in the movement, as indicated by the autograph serial symbols. 51 The two phrases, initially notated separately on two small clippings of paper, were then pasted onto a piece of cardboard (the continuity between the two phrases is indicated by Stravinsky’s autograph arrow).52 These phrases correspond respectively to bars 161–162 and 173–175 of the score, of which the clippings preserve a very rudimentary version. In the following sketches, Stravinsky added new musical material between the two phrases, which are at the same time then gradually reshaped. To this extended musical passage thus obtained (bars 163– 172) Stravinsky subsequently added bars 176–192, thus creating the entire episode for four flutes (bars 161–192), the largest and most important formal section of the piece. In summary, it seems that the two musical ideas contained in the sketches transcribed in Ex. 12a were indeed the point of departure in the composition of the Interlude. If this is so, they may well feature the original ‘intervallic designs’ to which Stravinsky alludes in the statement quoted above. In fact, the contrapuntal relations of the two musical phrases illuminate a very clear © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

239

motivic-intervallic construction, based on the 1–2 and 1–5 motives (Ex. 12b). The triplet in the first crotchet of the second phrase, shown on the right in Ex. 12b – probably composed first 53 – presents within itself a sort of polyphony: the lower ‘part’, delineated by the pitches F–G–E placed in the same register, produces a 1–2 motive; the D  of the upper ‘part’ forms, however, a relation of a semitone with the lower E. By holding these two pitches firm and adding the F , another 1–2 motive is obtained in the second crotchet of the phrase, this time vertically (D –E–F). Furthermore, the two motives (E–F–G and D  –E–F) are separated by the distance of a semitone. In the remaining part of the phrase, three overlapping 1–2 motives, in both [012] and [013] forms, are unfolded horizontally. In the first phrase (reproduced on the left in Ex. 12b), the first two vertical simultaneities of three pitches form two motives of class 1–5 – respectively in the forms [016] and [015] – while the following group of four pitches delineates a cycle of three ic5s (C  –D –G –F), divided symmetrically into two (F –C in the bass; G –D in the upper parts). The last vertical sonority of three pitches (F –E–G) forms a 1–2 motive which creates a strong link with the following phrase, beginning with the motive F–G–E, another member of the 1–2 motivic class. The link – illustrated also by Stravinsky’s cue in the upper righthand corner of the first sheet of Ex. 12a – is reinforced by the presence of pitch classes E and G in both of the motives. The ‘intervallic designs’ contained in the two ideas thus become relatively clear.We might ask at this point which came first, these two musical ideas or the two twelve-note rows – whether, in other words, the rows were obtained from the musical ideas or could instead have been fixed in advance as an abstract sequence of pitches on the basis of which the musical ideas were subsequently elaborated. The fact that the two musical ideas contain all twelve notes without repetition does not mean we must prefer the second solution: generally speaking, in fact, we may suppose that Stravinsky initially elaborated his musical ideas following a predominantly motivic-intervallic logic, and although even at this stage – of which, however, hardly any written traces remain – he tended to exploit all twelve notes of the chromatic gamut, that did not prevent him from using some pitches more than once. Only in the final formulation of the idea were the repetitions eliminated until a fundamental twelve-note row was obtained.This is clearly demonstrated by an important document to which Joseph Straus has drawn attention:54 the photographs taken in 1967 by Arnold Newman in Stravinsky’s Hollywood studio.55 Like the stills of a film, Newman’s photographs record step by step the creation of a musical idea – a brief instrumental passage – and its successive transformation into a twelve-note row. 56 According to Straus, the musical passage reveals, above all else, some semitone-tone motives belonging to set class [013]. 57 From my point of view, conversely, the rethinking which took place in the course of elaboration was determined by a motivic idea of the semitone–major third type (1–4) in its two possible forms, [014] and [015]. In the very first bar, Stravinsky notated a portion of an Allintervallreihe (all-interval row; Ex. 13a) – as Music Analysis, 28/ii-iii (2009)


240

 

Ex. 13a–g See Arnold Newman’s photos, reproduced in Craft (1967), pp. 14–15 and 16–17. The sequence of photos goes across the volume’s two-page spreads of the sketches; photos 1 and 2 are on p. 14, photos 3 and 4 on p. 15, and so on (a) stage 1 (cf. photos 1–10)

(c) stage 3 (cf. photos 14–17)

(e) analysis of stage 5 (cf. photos 18–25)

3

E G 5

5

E

(b) stage 2 (cf. photos 11–13)

D 2

D

2

[025]

[3]

A [027]

3

(d) stage 4 (cf. photos 18–20)

inverted

3

(g) analysis of stage 4 G

4

D

4

D

B

B 1

B

D

4

B

1

4

D

1

B

4

A

1

G 1

4

E

B

1

D 1

4

E E

A

[3]

(f) analysis of stage 3

D [015]

G 1

B

D

4

A

1

G

4

E [015]

[015]

F [015]

F 3

[014]

[015]

[014]

[014]

[015]

3

[3]

[3]

Straus also observes. In the next stage of composition (Ex. 13b), he abandoned this initial idea to compose a brief counterpoint between two voices, without attempting to avoid the repetition of pitches (note the initial pitches B and C, repeated at the close of the passage). The third stage reveals the first significant stage of rethinking: comparing Ex. 13b with Ex. 13c, observe that Stravinsky replaces the first of the two Cs with an E, thus avoiding the presence of repetition. The choice of E throws light on the motivic-intervallic logic which guides the composition of the passage: the first three notes of the viola (B–E  –B) now form a motive of the semitone–major third type (1–4). This motive – in its two forms, [014] and [015] – appears at numerous other points within the passage: in the first five notes of the viola part (twice: B–E –B and B –D –A, with B in common); in the last three notes of the cello (B  –G –F), grouped together as a triplet; between the first two notes of the viola (B–E ) and the D of the cello which follows immediately afterwards (a semitone lower); and finally in the contrapuntal relationship between the B  –D of the viola and the D of the cello (Ex. 13f). There is a second significant redrafting at the following stage (Ex. 13d), where Stravinsky replaces the first and the third notes of the viola (B and B ), both repeated, with G and A respectively. By making this adjustment, Stravinsky not only obtains all twelve notes without repetition, but also preserves intact the © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

241

motivic construction of the passage, which remains based on the conspicuous presence of a 1–4 motive – now in the form [015] (Ex. 13g). The third and final phase of development occurs in the final stage (Ex. 13e), at the end of which Stravinsky obtains a twelve-note row, arranging in succession the notes of the passage just composed. 58 Here a small adjustment in the order of the pitches suffices to mask the original motivic-intervallic aspect of the passage while at the same time illuminating a new one. The second and sixth pitches (E and E) are inverted (see the circled notes in Ex. 13e). Thus, the first two segments of three pitches (G–E–D and A –D –E) become two motives of the class 2–5. Moreover, the four segments of three pitches which form the row delineate a symmetrical structure: the combination of the even-numbered segments forms a partial circle of fifths from G  to F, while the combination of the odd-numbered segments forms the remaining part of the circle (from C to B): 59 1. E –D –A (segment 2) + B –G –F (segment 4) = G –D –A –E –B –F; 2. G–D–E (segment 1) + A–B–C (segment 3) = C–G–D–A–E–B. In the end, the simple exchange of E with E  in the final row creates, in this case, a marked estrangement of the motivic-intervallic construction of the original musical idea.60 From the Row to Intervallic Motives At this point it is worth reflecting on the ways in which motivic-intervallic logic influences the musical concretisation of the row, once it has been definitively established. I will first consider a brief musical fragment drawn from the beginning (bars 46–48) of the second of the five Movements (Ex. 14a and b).61 The passage is based on the two discrete hexachords (labelled a and b) of the fundamental row Ex. 14a Stravinsky, Movements, ii: hexachordal forms employed in the sketch shown in Ex. 14b [016]

[016]

Hexachord α 1

2

3

4

[016]

5

6

[016]

RI (T6 ) 1

2

3

4

[012]

5

6

[012]

Hexachord β 1

2

3

4

[012]

5

6

[012]

R 1


2

3

4

5

6


242

 

Ex. 14b Stravinsky, sketches for Movements, ii (cf. bars 46–48 of the printed score) (Paul Sacher Foundation, Igor Stravinsky Collection) 5

6

4

3

1

2

1

2

3

4

5

6

Riv-Inv α

Riv β 3

6

Riv- Inv

1 2

4

5

Riv. 2

1

3

4

5

6

used throughout the entire composition (Ex. 14a, first and third lines). In the upper part of the sketch transcribed in Ex. 14b, Stravinsky wrote the RI (T 6) form of hexachord a and the R form of hexachord b (Ex. 14a, second and fourth lines) – as indicated also by the autograph labels ‘Riv-Inv a ’ and ‘Riv b ’.62 As my analysis in Ex. 14a shows, hexachord b can be divided into two trichords belonging to set class [012], which can in turn be related to motive class 1–2 (see again Table 1). Hexachord a is formed by two trichords of set class [016], which can be related to three different intervallic motives: 1–6, 1–5 or 5–6. In this case, Stravinsky clearly placed the intervals of a semitone and perfect fifth (motive 1–5) in relief. To this end, a particular permutation of the order of the pitches of hexachord a is carried out:63 besides placing the pitches in reverse order (from the sixth to the first), he also reversed the order of the first two pitches of each trichord. In this manner the pitches which form ic5 (represented in bold in the schema below) are always adjacent: 6–5–4/3–2–1 becomes 5–6–4/3–1–2 (G –F – C/D– D – A becomes F – G – C/D– A – D). The purpose behind this particular reordering can be appreciated in the musical passage outlined in the sketch transcribed in Ex. 14b, immediately below the two hexachords: the pitches which form ic5 are arranged vertically as a perfect fifth; the pitches which form ic1 precede the fifth in a register at the distance of an octave. The two fifths (C–G/D –A) are separated by a semitone, thereby producing a symmetrical configuration. All these choices are clearly intended to throw the ic1 and ic5 into relief. © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

243

Ex. 15a Stravinsky, first page of the short score for Requiem Canticles, ‘Rex tremendae’ (compare bars 203–207 of the printed score) (Paul Sacher Foundation, Igor Stravinsky Collection) I R α

β

S

Rex

Rex

tre

me n

da e

inv α 3 rd

I 1 2 3

3 1

Verticals

ma je

4 5 6

sta tis 3 Fl

A 4 5 6

Rex

4

vla vc cb

T 8

Rex

6

B

3

rd

line

3 Fl

[ ] I

inv α 1st line

vlc

Strings

[ ]

vc

6th line I

R α 5 th 3 trmb

I

inv α 4 th line

3 rd line

β5 4

th

5

st

Rα1

6

5

4

5

6

4

This brief example shows how some operations which alter the physiognomy of the row were intended by Stravinsky to facilitate the transformation of an abstract row in a specific musical passage which highlights some particular motivic-intervallic characteristics. One such operation is order permutation, as we have just seen; another consists of extrapolating small segments, usually of two to four notes in length, and successively reconfiguring them. This technique, which I call serial fragmentation-recombination, was probably adopted for the first time by Stravinsky in Threni and was subsequently used in an increasingly sophisticated fashion.64 We have already observed one application, albeit a rather limited one, in the ‘Dies irae’ of the Requiem Canticles. To further illustrate its function in relation to the motivic-intervallic syntax, I will now consider its use in the first part of the ‘Rex tremendae’ of the Requiem Canticles. The serial construction of the passage is clearly illustrated on the first page of the autograph short score (containing bars 203–208), transcribed in Ex. 15a. 65 The symbol ‘I R a’ stands for row number I, retrograde form, hexachord a .The Music Analysis, 28/ii-iii (2009)


244

 

Ex. 15b Stravinsky, Requiem Canticles, twelve-note row I: rotational arrays of the hexachords a and b of the retrograde form, with encircled serial segments employed in the sketch of Ex. 15a Row I – Retrograde

α

β

1

2

3

4

5

6

circled numbers at the beginning of each choral part in the short score indicate the lines of the rotational arrays of the first hexachord. Only limited portions (three to five notes) of each line are used (shown circled in Ex. 15b).The zigzag line traced across the choral parts 66 corresponds to the brass part (trumpet and trombone) elaborated on the lower portion of the page. The autograph symbols indicate that even this line was obtained by the combination of three serial segments drawn from the two rotational arrays of the R hexachords. For example, the symbol ‘R a 5th 3 4 5’ stands for retrograde, hexachord a , fifth line of the rotational array, notes 3–4–5 (see also Ex. 15b, where the segments used in the brass part are indicated within boxes). In sum: the first three bars 67 of the choral part and the brass parts are obtained exclusively through a combination of serial segments extrapolated by two rotational arrays produced by hexachords a and b of the retrograde form of row I. As in the case of the ‘Dies irae’, the segments are selected in an apparently arbitrary manner. Nevertheless, they demonstrate a significant presence of motives of class 1–2: four of the five segments of three-note segments (R a 1st 4–6, R a 4th 4–6, R a 5th 3–5, R a 6th 4–6 and R b 5th 4–6) directly correspond to this motive class; one of the two segments of five notes (R a 3rd 2–6) contains two overlapped 1–2 motives (C –C –C + C–B–A); and the other (R a 1st 1–5) begins with a 1–2 motive. The reason for this arrangement was Stravinsky’s desire to create an imitative texture based on the motivic-intervallic element: at regular intervals of a minim the contralto, the trombone, the sopranos and the tenors display motive 1–2; but because this motive can assume two different forms – [012] and [013] – and given that the three pitches can be combined in any order, the imitative responses repeat neither the same melodic profile (as in traditional imitative style) nor the © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

245

Ex. 16 Stravinsky, Movements, i: subset structure of the original twelve-note row α

β

[016]

[016]

[012]

[012]

Orig. [012]

[016]

same set class. Therefore, motive 1–2 is repeated three times in the brass part which runs throughout the choral passage. Note also that the initial pitches of each imitative part (A –G –D –F) gradually take the form of a sequence of perfect fifths (F –C –G –D –A), which is completed in bar 3 with the addition of the pitches G and C in the bass part. This homogenous motivic design is due largely to the structure of the row itself. Indeed, it should be evident that numerous 1–2 motives are already contained in row I of the Requiem Canticles (see again the right-hand section of Ex. 12b). Nevertheless, by segmenting the hexachords selectively, Stravinsky created an imitative texture which was more coherent than would have been possible had he used complete hexachords. One might ask in what sense and to what degree such a procedure could be defined as authentically serial. However, the fact that the composer had indicated the serial origin of the various segments in the short score demonstrates that he conceived of the row as a reservoir of motivic-intervallic material, and that he understood serial technique as a means of managing this material systematically. The beginning section of the first of the five Movements (see again Ex. 6) is likewise based on a systematic application of serial fragmentationrecombination. The passage divides into an initial introduction (bars 1–6) and three solo episodes for, respectively, piano, first flute (accompanied by piano and clarinet) and piano again (accompanied by strings).The central flute solo is very familiar to Stravinsky scholars; indeed, the composer himself drew attention to its complex serial construction, thereby instigating a long series of attempts at analysis.68 As I will try to show, a motivic-intervallic approach can provide a new and logical key to reading the passage. To this end, it is useful to begin with the subset structure of the two hexachords of the fundamental row (Ex. 16). The first hexachord is formed by two disjunct trichords belonging to set class [016]. In the middle, starting with the third note, one finds a trichord of set class [012].The second hexachord contains two disjunct trichords of set class [012] and one [016] trichord at its centre, thus complementing the first hexachord. Other interesting properties of the two hexachords emerge when one takes into consideration their rotated forms. Ex. 17 cites one of the rotational arrays employed by Stravinsky for the composition of Movements: columns a and b contain the rotated forms of the two hexachords of the original form of the row; columns g and d display the rotatedtransposed forms. Ex. 18 reveals the subset structure of all these rotated (-transposed) forms. Eight of the twelve hexachords contain within them three Music Analysis, 28/ii-iii (2009)


246

 

Ex. 17 Stravinsky, Movements, sketch showing the rotated (columns a and b) and rotated-transposed (columns g and d) forms of the two hexachords of the original twelve-note row (Paul Sacher Foundation, Igor Stravinsky Collection)

α

β

γ

δ

I

II

III

IV

V

Ex. 18 Stravinsky, Movements: subset structure of the rotated-transposed forms of the two hexachords of the fundamental row γ

δ

[016]

[016]

[012]

[012]

Orig. [012]

[016] [016]

[016]

[012]

I [012]

[016] [016]

[016]

[012]

II [012]

[012]

[016]

[016]

[016]

[012]

[012]

[016] [016] III [012]

[016]

[016] [016]

[012]

IV [012]

[016]

[016]

[012]

V [012]

[012]


[016]

[016]


‘C  I’

247

Table 3 Chronology and serial origin of the three episodes in Stravinsky’s Movements, i, bars 7–22 Episodes (in chronological order)

Twelve-note material employed

bb. 13–17: second episode (solo for flute I)

Serial segments drawn from columns g and d of the rotational array of the hexachords. The entire succession is transposed T4 to G. The accompaniment uses complete hexachords.

bb. 7–12: first episode (first solo episode for piano)

The same serial segments from the flute solo but transposed T2 (on F).

bb. 18–22: third episode (second solo episode for piano)

The same serial segments from the flute solo, not transposed (on E).

trichords belonging to set class [016] or [012]; two hexachords (II g and IIIg ) contain four which closely overlap with one another. The remaining two hexachords (Id and IVd) contain two each. It is evident, therefore, that the internal structure of the two hexachords is such that the rotated forms generate a large number of trichords belonging to set classes [012] and [016]. Now, set [012] can be understood solely as a 1–2 motive with the intervals arranged in opposite directions, 69 while set [016] could be associated with three different motives: 1–5, 1–6 or 5–6 (see again Table 1). A deeper analysis will clarify which of these intervallic motives was the object of Stravinsky’s interest. With the aid of the sketches, I have reconstructed the chronology and serial origin of the three episodes which form the entire section, summarised in Table 3.70 As can be seen, all three episodes are based on a combination of serial segments chosen from columns g and d of the rotational array. The serial segments employed for the second episode, the flute solo (bars 13–17), are indicated in the sketch transcribed in Ex. 19a; the symbols here refer to the sketch with the rotational array transcribed in Ex. 17 (the Greek letters refer to columns g and d of the array and the roman numerals to the lines; the arabic numeral indicate the selected segments). The 34 notes of the flute melody (Ex. 19a) are obtained by combining ten serial segments, freely chosen from the array (Ex. 19b). In the final version (Ex. 19c), the melody thus obtained was completely transposed a major third higher (T 4) to start on G instead of E . In the third episode (bars 18–22; see Ex. 20) the piano and string parts employ the same serial segments as the flute solo, as is suggested by the serial symbols and the indication ‘follow the flute solo before (same series)’ in the short score; however, this time it is not transposed (compare Ex. 20 with Ex. 19b). The first episode (bars 7–12; Exs. 21 and 22) is essentially based upon the same succession of serial segments, even if in the final version the resulting correspondence is obscured owing to some errors Stravinsky committed in the Music Analysis, 28/ii-iii (2009)


248

 

Ex. 19a Stravinsky, sketches for Movements, i, bars 13–17 (Paul Sacher Foundation, Igor Stravinsky Collection) Iγ 1

Iδ 2

3

4

Vδ 5

6

1

V γ

2

3

1

III δ

2

3

3

III γ [4] 5

6

4

5

II γ 6

4

γ

III

5

6

4

5

I γ 6

[ ]

3 [4] 5

II δ 6

2

3

4

5

6

[ ]

Ex. 19b Columns g and d of the array reproduced in Ex. 17 (hexachordal rotatedtransposed forms), with encircled serial segments employed in the sketch shown in Ex. 19a γ

δ

Orig. 1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

I

II

III

IV

V

Ex. 19c Final version of the flute solo in bars 13–17 showing the serial segments employed in it γ I 1–3 (T4 ) δ I 4–6 (T4 )

δ V 1–3 (T4 ) γ V 1–3 (T4 )

δ III 3–6 (T4 )

γ I 4–6 (T4 )

γ II 4–6 (T4 ) γ III 4–6 (T4 )

γ I 3–6 (T4 )

δ II 2–6 (T4 )

Fl. I

preparation phase. On the first two lines on the page of sketches transcribed in Ex. 21, up to the pitches B–C–D before the notated clefs, the composer had initially outlined a first version of the passage transposed to begin on G, in a manner identical to the final version of the episode for flute. Ex. 22 presents this first version together with the related serial symbols derived from his autograph short score. As is evident by comparing Ex. 22 with Ex. 19c, Stravinsky obtained exactly the same pitches as the final version of the flute episode by utilising only slightly different serial fragments. 71 Up until this point, therefore, the first piano episode corresponds exactly with the flute solo, with respect to pitch content. At a later point, represented in lines 6–9 of the sketch in Ex. 21, Stravinsky elaborated a second version – different from the first in both rhythm and the octave registration of some pitches – transposed to begin on F instead of G. Later, after © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

249

Ex. 20 Stravinsky, Movements, i, bars 18–22 γ I 1–3

δ I 4–6

δ V 1–3

γ V 1–3

δ III 3–6

γ I 4–6

γ II 4–6

γ III 4–6

γ I 3–6

δ II 2–6

, 3

18

19

20

21

2

1

3 2

r.h.

3

Piano l.h.

3

22

Vle.

{ pizz .

{ sim.

3

Vc. (non div.)

pizz .

3

C. B. 3

the clefs (where the elaboration of the first version was interrupted) on lines 1–2 of the same page, Stravinsky completed the episode with the final missing part. Although neither the sketch nor the short score presents serial symbols at this point, it is obvious that the segments employed are the same as those used for the last part of the flute episode (transposed by T 2).72 To summarise, the second version of the piano passage stretches in part across lines 6–9, up to the dyad A–B  circled in the middle of the ninth line – which corresponds to the pitches B and C of the preceding version on G, as demonstrated by the vertical line drawn across the page – and in part (following Stravinsky’s arrow) on lines 1–2, to the right of the treble and bass clef. 73 In setting the entire passage in the short score, however, Stravinsky failed to recopy pitches B and C, placed on the first line immediately after the treble clef, perhaps mistaking them for a repetition of the B and C immediately preceding it on the second line – which, however, belonged to the first version on G.Thus these two notes do not appear in the final score. By restoring them, one will easily notice that the entire sequence of pitches in the piano’s first episode corresponds exactly to that of the flute’s solo episode, transposed a tone lower. 74 According to Stravinsky’s initial intent, then, all three episodes were to be based on the same succession of pitches, transposed onto three different levels: G, F and E. It was most likely in this manner that Stravinsky sought to obtain something similar to ‘tonal’ organisation on a broader formal plane. 75 However, considerations of this type are beyond the scope of this study.What is important from my point of view is to observe how the intricate combination of serial segments on which the three episodes are based produces a homogeneous and cohesive motivic-intervallic texture. Music Analysis, 28/ii-iii (2009)


250

 

Ex. 21 Stravinsky, page of sketches for Movements, i, bars 7–12 (Paul Sacher Foundation, Igor Stravinsky Collection)

8va

[ ]

5

[

[

]

]

[ ]

[ ]

[

]

[ ]

5

[

] 8 vb va

8

[

[

]

]

[ ]

[

]

[ ] 8 vb

[


]


‘C  I’

251

Ex. 22 Stravinsky, Movements, i (compare bars 7–10 of the printed score). The symbols above the staves represent serial segments drawn from the short score (Paul Sacher Foundation, Igor Stravinsky Collection). Below them is an excerpt (first two staves) from the sketch transcribed in Ex. 21 γ V 3–6 (T 2 ) δ I 5–6 (T4 )

δ V 1–3 (T4 )

γ V 1–4 (T 4)

5

δ III 4–6 (T4 ) γ I 4–6 (T4 )

γ II 4–6 (T4 )

[ ]

To this end, the question which arises is: according to what criterion did Stravinsky select and combine these serial segments? Typically, if one takes into consideration the original hexachords from which the segments were extrapolated, it becomes apparent that a procedure of utilising pivotal pitches is rendered central. For example, the first segment of three pitches ( g I 1–3) is followed by the pitch A  from the middle of its original hexachord g I (see again Ex. 19b). The second segment must therefore begin with this pitch. In its turn, the second segment (dI 4–6), also containing three pitches, is followed,76 in its original hexachord, by the pitch C; thus the third segment must begin with that pitch. The passage consequently unfolds as follows: γ I 1−3 ( −4 )

= E −A−G−( A  )

δI 4−6 ( −1) = δV 1−3 ( −4 ) =

A  −G −D−( C) C−G−G  −( E  )

Nevertheless, this criterion establishes only the first pitch of the following segment and not the internal characteristics of that segment (as the serial table shows, there are different segments which also begin with the same pitch). Moreover, the mechanism of pivotal pitches is employed only in a limited number of cases. A fuller rationale nevertheless emerges if the ten serial segments employed across the three episodes are re-examined in relation to the concept of intervallic motive. Given the structure of the hexachords (see again Exs. 16 and 18), these segments are almost all members of set classes [012] and [016], as Ex. 23 demonstrates (the only exceptions are the two segments indicated by the exclamation marks). All of the four-note segments (nos. 5, 9 and 10) contain overlapping sets [012] and [016], as Ex. 23 indicates. What is intriguing, however, is the global result obtained from the combination of the segments. Ex. 24 examines all of the consecutive three-note groups (bracketed above and below the musical stave) starting from each note of the Music Analysis, 28/ii-iii (2009)


252

 

Ex. 23 Stravinsky, Movements, i: serial segments employed in the succession of pitches contained in each of the three solo episodes of bars 7–22 1

γ I 1–3

2

3

4

5

6

7

8

9

10

δ I 4–6

δ V 1–3

γ V 1–3

δ III 3–6

γ I 4–6

γ II 4–6

γ III 4–6

γ I 3–6

δ II 2–6

[012]

[012] [016]

[016]

[012]

[016]

!

!

[016]

[016] [016]

[016] [012]

Ex. 24 Stravinsky, Movements, i: intervallic motives in the succession of pitches contained in each of the three solo episodes of bars 7–22 [012] [012]

!

[016] [016]

!

[013]

[016] [016]

!

[016]

[012]

[013] [012]

[016]

[016] [016]

[016]

[016]

1–2 motive

2 1

6

(5)

[016] [016]

[013]

[012]

!

!

[016]

!

1 [012]

6

[7] = 5

2 1

[013]

[012]

!

1–6 motive

(1) (3)

[012] [012] [016]

1 [016]

[016]

complete succession of pitches: 77 with the sole exception of seven groups (indicated by the exclamation marks), all of the trichords belong to set class [012], [013] or [016]. These set classes, in turn, can be obtained from only two motivic-intervallic classes; set classes [012] and [013] are, in fact, the two forms assumed, according to the orientation of the two intervals, by the characteristic tone-semitone motive (1–2). It is important to note that the [013] form of this motive is not included in the serial hexachord, which contains only the [012] form (see again Exs. 17 and 18). The presence of form [013] in the succession of pitches on which the three episodes are based is therefore the result of a collection of serial segments created ad hoc, which clearly demonstrates how the technique of serial fragmentation-recombination permitted the composer to generate different motivic forms without limiting himself to those contained in the row. Set class [016] could have been generated by three different motivicintervallic classes: 1–5, 1–6 or 5–6 (see again Table 1). Nevertheless, the form [015] of motive 1–5 – obtained by orienting the two conjoined intervals in opposing directions – never appears in the entire succession of pitches, which suffices to exclude it as a possibility. Of the remaining two motives (5–6 and 1–6), it is more logical and economical to think primarily in terms of motive 1–6 since the entire passage can then be read from the point of view of only three interval classes – ic1, ic2 and ic6 – contained in motives 1–2 and 1–6. It is evident, therefore, that the selection and arrangement of the serial segments was done in such a way as to obtain a continuous interlocking of two © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

253

motivic classes (1–2 and 1–6), 78 generated by just three interval classes (ic1, ic2 and ic6). The use of complete serial forms (twelve-note rows or hexachords) would not produce so dense and coherent a fabric: hence the exigency of fragmenting the hexachords into smaller units, which can then be recombined at will.

Conclusions In the evolution of compositional technique which runs from the melodic chains of Agon to the complex combinations of serial segments in Movements or the Requiem Canticles, it is possible to discern a continuity of thought centred on the problem of interaction between motivic-intervallic syntax and twelve-note technique. In Agon, the motivic-intervallic logic determines, above all, the construction of ordered sets, the combination of which gradually forms larger agglomerations, employed in their turn as fundamental rows. In later compositions, the row confronts a continuous motivic rereading, whether through different means of musical realisation or through fragmentation into small groups of pitches, which are then recombined into new configurations. Examination of the creative process reveals that the tendency towards disintegration resulting from the direct manipulation of single intervals is not incompatible with serial technique, providing the latter is understood in a creative rather than a strictly procedural sense. Stravinsky’s adoption of serialism relies upon an aesthetic vision which does not attribute to the row the value of a fundamental Gestalt for the composition. The same can be said of Stravinskian motivic-intervallic syntax, at the base of which lies an aesthetic conception foreign to the ideal of organic coherence which characterises the Austro-German tradition. The idea that intervallic configurations should provide a unifying function for the general internal relations which govern an entire composition – a function comparable to that of traditional tonality – is largely alien to Stravinsky’s approach, which conceives of the intervallic motives simply as starting materials for the act of musical construction. This creative process consequently proceeds from the particular to the general, following an itinerary open to deviations and metamorphoses which are realised through continuous motivic-intervallic rereading of both the precompositional row and its concrete musical correlates. The elementary materials (the intervallic motives) from which this mode of construction primarily derives evidently leave a mark, a recognisable impression on the final physiognomy of the musical edifice, without, however, assuming a determining role with regard to structural connection. To what degree and at what level this impression is discernible and perceptible is a question which evidently remains open. Whatever the answer, we must not lose sight of the essential significance of working with intervals that characterised Stravinsky’s musical thought. Music Analysis, 28/ii-iii (2009)


254

 

NOTES This article derives, in large part, from my doctoral thesis (Locanto 2002). All transcriptions and facsimiles are published with the kind permission of the Paul Sacher Foundation in Basel. The sketch transcriptions aim to reproduce the originals as faithfully as possible: all of the author’s annotations are either enclosed within square brackets or signalled in the accompanying captions. Since the numbering of the microfilms in the Paul Sacher Foundation may change from time to time, items are identified here not by microfilm number, but by the collection to which they belong and the type of material (sketch, short score, full score, etc.). In the case of the sketches for the Requiem Canticles, for which a microfilm copy has not yet been made, I refer only to the collection to which it belongs. Copyright clearance for musical examples was secured from the following sources: Stravinsky, Requiem Canticles © copyright 1967 by Boosey & Hawkes Music Publishers Ltd., reproduced by permission of Boosey & Hawkes Music Publishers Ltd.; Stravinsky, Movements © copyright 1960 by Hawkes & Son (London) Ltd., reproduced by permission of Boosey & Hawkes Music Publishers Ltd. 1.

See for example Stravinsky and Craft (1959), p. 11: ‘I begin work by relating intervals rhythmically’. (See also Stravinsky and Craft 1966, pp. 60–1, on the Variations, and Craft 1972, p. 98, on the Requiem Canticles.) In an interview with Jay S. Harrison in the New York Herald Tribune, 21 December 1952 (cited in Tucker 1992, vol. 2, p. 187), Stravinsky emphasised: ‘Always I have been interested in intervals. Not only horizontally in terms of melody, but also the vertical results that arise from the combinations of intervals’.This point has been strongly endorsed by Milton Babbitt: ‘One of the remarkable things that Stravinsky said, when people felt that he committed a treasonable act by starting to write pieces where you could find a succession of twelve [notes] at the beginning, was “There’s nothing to it; I’ve always composed with intervals”. Basically, of course, it was something of a witticism, but what it did show, much more than a witticism, was how profoundly this is an interval kind of syntax and not just a pitch-class syntax – fundamentally and centrally an interval syntax’ (Babbitt 1987b, p. 20; see also Babbitt 1968, p. 167).

2.

On these topics, see especially Berger (1963), van den Toorn (1983) and Taruskin (1996), pp. 255–307. On the use of other non-diatonic collections in Stravinsky’s music, see also Johnson (1987), Tymoczko (2002) and van den Toorn and Tymoczko (2003).

3.

After Threni , the systematic use of diatonic collections, which characterised even Stravinsky’s earlier serial compositions, is noticeably reduced in favour of more markedly chromatic situations, even if the latter contain a diatonic core (see Locanto 2002, pp. 177–212). On the diatonic component in serial compositions up to Threni , see Neidhöfer (1999). Taruskin (1993) and (1996), pp. 1648–73, has hypothesised the persistence, up to the final serial compositions, of a similar routine based on the use of octatonic collections. More recently this idea has been placed in a markedly different perspective, especially by Straus (2001), p. 39 and n. 79.

4.

On the use of intervallic motives in Stravinsky’s pre-serial music, see for example Straus (1991).



‘C  I’

255

5.

The underlying theoretical perspective is neatly summarised by Wason (1996), p. 111: ‘In tonal music, motivic events are generally regarded as intervallic relationships, whose actual pitch-class representations change with reference to a fixedpitch background – the tonal centre itself, or a related tonal region which temporarily comes to the fore. In so-called “atonal” music, that background is presumably absent, leaving us with only the intervallic relationships – the immediate object of most analytical investigations of this repertoire’.

6.

For example, Straus, in attributing a basic role to the manipulation of single intervals, defines the concept of motive in a way which differs from the definition offered here. For him, a motive results from the combination of a limited number (usually two) of ‘atomic’ intervals (one of which is generally a tone or semitone).Through the choice of an appropriate transpositional level, these intervals produce particular sets (see Straus 2001, pp. 82–92), which are then used as motives in melodic construction (Straus 2001, pp. 92–103). In this case, a motive, although initially obtained by a particular combination of elementary intervals, corresponds to a set of pitch classes which could be represented in retrograde, inverted or reordered, but would continue nonetheless to belong to the same class. From my point of view, on the other hand, a motive is created by a variable configuration of intervals which can produce sets belonging to different classes. Furthermore, Straus conceives of motives in an exclusively melodic sense: his analyses demonstrate the use of motives only in the horizontal dimension. To my mind, however, the pitches produced by a particular arrangement of basic intervals can be situated either horizontally – in any order – or vertically. As an example of the different results to which these two approaches can lead, see n. 40.Yet another approach is adopted by Smyth (1997), pp. 21–3, which considers interval types (not interval classes). See also Smyth (1999) and (2000).

7.

As other documents also demonstrate: see for example Stravinsky and Craft (1959), pp. 11–12: ‘This exploration of possibilities is always conducted at the piano. Only after I have established my melodic or harmonic relationships do I pass to composition. Composition is a later expansion and organisation of material ... . I start to look for this material, sometimes playing old masters (to put myself in motion), sometimes starting directly to improvise rhythmic units on a provisional row of notes (which can become a final row)’. Other sentiments of this type can be found in Stravinsky and Craft (1962), p. 52, where the keyboard is described by Stravinsky as ‘the center of my life and the fulcrum of all my musical discoveries’; in Stravinsky and Craft (1966), pp. 23–4 and n. 8; and in Craft (1972), p. 131. See also the testimony of Nicolas Nabokov (1949), p. 146, along with that of Stravinsky himself in the documentary A Conversation with Igor Stravinsky, directed and produced by Robert D. Graff for the National Broadcasting Company in 1957 (the passage in question is transcribed with commentary in Tucker 1992, vol. 1, p. 23).

8.

In this study, the prime forms (see Straus 1990, pp. 41–2) of unordered sets are represented by a sequence of numbers – each of which stands for a pitch class – between square brackets, arranged according to the conventional criterion discussed in Straus (1990), pp. 41–2. Ordered sets are, however, represented by a numerical sequence in angle brackets which follows the actual order of the notes. For example: the succession of notes B  –A–C–B belongs to set class [0123]; considered as an ordered set, however, it would be represented as <1, 0, 3, 2 >.

9.

For a definition of interval class see Straus (1990), pp. 6–8. In this study, interval classes are indicated in the orthodox manner by ‘ic’ followed by an arabic numeral



256

 

indicating the interval class measured in semitones. The terms of traditional tonal theory, when used, refer – unless otherwise indicated – to interval classes. For reasons of space, in most of the musical examples the ‘ic’ is omitted and the intervals are indicated by arabic numerals alone. 10.

See Straus (1990), pp. 128–30.

11.

This allows different row forms to project set class [0126] using the same global pitch-class content, a property which Berg exploits to create a network of formal relations.

12.

This concerns, in essence, the phenomenon of pitch-class invariance, to which Milton Babbitt drew attention in a fundamental collection of essays; see in particular Babbitt (1960) and (1961). On invariance see also, for example, Lewin (1962) and Beach (1976).

13.

On which there is an extensive body of literature; for an overview, see Perle (1991), pp. 98–9.

14.

The example is based on Webern’s autograph row chart transcribed in Bailey (1996), p. 196.

15.

It is instructive to compare this definition of intervallic motive to the following affirmation of Stravinsky’s: ‘Always I have been interested in intervals. Not only horizontally, in terms of melody, but also the vertical results which arise from the combinations of intervals’ (see again n. 1).

16.

Since I am considering unordered pitch-class intervals, it may seem senseless to speak of their ‘direction’ or ‘orientation’. However, the intervallic motives which are the focus of my interest here always result from the union of two (or more) conjoined intervals, for which these terms refer simply to the orientation assumed by the intervals relative to each other. In fact, two conjoined intervals united in the same direction produce a third interval corresponding to their sum (such as ic1 and ic4, which together produce ic5 in Ex. 4) and, conversely, two conjoined intervals united in opposite directions produce an interval corresponding to their difference (such as ic1 and ic4, which together realise ic3 in Ex. 4). This is represented graphically by the arrows in my examples, in which the pc sets are conventionally arranged in their normal form from lowest to highest (for a definition of ‘normal form’ see Straus 1990, p. 27).

17.

From here on, the intervallic motives will be represented by two or more arabic numerals (corresponding to the interval classes) separated by a dash (–) and ordered, only as a convention, from the smallest to the largest. For example: 1–2 indicates a motivic class which includes the following possible configurations: <+1, +2>, <+1, -2>, <-1, +2>, <-1, -2>, <+2, +1>, <+2, -1>, <-2, +1>, <-2, -1>. In what follows, I will often use, for the sake of simplicity, the term ‘motive’ in the more precise sense of ‘motive class’.

18.

See in particular Table 1.

19.

See for example the definition given in Schoenberg (1967), p. 8. According to Dahlhaus (1986), p. 283, the concept of ‘motive’ which correlates with the Schoenbergian idea of ‘developing variation’ essentially concerns only the intervallic aspect. Nevertheless, in Schoenberg’s pedagogical writings, the motive is conceived



‘C  I’

257

always as a complex of different interconnected aspects (intervals, rhythm, metrical position, dynamic level, and so on). See for example Schoenberg (1995), pp. 168–71. 20.

In Stravinsky’s own words: ‘I begin work by relating intervals rhythmically’ (see n. 1).

21.

See Sichardt (1990), pp. 30–52.

22.

See for example the motives identified by Sichardt (1990), pp. 50–2, in the compositions and fragments dating from the years immediately preceding 1919.

23.

See Boss (1992), pp. 125–50.

24.

See Boss (1994), pp. 194–6.

25.

It is more difficult, especially in twelve-note music, to establish whether (and, if so, to what extent) motivic elaboration, applied in the sense of the Schoenbergian concept of developing variation, also confers a teleological orientation on the musical discourse, as maintained, for example, in Haimo (1997).

26.

See for example Perle (1991), pp. 9–38, in particular his analyses of Schoenberg’s Op. 23 No. 1, based on a minor third–semitone cell. A ‘cell’ is defined by Perle (p. 9) as a group of pitches which ‘may operate as a kind of microcosmic set of fixed intervallic content, statable either as a chord or as a melodic figure or as a combination of both’.The difference between this and my definition of ‘intervallic motive’ is obvious.

27.

The same thing can be said of the cells which, according to different authors (see especially Perle 1955, Treitler 1959 and Antokoletz 1984, pp. 78–137), play a determining role in the music of Béla Bartók. Nonetheless, Bartók’s use of intervallic cells presents some analogies with Stravinsky’s practice, especially in the preference for symmetrical aggregates (see for example the cells labelled X,Y and Z in Treitler’s analysis). Different theoretical aspects concerning the use of intervallic cells in the music of Bartók are addressed in Antokoletz (1984), p. 16 n. 27 and pp. 78–137.

28.

This is because the tritone subdivides the octave into two equal parts.

29.

The global intervallic content of a set class is represented synthetically by the ‘interval vector’ defined in Forte (1972), p. 179.

30.

In order to obtain all of the set classes produced by the union of three different intervals, one can proceed as follows. For each of the six permutations of the three intervals (1–2–3, 1–3–2, 2–1–3, 2–3–1, 3–1–2, 3–2–1) all of the possible arrangements of their directions (ascending or descending) are formed (four: <+ + +>, <+ + ->, <+ - +>, <+ - ->). (Note: the four arrangements with initial descending intervals produce sets of the same classes as the four preceding arrangements,of which they are simply inversions.) The number of set classes thus obtained will not necessarily be 6 ¥ 4 = 24, because some arrangements will generate the same set class.

31.

This latent discrepancy is also recognised by Straus (2001), p. 92, who notes ‘the basic formal paradox of [Stravinsky’s] music, namely the centrifugal tendency of the musical units [intervals] toward isolation and the centripetal tendency of the transpositions and inversions to link them together into larger wholes’. Nevertheless, in Straus’s vision the discrepancy concerns ‘the very immediate level of



258

 

structure’, that is, the structuring of the motives and ordered sets used in the composition. From my point of view, conversely, the necessity of finding a compromise between the two different constructive logics conditions the compositional process across multiple levels. 32.

The serial symbol ‘II inv’ in the sketch transcribed in Ex. 8a indicates that the passage is based on the inverse form of the second fundamental twelve-note row of the Requiem Canticles.

33.

The version featuring the move of a semitone from F  to G is found also in the lower system of the sketch reproduced in Ex. 8b. In the upper system of this last sketch one finds a third version, with the F  which leaps directly to B, thus anticipating the B of the following chord.

34.

The serial topography of this passage would be difficult to reconstruct without the assistance of the sketches: see for example the serial analyses of Powles (1995), p. 288, which are theoretically plausible but in total contradiction of the documentary evidence.

35.

A clarification is needed with respect to the serial symbols O, R, I and RI employed in the sketches. Normally, Stravinsky does not obtain the fourth basic ordering of the row (RI) by reading the inverse form (I) backwards (as is typical of Schoenberg and his students), but by inverting the retrograde form (R) (on the respective consequences, see for example Krenek 1940, p. 11). The two forms differ with respect to the level of transposition: the inversion of the retrograde begins on the same pitch as the retrograde; the retrograde of the inversion begins on the last pitch of the inversion. In order to avoid a disparity with the sketches which I have transcribed, I will likewise employ the symbol RI to indicate the inversion of the retrograde. The factor of transposition (T n) is computed in ascending semitones from 0 to 11 (taking octave equivalence into account).

36.

On which there already exists copious literature: see especially Spies (1965a), (1965b) and (1967); Rogers (1968); Hogan (1982); Van den Toorn (1983), pp. 442–4; Babbitt (1986) and (1987a); Morris (1988); and Straus (2001), pp. 26–33. Stravinsky’s first composition to make use of rotational arrays is Movements (1958– 9). In Locanto (2002), pp. 59–61, I interpret some characteristics of these tables in relation to the serial procedures employed by Stravinsky in earlier serial composition of the 1950s.

37.

The two steps in which the procedure (rotation and transposition) is articulated are clearly illustrated in the autograph table transcribed in Ex. 17: columns a and b contain the rotated forms; columns g and d contain the rotated-transposed forms.

38.

The serial symbols of the sketch can be deciphered as follows: ‘II’ = second fundamental row; ‘Inv’ = inversion (I); ‘R inv’ = retrograde inversion (RI); ‘ a’ = first hexachord; ‘1st’ = first line of the rotational array; ‘2 nd’ = second line of the rotational array (etc.); ‘1 st, 1 & 2’ = first and second notes of the first line of the array; ‘2nd, 1 & 2’ = first and second notes of the second line of the array; and so on.

39.

See in particular Tucker (1992), vol. 2, pp. 60–92; see also Pousseur (1971/i), pp. 27–30, and Van den Toorn (1983), pp. 390–413.

40.

See Locanto (2002), pp. 30–49. The use of motives formed by the combination of tones and semitones is a typical trait of many of Stravinsky’s serial compositions.



‘C  I’

259

Particularly common are the motives defined by Straus as ‘twist motives’, formed by the tone and semitone conjoined in opposite directions to form set class [012] (see for example Straus 2001, p. 91). These motives can be identified in many twelvenote rows, from Surge, Aquilo (Canticum sacrum) to The Owl and the Pussy-Cat (see the statistic in Straus 2001, p. 90 n. 13, based on Jers 1986, pp. 33–5) and in several pre-serial compositions (see for example Carter 1997). Although Straus (p. 90) observes that the semitone and tone often appear united in the same direction to form a set of class [013], in his analyses the two forms are considered to be distinct motives. For example, his analysis of the serial melody of Fanfare for a New Theater (p. 91) notes only the presence of the motive [012] – in which the two intervals are oriented in opposing directions (see Schema 1). However, considering the set [013] as another form of the same motivic class 1–2, one will see that the row contains two more motives between B and C  –D and between D–C and D , thus appearing as a continuous chain of seven motives (see Schema 2). Schema 1

<–1, +2> A

A

B

<+1, –2> C

D

<+2, –1> C

D

F

E

<+2, –1> F

G

G

<–1, +2>

Schema 2

41.

As was demonstrated by Tucker (1992), vol. 2, p. 186, on the basis of a thorough examination of the sketches. For the sake of further clarity and completeness, I will briefly summarise the way in which the principal rows employed in this part of the ballet are obtained from the initial tetrachord (for further details I refer the reader to Tucker 1992, vol. 2, pp. 182–242; on the technique of tetrachordal linkage, see also Van den Toorn 1983, pp. 409–14, and Locanto 2002, pp. 34–47). The serial heptachord G–A  –C –B –A–C–D that appears in the coda of the Pas-de-Deux (bars 495–496) results from the union through a common tone of a <0, 1, 4, 3> tetrachord (G–A –C –B) and its RI form (B  –A–C–D). Then, by combining through a common tone two forms of this heptachord placed a tritone apart (D–E  –G –F–E– G–A + A  –A–C–B–B –D –D), Stravinsky forms the thirteen-note row employed in the second section (Adagio) of the Pas-de-Deux – a row containing all twelve pitch classes with a single repetition. The twelve-note row used in the two final movements of the ballet (Four Duos and Four Trios) is obtained by uniting, through two common tones, the heptachord of the coda of the Pas-de-Deux with another row of seven notes, arrived at through the union (again via a common tone) of the fundamental tetrachord <0, 1, 4, 3> and a slightly modified form of that tetrachord, ordered as <1, 4, 3, 0 > instead of <0, 1, 4, 3 >.

42.

That is, from the Pas-de-Quatre to the Triple Pas-de-Quatre.

43.

As Tucker (1992), vol. 2, pp. 76–80 (on the basis of the transcribed sketches, p. 13), demonstrates, a point of contact between the use of intervallic motives in the strictly melodic sense, which characterises the non-serial movements of the ballet, and the serial technique employed in the following movements can be glimpsed in bars 104–107 of the Triple Pas-de-Quatre, where the 2–1–2 motive, which first appeared in various configurations (see for example its use in the melody of Ex. 11), now becomes fixed in the form of the ordered tetrachord <1, 3, 2, 0 >, which from that moment comes to be used as the referential row.



260

 

44.

See also the clarinet melody in bars 67–68 of the Double Pas-de-Quatre, analysed in Pousseur (1971/i), p. 42.

45.

See for example Stravinsky and Craft (1966), p. 60, where the twelve-note row of the Variations is described as ‘a succession of notes that came to my mind as a melody’.

46.

The genesis of the row for Epitaphium finds strong confirmation in a page of sketches which was addressed recently by Straus (2001), pp. 61–3. Straus’s analyses find within the row’s structure a certain number of segments belonging to set class [016], separated by the distance of T 4 (see Straus 2001, pp. 61–3, 99–102 and 130–1). The importance of the semitonal relation, which Stravinsky pointed out, is set in relief in Locanto (2002), pp. 128–31.

47.

See Craft (1972), p. 98. As I have already mentioned, in the Requiem Canticles two different fundamental rows are employed, indicated in the sketches by roman numerals I and II. Nevertheless, the two rows are employed simultaneously only in the Interlude and the Postlude, while the remaining movements employ them alternatively.

48.

According to the date of the sketches and the testimony of Robert Craft (see Stravinsky 1984, pp. 467–71), the Interlude was composed between the middle of March and 17 October 1965.

49.

For a complete inventory and a summary description of these sketches, see Locanto (2002), pp. 115–17.

50.

See Locanto (2002), pp. 116–17.

51.

Stravinsky (1984), p. 467, maintains that this sketch was preceded by a little sketch, dated March 1965, containing three annotations of row II, in each of which various metrical indications are visible, followed by a brief musical passage (also based on row II) of which there is no trace in the final score. However, there is no proof that this sketch definitely preceded the sketch transcribed in my Ex. 12a, and in any case it does not contain annotations of row I.

52.

Currently the second clipping is detached from the piece of cardboard, on which remain the traces of the adhesive tape which originally held them together.

53.

Indeed, the row extracted from this phrase is numbered I.

54.

See Straus (2001), pp. 49–52.

55.

Reproduced in Craft (1967), pp. 13–17.

56.

The row was then to have been employed in a symphonic composition, which was never brought to completion.

57.

See Straus (2001), pp. 49–52. The divergence between my analysis and that of Straus depends, even in this case, on our different conceptions of ‘intervallic motive’, with respect to which see nn. 6 and 40. In this case, moreover, the difference is accentuated by the fact that in my analysis, as opposed to Straus’s, the presence of the motive also arises in the vertical dimension.

58.

The row is clearly visible in Newman’s final photograph.

59.

Note also that the enharmonic spelling of the row clarifies its basis in the circle of fifths.



‘C  I’

261

60.

One could perhaps glimpse an allusion to this substantial modification in Stravinsky’s story, reported by Craft, commenting on Newman’s photographs: ‘During the morning of December 13, Stravinsky mentioned the “need to put an idea in order”, but when the sketch was completed, in about thirty-five minutes, he said that the music he had actually written was something different and that it had not been in his mind as long as an hour before. And he always seems to know exactly when his imagination is at the starting line. Shortly after he had finished, Mrs. Stravinsky clapped her hands together in the hall below his studio, her signal that lunch is ready, and Stravinsky applauded back, his signal that he is, too. At table, to show what he meant by putting in order, the composer placed three wine glasses in parade formation, then interchanged the first and third, saying, “ It is a matter of knowing that the notes must be this way and not the other ” ’ (Craft 1967, p. 13, italics added; see also Craft 1972, pp. 303 and 311).

61.

The dotted minim in the middle of the third line of the sketch shown in Ex. 14b clearly appears to be a B3 in the sketch. However, this is obviously an error deriving from the inconsistent inscription. The understood note is doubtless C4, as is seen either in the serial hexachord employed in the passage (first line above in the sketch), or in the final score (bar 47, trombone I).

62.

Which stand for RI a and R b, respectively.

63.

This demonstrates, once again, that from Stravinsky’s point of view the order of succession of the notes was less important than their global intervallic content.

64.

On the use of this technique in ‘De elegia tertia (Sensus spei)’ of Threni , see Tucker (1992), vol. 2, p. 251, where the author establishes, with the assistance of the sketches, the serial segments employed for the construction of the tenor melody of ‘Eradicationem’ (bars 252–259). However, according to Tucker, Stravinsky’s choice of various segments ‘was determined by no compositional “system” ’ (p. 251). On the contrary, in Locanto (2002), pp. 134–7, I attempt to demonstrate that in all of the preliminary versions of the passage, as in the final version, the choice is determined by the desire to create a dense chain of overlapping 1–5 motives.

65.

The complete autograph short score comprises four separate pages. Only the page transcribed in Ex. 15a – which, unlike the others, is merely drafted – contains serial symbols. Its content corresponds to the printed score, with the sole exception of the E in place of D in the third bar of the tenor.The reading in the score (D) is probably incorrect, inasmuch as the E of the autograph short score finds confirmation in the serial tables. However, even if this reading is treated as an intentional variant introduced by Stravinsky (it appears for the first time in the clean copy of the score), that does not challenge the validity of my analysis, which concerns the creative process from its earliest stages.

66.

Note also the effect created by the occasional doubling of pitches in the vocal parts.

67.

Starting in bar 4, the pitch organisation of the choral part is based on a different serial technique, which involves reading the rotational arrays vertically. On this technique see especially Straus (2001), pp. 152–64.

68.

See Stravinsky and Craft (1960), pp. 100–1. Analyses of the flute solo can be found in White (1966), p. 612; Müller (1984); Babbitt (1986), p. 255; Tucker (1992), vol. 2, p. 258; Rust (1994), pp. 64–71; and Straus (2001), pp. 65–8 (based on Rust) and 125–30.



262

 

69.

Set class [012] could also be formed by uniting two semitones, but the motives formed by two different intervals are far more typical of Stravinsky’s music.

70.

The sketches which I consider (all in the Paul Sacher Foundation, Igor Stravinsky Collection) include (1) the sketch for bars 13–17 transcribed in Ex. 19a; (2) the page of sketches with two versions of bars 7–12 transcribed in Ex. 21; (3) a clipping with a preliminary version of bars 18–21, without serial symbols (not reproduced here); (4) a clipping with the definitive version of bars 18–21 and (on the other side) bar 22, without serial symbols (not reproduced here); and (5) the autograph short score, some of the serial symbols from which are transcribed in Ex. 22. If one excludes the serial analysis of the accompaniment in bars 13–17 in Rust (1994), p. 70, based on the score (no. 5), sketches nos 2–5 of the list have never been considered until now. In contrast, sketch no. 1 has been cited and discussed numerous times in the musicological literature. One of the first transcriptions appeared in Neidhöfer (1991) (in the same year Joseph Straus presented this document in a paper at the Annual Meeting of the Society for Music Theory in Cincinnati, OH). Later the document was analysed by Tucker (1992), vol. 1, p. 66 (transcription) and (1992), vol. 2, p. 258 (commentary); Rust (1994), pp. 63–4; and Straus (2001), p. 67, which finally established the serial construction of the flute solo, without, however, comparing it with either the construction (actually quite similar) of the other two episodes, or with the motivic-intervallic construction to which it is subjected.

71.

The major discrepancy concerns the first two segments: in the short score of the piano episode they are labelled segment 3–6 of hexachord g 5 and segment 5–6 of hexachord d1. In the sketch for the flute episode, however, they are labelled segment 1–3 of hexachord g 1 and segment 4–6 of hexachord d1. However, note that when the two piano segments are transposed by T 2 (rather than T 4, as in the flute), the resulting pitches are the same as in the flute episode.

72.

In the first version, the serial segments were transposed a major third higher (T 4); the second version, on the other hand, was obtained by lowering the first version by a tone (T2). Therefore, in the second version, the serial segments prove to be transposed a tone higher (T 4 - T 2 = T 2). The short score does not contain serial symbols for the final part of the passage, formed by the succession of thirteen pitches notated in the final part of the third line of Ex. 21. The same succession of pitches – this time without the initial C  – is transcribed again lower on the page (lines 5–6) with a different choice of octave register for the single notes and using a rhythm outlined for the final cadence.

73.

The B that appears as the first note after the treble clef corresponds to the D  of the preceding version, placed immediately before the treble clef. See also the line drawn by Stravinsky. A different version of the final part of the phrase alone (starting with the dyad B –A on line 13) is also notated by hand in the lower part of the page (lines 12–14).

74.

The error in the printed score has created some difficulties in the analytical literature. See for example Rust (1994), p. 68, where the omission of the notes B and C prevented the author from recognising the T 2 relation between the last ten notes of the first piano episode and the corresponding notes of the flute solo. Moreover, Rust’s analysis omitted the last bar (bar 22) of the second episode for the piano, so that he failed to notice the T 8 relation with the flute solo in the last six notes.



‘C  I’

263

75.

See Boykan (1963), p. 158; Walden (1979); Rust (1994), pp. 62–76; and Straus (2001), pp. 124–8.

76.

On the basis of the principle of rotation on which the serial tables are based, one could say that the pitch ‘following’ the final pitch of a hexachord is the first.

77.

For the sake of convenience, in Ex. 24 the entire succession of pitches is transposed to F (as in the first piano episode).

78.

Note that, in the definitive score, one of the very rare points at which this continuous motivic chain is interrupted corresponds to the juncture at which Stravinsky omitted the notes B and C in the first episode.

REFERENCES Antokoletz, Elliott, 1984: The Music of Béla Bartók: a Study of Tonality and Progression in Twentieth-Century Music (Berkeley and Los Angeles, CA: University of California Press). Babbitt, Milton, 1960: ‘Twelve-Tone Invariants as Compositional Determinants’, Musical Quarterly, 46/ii, pp. 246–60. ______, 1961: ‘Set Structure as a Compositional Determinant’, Journal of Music Theory, 5/ii, pp. 72–94. ______, 1968: ‘Remarks on the Recent Stravinsky’, in Benjamin Boretz and Edward T. Cone (eds.), Perspectives on Schoenberg and Stravinsky (Princeton, NJ: Princeton University Press), pp. 165–85. ______, 1986: ‘Order, Symmetry, and Centricity in Late Stravinsky’, in Jann Pasler (ed.), Confronting Stravinsky (Berkeley, CA: University of California Press), pp. 247–61. ______, 1987a: ‘Stravinsky’s Verticals and Schoenberg’s Diagonals’, in Ethan Haimo and Paul Johnson (eds.), Stravinsky Retrospectives (Lincoln, NE: University of Nebraska Press), pp. 15–35. ______, 1987b: Words about Music, ed. Stephen Dembski and Joseph N. Straus (Madison, WI: University of Wisconsin). Bailey, Kathryn, 1996: ‘Webern’s Row Tables’, in Kathryn Bailey (ed.), Webern Studies (Cambridge: Cambridge University Press), pp. 170–228. Beach, David, 1976: ‘Segmental Invariance and theTwelve Tone System’, Journal of Music Theory, 20, pp. 157–84. Berger, Arthur, 1963: ‘Problems of Pitch Organization in Stravinsky’s Diatonic Music’, in Benjamin Boretz and Edward T. Cone (eds.), Perspectives on Schoenberg and Stravinsky (Princeton, NJ: Princeton University Press), pp. 123–55. Boss, Jack, 1992: ‘Schoenberg’s op. 22 Radio Talk and Developing Variation in Atonal Music’, Music Theory Spectrum, 14/ii, pp. 125–50. ______, 1994: ‘Schoenberg on Ornamentation and Structural Levels’, Journal of Music Theory, 38/ii, pp. 187–216. Boykan, Martin, 1963, ‘Neoclassicism in Late Stravinsky’, Perspectives of New Music, 1/ii, pp. 155–69. Music Analysis, 28/ii-iii (2009)


264

 

Carter, Chandler, 1997: ‘Stravinsky’s “Special Sense”: the Rhetorical Use of Tonality in The Rake’s Progresss’, Music Theory Spectrum, 19/i, pp. 55–80. Craft, Robert, 1967: Bravo Stravinsky. Photographs by Arnold Newman (Cleveland, OH: World). ______, 1972: Stravinsky:Chronicle of a Friendship,1948–1971 (NewYork: Knopf). Dahlhaus, Carl, 1986: ‘Was heisst “entwickelnde Variation”?’ in Rudolph Stephan and Sigrid Wiesmann (eds.), Bericht über den zweiten Kongress der Internationalen Schönberg-Gesellschaft (Wien: Universal), pp. 280–5. Forte, Allen, 1972: The Structure of Atonal Music (New Haven, CT: Yale University Press). Haimo, Ethan, 1997: ‘Developing Variation and Schoenberg’s Serial Music’, Music Analysis, 16/iii, pp. 349–65. Hogan, Catherine, 1982: ‘Treni : Stravinsky’s “Debt” to Krenek’, Tempo, 141, pp. 22–9. Jers, Norbert, 1986: Igor Stravinskys spate zwölf-tonWerke (1958–1966) (Regensburg: Gustav Bosse). Johnson, Paul, 1987: ‘Cross-Collectional Techniques of Structure in Stravinsky’s Centric Music’, in Ethan Haimo and Paul Johnson (eds.), Stravinsky Retrospectives (Lincoln, NE: University of Nebraska Press), pp. 55–75. Krenek, Ernst, 1940: Studies in Counterpoint Based on the Twelve-Tone Technique (New York: G. Schirmer). Lewin, David, 1962: ‘A Theory of Segmental Association in Twelve-Tone Music’, Perspectives of New Music, 1/i, pp. 89–116. Locanto, Massimiliano, 2002: ‘Pensiero musicale e procedimenti costruttivi nell’ultimo Stravinsky’ (PhD diss., University of Pavia). Morris, Robert, 1988: ‘Generalizing Rotational Arrays’, Journal of Music Theory, 32/i, pp. 75–132. Müller, Alfred, 1984: ‘Igor Strawinsky: Movements for Piano and Orchestra’, Melos, 46/ii, pp. 112–39. Nabokov, Nicolas, 1949: ‘Christmas with Igor Stravinsky’, in Edwin Corle (ed.), Igor Stravinsky (New York: Sloan & Pearce), pp. 123–68. Neidhöfer, Christoph, 1999: ‘An Approach to Interrelating Counterpoint and Serialism in the Music of Igor Stravinsky, Focusing on the Principal Diatonic Works of His Transitional Period’ (PhD diss., Harvard University). ______, 1991: ‘Analysearbeit im Fach Komposition/Musiktheorie über die Movements for Piano and Orchestra von Igor Strawinsky’ (master’s thesis, Musik Akademie der Stadt Basel). Perle, George, 1955: ‘Symmetrical Formations in the String Quartets of Béla Bartók’, Music Review, 16, pp. 300–12. ______, 1991: Serial Composition and Atonality: an Introduction to the Music of Schoenberg,Berg,andWebern, 6th revised edn (Berkeley and Los Angeles, CA: University of California Press). Pousseur, Henry, 1971: ‘Stravinsky selon Webern selon Stravinsky’, Musique en jeu, 3/i–ii, pp. 21–47 and 107–26. © 2011 The Author. Music Analysis © 2011 Blackwell Publishing Ltd


‘C  I’

265

Powles, Jonathan C., 1995: ‘Continuity and Discontinuity in the Music of Stravinsky: Analysis, Theory and Meta-Theory’ (PhD diss., Oxford University). Rogers, John, 1968: ‘Some Properties of Non-duplicating Rotational Arrays’, Perspectives of New Music, 7/i, pp. 80–102. Rust, Douglas, 1994: ‘Stravinsky’s Twelve-Note Loom: Composition and Precomposition in Movements’, Music Theory Spectrum, 16/i, pp. 62–76. Schoenberg, Arnold, 1967: ‘Fundamentals of Musical Composition’, ed. Gerald Strang and Leonard Stein (Boston and London: Faber and Faber). ______, 1995: The Musical Idea, and the Logic,Technique, and Art of Its Presentation, ed. and trans. Patricia Carpenter and Severine Neff (New York: Columbia University Press). Sichardt, Martina, 1990: Die Entstehung der Zwölftonmethode Arnold Schönbergs (Mainz: Schott). Smyth, David H., 1997: ‘Stravinsky at the Threshold: a Sketch Leaf for Canticum sacrum’, Mitteilungen der Paul Sacher Stiftung , 10, pp. 21–6. ______, 1999: ‘Stravinsky’s Second Crisis: Reading the Early Serial Sketches’, Perspectives of New Music, 37/ii, pp. 117–46. ______, 2000: ‘Stravinsky as Serialist: the Sketches for Threni ’, Music Theory Spectrum, 22/ii, pp. 205–24. Spies, Claudio, 1965a: ‘Some Notes on Stravinsky’s Abraham and Isaac’, Perspectives of New Music, 3/ii, pp. 186–209. ______, 1965b: ‘Some Notes on Stravinsky’s Variations’, Perspectives of New Music, 4/i, pp. 62–74. ______, 1967: ‘Some Notes on Stravinsky’s Requiem Settings’, Perspectives of New Music, 5/ii, pp. 98–123. Straus, Joseph N., 1990: Introduction to Post-Tonal Theory (Englewood Cliffs, NJ: Prentice-Hall). ______, 1991: ‘The Progress of a Motive in Stravinsky’s The Rake’s Progress’, Journal of Musicology, 9/ii, pp. 165–85. ______, 2001: Stravinsky’s Late Music (Cambridge: Cambridge University Press). Stravinsky, Igor, 1984: Selected Correspondence, ed. Robert Craft, vol. 2 (Boston and London: Faber and Faber). Stravinsky, Igor and Craft, Robert, 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). ______, 1966: Themes and Episodes (New York: Knopf). ______, 1969: Retrospectives and Conclusions (New York: Knopf). Taruskin, Richard, 1993: ‘TheTradition Revisited: Stravinsky’s Requiem Canticles as Russian Music’, in Christopher Hatch and David W. Bernstein (eds.), Music Theory and the Exploration of the Past (Chicago: University of Chicago Press), pp. 525–50. Music Analysis, 28/ii-iii (2009)


Locanto - Stravinsky's Late Technique

Recommend Documents