koivisto - 1997 - the defining moment the thema as relational nexus

The Defining Moment: The Thema as Relational Nexus

in Webern's Op. 27

Tiina Koivisto

While most analysts currently agree that the actual set of variations in Anton Webern's Varia tions for Piano, Op. 27 is to be found in the third movement, Webern 's own co=ents suggest that the initial eleven measures of that movement serve as a thema not only for the subsequent five variations, but also for the composition as a who le. In a letter to Eduard Steuermann, in which he included a copy of the piece, Webern wrote:

[The Variations] are div:ided into three indepe nden t movements . I do not display the thema explicitly (at the top, like before). It is almost my wish that it could stay as such unrecognized . (But if people ask me abou ~ it, I wou ld not hide it from them.) Neverthe less it is bette r that it stay ba ck the re. (It is- to you I tell it right away-the first eleven measures of the third movement.)' (Webern 1983, 32 -33; author's trans lation)

' "lch schickc Dir mit gleicher Post meine 'Variationen' u . bin se hr glucklich , de Dich meine Widmung an Dich freut. Wie ich Dir , glaube ich, schon angedeutet habe, sind sie in fur sich abgeschlosse ne Satze (drei l aufgetcilt . !ch steUe auch das 'Tbema' gar nich t ausdru ck:lich hina us [etwa in fruherem Sinne an die Spitze]. Fas t ist es mein Wunsc h, es moge al s so lch es unerkannt bleiben. (Aber wer mich danach fragt , dem werde ich es nicb t verheimlichen) . Dach moge es lieber gleichsam dahinter stehen. [Es sind -D ir vecrate ich es natiirlich gleich-die ersten 11 Takte des 3 . Satzes]."

30 In Theory Only

This article seeks to explicat e Webern's remarks and suggests that the thema emerges as the kerne l of the relationships em ployed in the ent ire piece. By examining the relationshi ps inhe rent in the thema, it is possible to develop meaningful ways to approach and describe the unde rlying structural features not only in the set of variations, but also in the preceding two movements.' Furthermore, this approach reveals the manner in which the thema lies at the midpoint of a series of nested symmetrical structures, against which one hears the te mporal accretion of the music.

TheThema Example 1 shows the thema of Op. 27 with Webern's remarks about the performance of the piece, as they appear in the Stadlen edition (Webern 1979).3The thema contains three phrases (A, B, and A'), each of which comprises a single member of the work's row class. There are a multitude of ways to hear this musical surface. The specific articulation of the thema phrases invites us to hear several prominen t groupings. For example, one may hear strands of long and short notes, in which the long notes can be described as a melodic part and the short notes as an accompanying part. 5 Furthe rmore , one may hear strands of slurred and nonslurred dyads.' Both these groupings partition the phrases into chromatic hexachords. In addition, the single tritone of the thema's intervallic vocabulary, marking the midpoints of the phr as es , parses the phrases yet another way into pairs of chromatic hexach ords: in this instance into the actual hexachords of the rows.

2Anton Webern's Op. 27 has been discussed from various points of view; see Babbitt (11960) 1962, 1987), Bailey(J99 1), Hasty (1981), Leibowitz (11949) 1970), Lewin (1962, 1987, 1993), Mead (1992, 1993), Nolan (19891, Schoebel (1984), Stadlen (1958), Travis (1966), Wason (1987 ), and Westergaard (1963, 11962) 1972).

"These remarks were made by Webern to Stadlen as instructions for the world premiere of the work in 1937 . Stadlen~s annotations include both verbal recollections and comments written on the score.

4 In cliscussion of structural features , tbe tbema phrases will be referred to as A and B if there is no need to differentiate between the outer phrases.

5Robert Morris was the first to point this out in a seminar at Yale University in 1975 (Mead 1992, 123). Also Wason (1987 ,78) cites Monis as the source of his way of construing the thema.

6An alternative interpretation of the thema that also uses the clistinction betw een slurred and nonslurred dyads is deve loped by Lewin {1987, 39) .

Koivisto, The Defining Moment

Bxample 1. Webern, Varia tionen , mvt. ill, mm. 1- 12, them a Reprinted by permission of Universal Edition.

Thema ph"',e A (P) .,& .. l,,',cit,1,n, r .... ,.._ ..... ...;n~ ............. -~ .. ..

Ruh!g lliafJend J, ea 80 1 ,..,,..;:....,..,~~~~~~"""=

-

Thema phrase B ('

32 In Theory Only

indicates, each interval class (ic) is represented a unique number of times. Thi s property allows the row class the highest degree of differentiation among its hexachordal area s. 7 Second, the exclusion of ic 6 from the hexachords places special significance on tri tones as intervals that can only occur between hexachords.

Example 2. Segmental , motivic, and slurred/non -slurred hexachordal areas of thema phrases A and B

P: 3et210 647598

phrases A B Hcxachordal areas (segmental) segmental motivic non/slurred

p me lody 3 2 6475 {te0123 } {23 456 7) {6789te} accomp . et 10 98 {456789} {89te0 !) {012345) (motivic)

I6P melody 3 4 02el {345678} {e0!234} f789te0 ) acco mp . 78 56 9t {9te012 } {56789t} (123456}

As example 2 illustrates, the three criteria for parsing each of the thema phrases yield all possible members of the (012345 ) collection class exactly once. The presence of all hexachordal areas in the thema exhausts the possibilities for th e various degrees of pitch -class (pc) intersection available ,vith this type of collection class. As shall be seen, the di screte degrees of pc intersection int roduced in the thema become an important facto r in the formal shaping of the mus ic. The actual pcs of the pc intersection have significant roles as well.

Among the hexachordal areas of the thema one may define more close and more remote relationships having as their criteria properties arising from the orderings or partial orderings of the hexachords . As will be discussed below, one may define a close relationshi p between the segmental and motivic hexachordal areas arising from ordering properties. Based on th is, comparison between the segmental and motivic hexachordal areas alone throughout the thema reveals the presence of all the possible degrees of pc intersection (ex. 3). Degree of pc intersection is indicated with two digits separated by a slash, the firs t showing the number of pcs shared between hexachords a t like

7This property is shared by only on e other hexa chordal collection-class, 1024 579 ), the diato ni c hexachord .

Koivisto, The Defining Moment 33

order positions, and the second showing the number of pcs unique to each hexachord. As comparison between, for example, the segmental hexachords of P and I6P shows , the hexachords at like order positions, that is, the first hexachords of both rows, have pc intersection 1/5 sharing pc 3; the second hexachords of these rows share pc 9.

Example 3. Pc intersection between segmental and motivic hexachordal areas of the thema

s

34 In Theory Only

Example 4. Ordered sets of dyads of segmental and motivi c hexachordal areas of thema phrases A and B

A/seg {{23l{leH01) {67){45H89)) A/mot {{23H67){45) {teH01H89})

rMI. ac::c.

Biseg {{34}{78H56) {eOH12H9t)) Bimot {{34HeOH12) {78H56){9t}}

- acc.

Example 5. Rows connected with the ordered sets of dyads of thema phrases A and B

A/seg P: rmn 3et210

RTsP: 23e 1 t O u LY-I

A/mot n rr=r, Rl9 P: 32647 5

8/seg

l5P:

lsP:

267345 l u I LJ

l nln 378456

RloP: 1J I_ijj B/mot n ri9-,

RT7P: 3 4 () ~ e 1

T1P: 1oef21 u u

rFi1 n 647598 0

}->{{23){te }{01 ){67){ 45}{89)} 67845/ u 1u1

.rlJf3d )....c{23}{67){45l{le){01){89)}

tUJU JJJl9~

~{{34}{78){56l{eOH12){9t)} Oet219 u UJ.J 1fJ~n1

r{{34){e0}{12}{78}{56}{9t}} 758619 LWU

The relationships articulated in the thema have further consequences. One may group the rows of the work's row class into six equivalent four-row families (eight -row families if one distinguishes the retrogrades) that represent the relationships between the rows yielding the ordered sets of segmental and motivic dyads of phrases A and B.


Examp le 6 . Two main four -row families

JJ, ,U, Ord. Ord. Ord. Ord. Nmot Nseg Blseg Blmol

ord. Ord. Ord. Ord. Nmot Nseg Blseg B/mot

Among these six families, the four-row families containing P and 16P (ex. 6) will be referred to as the two main four-row fam ilies. One may consider partial orderings of the hexachords yet another

way, as unordered sets of unordered ic l dyads. This approach yields two additional rows (and their retrogrades) that produce se ts of dyads connected with the thema phrases, in this instance the unordered sets of the dyads within the hex.a.chordal areas. Example 7 illustrates th is by showing the rows yielding the unordered sets of dyads of the segmental hexachords of thema phrase A. The six four -row families, es tablished above among the rows of the work's row class, comprise rows that yield the ordered and unordered se ts of segmental, mot ivic, and slurred/no n slurred dyads of phrases A and B. Thus, in addition to the two main four -row families, which are closely connected to the thema, one has four additional four -row families that reflect to various degrees th e thema through the properties arising from its segmental , motivic, and s lurred/nonslurred hexachords. Most significantly, howeve r , these additional four-row families produce the same relationships between them and among their rows as the two main four-row families . In this manner , the relationships arising from all the various hexachordal areas of the thema may be expressed to represent the relatio nships among the rows of the two main four-row families.

36 In Theory Only

Example 7. Rows producing the unordered sets of dyads of the segmental hexachordal areas of thema phrase A

t23e01 LilJ u

n5 76 598 {{te ){23 ){O 1 ){67){89){ 45)} 796845 I I I I U

Relationships within the row class may be helpfully illustrated using relational diagrams. Example 8 shows a relational diagram comprising the rows of the row class. In the diagram, the two concentric rings of nodes each represent rows related by T. The aligned nodes represent inversionally related rows whose individual hexachords map onto themselves. Each axis represents one hexachordal area. Any row .of the row class may be inserted in any one of the nodes, and the remainder of the nodes would be filled automatically. 6

We shall now further explore the relationships among the rows of the work's row class by using this relational diagram and by invoking two ways to view inversional relations. In this composition, Webern deals with relationships between pairs of inversionally related rows both in terms of a preserved index number and in terms of a fixed degree of hexachordal pc intersection. The relational diagram will be used to show the two ways of expressing inversional relations, followed by an illustratio n of relationsh ips within and between the four -row families, invoking these two ways of construing inversional relationships.

In example 9 the various degrees of pc intersection are indicated with dotted lines. A similar chart may be made for any row in the diag ram , either by inserting the row in the appropriate node, or by reorienting the net of dotted lines. Doing so groups the rows of the row class into twelve discrete sets of inversionally related row pairs that fulfill two conditions. First , the row pairs have the same degree of pc intersection between hexachords at like order positions, and second, they have the same properties when considered as ordered row pairs. 9

8rhe diagram shows the rows related by T and I; operation R would reverse the num ber of pcs shared and held unique between hexachords of the rows.

9As an exam.p ie, by inserting the main row pair P-10P into the nodes marked by asterisks (P at the top} and by inserting rows into the rest of the nodes according to example 8, the eleven other members fulfilling the two conditions are found by r eorienting the net of dotted lines until the initial position is reached . These eleven


Example 8. Relational diagram of rows in the row class

~ I etc..

i represents the appropriate index number to map segmental hexachords onto Uiemselves

et,.

same hexachordal areas

37

other row pairs of the same set are l;P-1,P . . . T,P-l;P. (The row pairs also represent th eir retrogrades, tbat is RP-RIJ', etc.)

38 In Theory Only

Ezample 9. Relational diagram showing degree of pc intersection between hexachords at like order positions of rows

, I

I ,

1/5,' I

I I o/6 I

'

'

' ' \1/5 ' ' '

' ' ' ;lfr

' '

Additionally, the same two conditions are fulfilled in the twelve discrete sets of transpositionally re lated row -pairs, thus allowing extension of pc intersection to transpositionally related rows. 10

In example 10 the index number of inversion between the rows of the row class is indicated by showing the two patterns that arise from even and odd indices of inversion. A given index groups the rows into twelve sets of row pairs that share pc pairs determined by the index but do not maintain the same degree of pc intersection. 11

1For example, the hexachords of P and T,P have pc intersectio n 1/5 in the same

fashio n as the hexachords of P and J.,P. 11In example 10, by inserting rows into the nodes like in example 9, the net of

solid lines indicates all twelve members of one set of inversionally related row pail's sharing the same index of inversion . In example !Oa the rows are related by 16. The [, related row pairs are P-1,P, T,P-1,P . .. TJ' l,P (and their retrogrades). A reorientation of the net of solid lines yields a different set of row pail's sharing another


Example 10. Relational diagrams of rows related by (a) even and (b) odd index numbers

lOa.

Finally, example 11 shows row relationships within and between the two main four-row families. The roost significant relations preserving the degree of pc intersection between inversionally related rows within and between the four -row families are labeled as follows. (l) The inversion relation specifying the degree of pc intersection between the hexachords at like order positio ns of P and lJ' and addi tional such pairs is labeled an ls relation (s ; segmental). Thus, the inversion relation between the rows of the thema can be expressed bo th as Is and as 16 , depending on the analytical orientation; both relations are important in the work. In the diagram one may also see

index of inversion.

,

40 In Theory Only

Example 10 (cont.)

lOb.

how moves between ls and T5 related rows are identical in terms of degree of pc intersection, a feature that is significant in the work, as well. (2) The inversion relation specifying pc intersection between hexachords of the rows yielding the segmental and motivic hexachordal areas of a thema phrase will be labeled as an Ism relation (sm = segmental/motivic). The first Ism relation (Ism') denotes pc intersection 4 /2 and the second Ism relation (Ism2) denotes pc intersection 2 / 4 between hexachords at like order positions of these rows and additional such pairs. As was discussed above, this type of inversion relation specifies also the properties of ordered rows. Example 12 illustrates this by showing the ordered rows of the four -row family containing P. Most prominently, in the first Ism relation the melodic hexachord possesses the same order as one of the


segmental hexachords. 12 The second Ism relation yields an invariant linking dyad .

Example 11. Relational diagram of pc intersections among the two main four- row families

"' I I \

\

' ' '-, , ___ ..........

'

' ' ' ' ' ' I

\ ' \ I \ I ) ,,

I l I I

I I I I

I t I I

I ( I I

// I le I

'-"'..r-.,,;: / /

,, ,, .,,,/'

I

// Jsn,2.

12Monis pointed out this property in a senunar at Yale Uruversity in 1975 (Andrew Mead, personal communication).

42 In Theory Only

Exampl e 11 (cont.)

15:

I 1. sm

l5P TsP loP T1P

18p 0 T7P two main four-row families

ordered sets of segmental and motivic dyadS of A and B, and additional such palrs

Ism 2: pc intersection 2/4 between hexachords at like order positions of rows yielding the ordered sets of segmental and motivic dyads of A and B, and additional such pairs

As will be shown , the relationsh ips inherent in the thema form the bas is of the pitc h organization of all three movements. The first and second movements em ploy the two different ways to express the relation between th e rows of th e th ema, the I. and 16 relations, and both movements employ one of the two lsm re lations , as well as inve rsionally related row chains generated by T, . In the third movemen t, the variation form is based on the us e of the sets of ordered and unordered dyads connected with the discrete hexac hordal areas of the thema, and the culminating variation emp loys both Ism relatio ns.

As is often noted, one of the most familiar aspects of this piece, as well as Webern's twelve-tone mus ic in general, is his penchant for symmetrical structures, both in time and in register. Neverth eless, one hears in this music a strong sense of progression, suggested by the plasticity of its phrases. This artic le pays special attention to the manner in which this sense of progr ession arises from the underlying structures and, furth er, to the manne r in which the symmetrical , frozen structural aspects of the pitc h organ .ization int eract with our sense of musical accret ion over time .

In order to demonstrate the various a spects of the underlying pitch organizatio n , the notion of compositional design, introduced by Morris (1987) , will be employed . Furthermore, the form of each movement will be explained as arising from an interaction between the underlying


des ign and its surface realization. Each analysis begins by e=ining the underlying design, continues by illustrating some of th e specific properties inh erent in the design, and then moves to a demonstration through brief examples of the ways in which the design becomes vivid on the musical surlace .

The First Movement The first movement is in tripartite fonn, the sections of wh ich consist, with a few exceptions, of mirror -symmetrical phrases. The un de rlyin g design may be characterized by focusing on four different aspects: (1) simultaneous retrograde- related row pairs, (2) consecutive row pairs forming row-pair couples, (3) hexachordal areas of the row pairs, and (4) pc intersection between these hexach ordal areas.

The retrograde -re lated ro w pairs form two inversionally related row-pair chains generated by T, (ex. 13). The beginn.ing retrograde -related row pairs are RT8P/T 8P (mm. 1-7 and 11- 15) and RI,P/L,P (mm. 8-10 and 15-18). As the diagram indicates, T8P and I2P (and RT8P and RI~) are rela ted by Is. The middle section of the movement consists solely of interlocked members of the two T5 chains (Lewin 1987, 182), whereas the outer sections are extended with T6-related row pairs.

Example 12. Two types of km relat ions in the fou r -row family contain ing P

P: I l 1 1 11,.......... 3 .!.!,2 ~ 6 4 7 5 9 8J I 1

leP: 111111 sm

80 1 9te 5 74623 .......... .._.

lsm2 l5P:

,..........

2 6 7 3 4 5 e 1 to 9 8) lsm1

T5P: 954876 011 e32

44 In Theory Only

Example 13. Underlying design of mvt. I: retrograde-related row pairs

An examination of the row-pair design in terms of consecutive row-pair couples reveals that the movement exhibits two discrete invers ion re latio ns inherent in the the ma (ex. 14). The outer sections (mm . 1-18 and 37-54) exhibit the Is relation, the relation between the rows of the thema, whereas the middle section (mm. 19-36) exhibits the second Ism re latio n, which arises from the segmental and motiVic hexachordal areas of the thema. The ls-related row-pair couples of the ou te r sections are T,P -1,P (with their retrogrades) in the first section and P-4P and tP -T5 P (with their retrogrades) in the last section; the hm2-related row -pair couples of the middle section are I,P -T2P, l0P-T1P, I,P -P (with their retrogrades). In this manner the underlying design manifests a tripartite formal layout. However, within this tripartite shape, the last section combines the relationships of the two preVious sections by generating the Is-re lated row-pair couples by T 5 in the same fashion as the middle section.

Example 14. Underlying design of mvt. I: row-pair couples

IEJ T. I!] T. T. 0 T. ~ ~ ~ ~

100100 .0100 11 I.,,,'

Yet another deep structural level emerges if one interprets the row pairs as hexachordal areas (ex. 15). In this interpretation two identical chains of hexachordal areas permeate the movement. In both chains, adjacent hexachordal areas have the same degree of pc intersection, that is, intersection 1/5, between hexachords at like order positions.

Koivisto, The Defin ing Moment

Examp le 15. Underlying design of mvt . !: pc intersection between hexachordal areas

(.limax End Epilogue ",/4 I 6(0

~ ~ --- .. - --

1 I

45

Hexachordal areas have several consequences for the formal shape of the movement . First, the identical haachordal areas at the ends of the chains punctuate two structurall y prominent moments: the first chain concludes with the row pair that forms the climax (mm. 32-34), and the second chain concludes with the penultimate row pair (mm. 47 -51 ). As such it leaves the last row pair, whose hexachordal areas are a repetition of the third -to-last row pair, as a separate unit. Th us, the role of the las t row pair as an epilogue (mm. 51-54), a role confirmed by Webern's remarks in the Stadlen edition , arises from a deeper level of the pitch organization.

Aspects of pc intersection between he:xachords also reveal how the row pairs manifest all the possible degrees of pc intersection with regard to the initial one. In the two chains, the maximum degree of remoteness from the initi al hexachords, pc intersection 3 / 3, demarcates strncturally significant moments. In the first chain the midpoint of th e middle section occurs after these hexachords are stated. At this moment the surlace interpretation of the rows changes as well: new configurations are introduced, and deviations from the symmetrical arrangements are made to help shape the climax and a transition to the las t section . In the second chain, the last row pair is singled out, since it repeats pc intersection 3/3, thus emphasizing the special role of the epilogue.

Lastly, the segmental hexachords of the thema have an important role as points of departure and arrival. Most importantly, the middle section is framed by the segmental hexachordal areas of phrase A, arising from the row pairs I7P/RI 7P and P/RP. In addition, the

46 In Theory Only

beginning of the last section is demarcated by entrances of the exact rows of the thema.

In light of the above, the form of the movement can be viewed as arising from an interaction among the various aspects of the underlying design. First, the design articulates a tripartite formal layout, within which there is a special emphasis pla ced on the last section. Second, the aspects arising from the hexachordal areas manifest a continuum stretching throughou t the movement, significantly, however, leaving the last row pair, which forms the epilogue, as a separate unit. Finally, the climax as well as the conclusion before the epilogue are demarcated as the last members of the two chains.

The propert ies inherent in the underlying desig n have manifold compositional consequences offering ways to shape the specifics within the overall flow of the music determined by the hexachordal areas. For instance, example 16 shows the manner in which th ree disc rete segme nt al ic 1 dyads of the work's row class are related by T, . Cons equ ently, invariant dyads arising from the T5 chains permeate the movement. Through the partitioning schemes and their surface realizations, these invariant dyads become a prominent feature in the shaping of the mirror-symmetrical phrases acting, for example, as their framing and middle dyads. Furthermore, the dyads are typ ically connected with an additional pc to form collections belonging to the collection class (016], a characteristic sonority of this movement.

These aspects may be illustrated with the movement's climactic phrase (mm. 32-34; ex. 16). The dyads E-Eb and A-G~, which arise from the T5 chains and form prominent elements in the previous phrases - most often emphasized by the same registers-become the framing and middle ic 1 dyads of the climaxing phrase. As another illustration of ways in which the underlying design offers opportunities to shape the climax, the example shows how the tritone BF, having its first entrance here as an axis tritone (m. 33), together with the pitch E3 evokes the movement's opening sonority. The opening retrograde-related row pair, T8P/RT 8P, and the row pair of the climaxing phrase, I5P/Rl 5P, exchange the first and middle trichords belonging to the set class (0161, that is {892) and {45e} (at order numbers {te0 and {456} of 15P). Moreover, the pcs of the work's opening me lodic dyad, E-C~, become the framing pcs of the climax's ascending line (mm. 32-33). (It is worth mentioning that the corresponding

Example 16. Surface promine nce ofT 5-related ic 1 invarian t dyads

/T 10~ nn n

TilxP: 012345 6789te V"-.._/

T3 T5

RT7P/T7P

1,m2 ,1.1 .... -clyld) "'

RloPnoP RT7PIT7P

. . ~ 3 4

u

n 3402e1 165987 uu

nn 789561 1 e20 43

, U '--- --

'--' -

Ri,Pn,P

RlsP/lsP

J10 I 1:e---54'B i$ 2 2 6 7 3:4 5 erf'1 0 9 8 u l..'.t"---- u

.......... .:.......,

"'*'Ing

RTgP/1,P

g: $: (f) .....

0 -

:f ~ 0

t ~-

JJ ~ 0

~ ::i .....

.IS, -..J

48 In Theory Only

gesture in the middJe section's opening phrase is framed by the tritone B-F. ) Th e goal of the ascent, Db 6, features the first two sect ions ' hig h registral extre me .

The richness with which the design becomes vivid on the musical surfac e may furthe r be illust rated using one parti cularly telling pass age , the epilogue, in which several traj ectories of relati onshi ps coincide. The special qualities of the ep ilogue arise from various structural levels, ranging from the underlying des ign, as demonstrated abov e , to its registral iso lation in the context of the last sec tio n. This register connects it to the climax of the moveme n t. Additionally, as the last member of a T5 chain, the epilogue merges invariances within the chains that have permeated the movement. One of the mos t intricate ways in which the epilogue brings back the even ts of the movement is the way in which it invokes the opening. The Stadlen edi tion reproduces Webern 's instructions to emphasize the melodic pi tches of the openi ng phrase (ex. 17). These nonadjacen t pitches of the rows form a hexachordal collection that belongs to the same cla ss as one arising betwee n segments of simultaneous row pairs, as Robert Wason has noted (1987 , 95 -9 6, 99). Most significantly , however , the pcs of the opening melody are precisely those tha t form the last trichord s of the epil ogue (ex. 1 7). That these last trichords form a hexachord tha t is a member of this same hexachordal collection-cl ass arises inevitably from Webern 's use of trichordal partiti oning and retrograde-re lated row pairs in thi s movement; that the trichords are formed of the exac t same pcs as the opening me lody reveals Webern 's sens itivity to the possibilities inherent in his com pos iti onal design for its surface realization.

The Second Movement The second moveme nt has been discussed in great detail by several analysts (Babbitt (1960) 1962, Bailey 1991, Lewin 1962 and 1993, Mead 1993, Nolan 1989, Wason 1987, and Weste rgaard 1963). As Babbitt has noted ([l 960J 1962, 117), the second movement is based on simul taneous row pairs generated by the same index numb er of inversion as employed for the rows of th e thema, and thus the row pairs yie ld the same simultaneous dyads . As is well known, the bipartite second movement is bas ed on a two-voice canon and the pitche s are , for the most part , registrally fixed and arranged around the axis of symmetry, A4

Example 17. Connections between the opening and conclud ing measu res of mvt. I

(D ""

f I I I I I

firs! R rel. row pair

@ 121

@5G)t@ e 7 a:i)s@

I ~

H'-

last R rel. row pair

: ~21 : t It 3 4 8

'

~ 0 ~-< ~

"' s -

:t 0 tj 0 1 5

(IQ

E;:: 0 s 0 ::l rt

.i,. \()

50 In Theory Only

Like the firs t movement, the formal layout of this movement can also be considered as an interaction among various aspects of its underlying design (ex. 18). The 16-related row pairs of the second movement are RP-RlJ' and RT J'-RlJ' in the first part, while the second part employs RT2P-Rl,P and RT5P-Rl,P. As example 18a indicates, the 16-related row pairs form Ism1-related row -pair couples, whic h articulate the bipartite shape of the movement. The T, chains (eit. 18b), wh ich run in opposite direction s, form a continuum over the entire composition connecting the last and first row pairs as adjacent members of the chains.

In this movement, the degree of pc intersection proves importan t both between ad jacent and simultaneous hexacho rdal areas, as it reveals the overall rhythm of change of the mus ic . In hexachords of adjace nt rows the degree of pc intersection decreases until the last row pair returns to the hexachordal areas of the very beginning (ex. 18c).

Example 18. Underlying design of mvt. II: (a) row pair couples, (b) row pairs" and (c) pc intersection between hexachordal areas

18a.

18b.

T,

1 '


Exam ple 18 (cont.) 18c .

'

16

.5 ~ .-----;. . 11/5 15/3 15/1 . ..._____,,,. .

~

A/seg B/seg

:'>/3

B/mot A/ mot

Bisi A/sl

b/0

'r.{o

1 ''~

A/seg B/seg

51

The degr ee of pc in tersection between simultaneous rows indicates how rapidly the dyads change within the hexachords , as noted by Mead (1993 , 184) and intimated by Wason (1987 , 84-85). The opening and conclusion manifest th e same rhythm of change , the most rap id, whereas the third row pair manifests a contrasting rhythm of change , the s lowest.

Finally, the second movement displays all the hexacho rdal areas of the thema. A-segme n tal and B-segmen tal hexachordal areas frame the movement acting as poin ts of departure and arrival, while the m iddle row pairs yield the ordered sets of motivic and slurred/ nonslurred dyads of thema phrases A and B. Thus, in the row pairs of the second movement, the intersecting pcs are precisely those between th e three pairs of discrete hexac ho rdal areas of the th ema phrases, and the pcs A and El>, ari sing from pc inte rsection 1/5, becom e the axes of symmetry .

The rh ythms of the phrases aris e from the rhythm of change inherent in the hexachords of the rows . With in th is overall rhythm of change the particularities are determined by the properti e s inherent in the Ts chains and in the lsm1 row-pair cou ples. The following analytical vignettes , the first showing th e opening phrase and the second comparing the opening an d concluding phrases, will demonstrate the mo re general principle of the manner in which the

52 In Theory Only

underlying design becomes, wit h its different rhythms of change, the source of the su rface composition.

The opening phrase (ex. 19) introduces the basic elements of the phrases . (Lewin ( 1993] calls the first three dyads of the opening phrase TUNE.) Th e parts of the phrase have thei r roles as opening , middle, and concluding elements , associated with the specific dy ads, dynam ics, articul atio n, and contour. The remaind er of the phrases are based on these same elements, and on their varied and extended forms (Westergaard 1963). In these varied forms the pcs may remain the same while some other characteristic, such as articulatio n ,or dynamics, changes; or in some cases the other featu res remain the same while the pc content is altered.

Example 19 further compares the opening and concluding phrases, which manifest the same rhyth m of change. The T5 relation between the rows resul t s in the segmental dyads forming the opening phrase occurring at every other order number of the conctuding row pair, that is , at order numbers {2468t}. Thus, these dyads maintain the same order while the intervening dyads are employed to vary or extend th e phrasal elements.

Finally, a closer look at these passages shows that the very end of the last phrase, before the stinger (m. 22) , brings back the events of the opening of the movement in a way that echoes by analogy the epilogue of the first movement. Example 20 indicates how the three last dyads of the concluding phrase (mm. 20-21) are RT6 of the three initial dyads of the movement. Furthermore, th is transposition level differentiates the three initial dyads as those dyads that have only one fixed regis ter all through the movement , from the three final dyads as those that may change their register according to their functions within the phrases (Mead 1993, 186).

Example 20. Opening and concluding dyads (mm. 1-2 and 20 -21) of mvt. II

mm.12

{81} {99} {15} '

{7e} {33} {24} mm. 20-21


Example 19. Elements of the opening and concluding phrases (mm. 1-3 and 18-22) of mvt . U

opeAing phrase

opening elements

conduding phrase 1

P: l5P:

~c: The Third Movement

tniddf.e element concluding element

l \

89574 : t91e2 \\\\

I I I I I 8697 1 Oe32 t09e 56734

upboatrstinger

53

With the entrance of the the ma at the beginning of the third movement, the relationships of the two previous movements receive a condensed interpretation, which elucidates the relationships of these movements in a crystallizing moment . This then serves as a basis for the subsequent five variations. The variation form arises from disc rete

54 In Theory Only

areas of the thema phrases, which comprise those rows that can produce the ordered or unordered dyads of the segmental and mot ivic hexachordal areas of the thema. Since the third movement is based for the most part on the partitioning scheme of the thema, the use of the discrete A and B areas makes possible an unfolding of the same dyads and te trachords within one area.

ln this manne r the surface composit ion of the variatio n s may employ the various possibilit ies inherent in the dyadic sets of the segmental and mo tivic hexachordal areas of the thema to form an intricate motivic interplay based on the thema phrases. The first two variations are based on discrete A and B areas , whereas th e fourth, the culminating variation, intermingles various relationships of the thema in the same fashion as the first and second movements ; the two variations surrounding it, the third and the fifth, initiate and conclude these chains of re lationships.

The first and second variations' underlying des igns are based on discrete A and B areas . In the first variation (ex. 21), the rows of th e B area belong to the main four -row family, whereas the rows of the A area are based on P and the two invers ionally related rows that extend its hexachordal areas (Mead 1992, 127-28).

Examp le 21 . Underlying design of mvt. Ill, var . 1: A and B areas

mm. ~p ~ ~1 0P R16P Rl1P Rl1P Rl7P

ordered/ Ord. Ord. Ord. unon:t. unord. unocd. orBlseg A/seg A/seg A/seg AJseg Blseg

The underlying design of the second variation (ex. 22) employs row pairs from the two main fou r -row families, in this ins tance those generated by R. from P and 16P and their I.m1-related row pairs. Hence, the relationships, which in the thema are interpreted with one row, are in the second variation interpreted with two consecutive rows that produce the sets of dyads heard in the corresponding phrase in the thema. Example 23 sketches some of the ways in which the possibili ties inherent in the underlying des ign become vivid on the musical surface. The example shows the variation's three ph rases by aligni ng their corresponding elements . It further shows the main partitioning scheme as it is applied to the first two rows. This scheme follows closely the partitioning of the thema , thus producing the same set of dyads (with one exception). A quick compariso n with the thema and the first variation reveals how th e motivic material introduced in


the thema and further developed in the first variatio n forms the bas is of the surface inte rpretation of this parti tioning. In additio n to the obvious motivic connections based on the various articulations of the ic 1 dyads , one could mention, for example , the accented four-not e fort e gesture (mm. 25-26). This gesture echoes, through its contour and pc content, m. 10 of the thema and its various elaborations in the first variation (mm. 13-14 and 18-22) . The Ism1 relation between the rows offers opportunities to shape the phrases as well. For instance, the Ism1-related row pairs produce an invarian t tetrachord at order numbers (2345) and these invariances are employed to connect the soft ritardando figures within the phrases.

Example 22. Underlying design of mvt. III, var. 2: A and B area s

mm. @ RlsP @ R,,P RloP Rlof' R1P on::leted/ on! . on!. Ord. On!. Ord. unord. set:s of dyads

AJmot A/5'Jg Blseg Blseg Btmot

The fourth and culminating variation is permeated by row chains tha t are initiated in the third variation. These row chains employ rows of two four-row faroiUes, th e first containing P and the second containing the rows yielding the unordered dyads of the motivic hexach ordal areas of the middle thema phrase . These families are connected by the same index number of inversion. In the music, the rows of these families are grouped to form row pairs exhibiting the second Ism relation (P-Rl5P, T3 P-RI,.P, T6 P-Rl,P , and T9 P-RI, P} in the same fashion as the row- pair coup les of the first movement's middle sectio n . Example 24 shows the manner in which these row pairs form two interlocked row -pair chains (Lewin 1987 , 182). The seven last hexachords of these chains form the culmination of the third movement as well as the climax of the entire work. One of the ways in which the special qualiti es of this passage are achieved is the particular manner in which it invokes the thema by unfolding its various dyadic areas (ex. 25).

56 In Theory Only

Example 23. Mvt. Ill, var . 2, mm. 23 -33

rit, __ __ _ ___ .. _ ,.

,if . - - -- - - - -->

rH, __ ___ ___ . kno.p::, >

Rl5P: 89 rn-, Ot 1 e 5 43 76 '2 c TeP:

_:]3 j1l9 6 78 45 9 The beginning of the culminating passage is demarcated first by the ordered accompanying tetrachord of thema phrase A and second by the ordered melodic dyads of the opening phrase of the thema. These ordered melodic dyads arise from the sole row of the row class tha t yields the ordered melodic hexachord of P as an ordered segmental hexachord (Mead 1992 , 130 -31) . The culminating passage then continues with dyads that combine accompanying dyads of A and B.


With th ese dyads th e climax reaches the extreme high register of the entire work (A6, mm . 53-54), a strncturally significant pc all through the piece. The pass age concludes with the dyadic sets of the B area, first with its melodic tetrachord and second with its accompanying and melodic hexachords.

Example 24, Underlying design ofmvt. III, var. 4: interlocked row-pair chains

culminalin9 passa~e

The fifth and concluding variation becomes a truly prominent moment in which the symmetrical aspects interact with the accumulation of the relationships that contribute to its sense of anival . This accumulation takes place on various structural levels. For example, as Lewin has poin ted out (1987, 183), there is a return to the five-beat phrasal units , which characterize both the thema and the first movement. The very end of this variation, the passage that follows these five-beat phrasal units, forms a coda based on the rows of th e thema, which concludes not only the third movement but also the entire work by representing in a condensed fonn the basic characte ristics of the piece. 13 That is, the passage manifests the way in which the phrasal shap ing and sense of progression interact with the symmetrical, frozen aspects of the pitch organization. This passage combines the register-symmetrical arrangement of the second movement with the mirror-symmetrical aspects of the first movemen t: the pcs that in the second movement are arranged symmetrically in register around the pitch A4 are in this concluding passage arranged

'3Le"''in calls the entire fifth variation a coda !l 987, 183). The final passage of the fifth variation may well be described as "a coda. within a coda."

Example 25 . Dyadic areas of hexac hords and tetracho rds in the culminatin g passage of mvt. UI (mm. 51-55)

- ~ ~ ' ~ . ~ I

> of.I , ~ .

' .... I

lf ~t > 4, ~ .,.!A,{( I ! -

U"!: '

~-

>

T6P Rl0P T9P Rl2P ord./unord. ord. Ord. hepta.: unord. unord. unord. sets of dyads tetr. hex. dyads tetr. hex. hex.

A/ace Almer A+B/acc B/mel 8/acc 8/mel

{le}(01) {23)(67)(45) (10}"(01 ){76J(le) 9 {12)(34) {56){91}{76) {12){34){eOJ

v, 00

S' ~ 0 t:J 0 ~


symmetrically in time around the second axis of symm etry, the pc Eb (ex. 26) . As the examp le further illustrates, registral differe n tiation in the coda extracts precisely th ose pitches that change registe r s in the second movement . Interacting with this symmetrical arrangement is a phras al shaping that divides the passage into three subphrases . In the conte xt of the fifth varia tion, the sense of conclus ion achieved with these subphra ses arises from various features, such as a mirror-symmetrical construction with regard to the very beginning of the variation and a T. transposition of the conclusion of the main body of the varia tion . On a deep er structural leve l, the sense of conclusion ach ieved with the last cho rds arises from the manner in which they complete the symmetrical arrang eme nt, which is a manifestation of the thema through the first and second mo vemen ts. Thus, as sketched in example 27a, just as the epilogue in the first movement and the conc luding phrase in the second moveme n t bring back the openings of these movements, the coda at the very end becomes a representation of the relationships of the thema and the first and second movements.

Examp le 2 6 . Symmetrical aspects in the coda (mm. 62-66)

...... A4

8 0 t 7 5 9 5 7 8 2 0 4 0 2 1 9 4 , 8 6 t

'-v.-' '-;-v--' ~

q:)61'1ir.g phrue/ m..t, II

60

"c 8 -

In Theory Only

' I

i :;;-"' .e. ~

'I' 0 ~ ,

' ..

~ ~

..

i 't'~ ~ ii 'l> > o: 'o

'

' I J ..

J~ ]J

l .. ]} J N J~ ] N


Example 27. Variations, op. 27 (a) temporal accretion and (b) symmetrical structures

----~ ' / '

" ' / ,. .. -,,

---- -- ,........A..... ',\ -1\ - ,,

- l,i, a. i~ ~ ,;,.,.,.m,,,a,.._ _________ ~~

I o

b.

1 1 II Ill ' 1 I

' '

A B I I

' ,. B A' ' I I A B A" AB A'

u, 1,: :I Jhema var. 1 II Ill

A"

A B 2 3

'

A' s

I

' I

' I

' ' ' I I 1

' I I I I I I !

Conclusion

61

As suggested at the outset, this work shows Webern's deep interest in symmetrical structures that interac t with through-composed aspects. This has been illustrated with =mples from the first and the second movements, as well as with an anal ysis of the manner in which the coda encapsulates the qualities of the piece as a whole. However , this dialectic exists in the formal layout of the entire composition (ex. 28). The third movement's first two variations reflect the second movement, and the concatenation of variations three , four , and five echo the tripartite structure of the first movement. The structural similarities arise from the use of the same hexa chordal areas but motivic connections also occur .

62 In Theory Only

Example 28. Parallels between mvt. Ill and mvt. I-II Mvt. Ill

The ma var. 1 2 3 4

motbAc same lsm2 connections hexachordal row

araas paira

same hexachordal motivlc areas coMections

l/ l 1 11, :II: :II !!

Mvt. ti Mvt. I

5

tOW$ of the Thema enter

1 A'

The third movement's first hvo variations are bas ed on the segmental and motivic hexachordal areas of thema phrases A and 8, which are the hexachordal areas of the second movement's firs t part." Example 29 illustrates ways in which the underlying structural similarities are signaled by motivic con nec tions by sketching the manner in which some of the significant moments in the first two variations invoke the second movement. First, both variations open with prominent motivic materials of the second movement: the first variation picks up as its initial motif the exact pitches of the concluding element of the second movement's final phrase (ex. 29a), and the second variation opens with the characteristic repeated staccato As of the second movement (ex. 29b). Moreover, the melody that leads to these ticking As in the first variation's concluding phrase is framed by pitches Ab 3 and B b5 , the exact pitches of the second movement 's opening phrasal elements. Examp le 29c illustrates the manner in which the first variation's climactic phrase (mm. 18-21 ) is

14\Vason has noted the $t!'UCtural sunilarity between the second variation and the second movement by pointing out common inversional-symmetrical aspects of the row organization in these two sections ( 1987, 70, 86) .

Koivisto , The Defining Moment 63

framed by gestures that evoke the middle phra sal elemen ts of the second movement through their pitch contents and melodic contours. Lastly, when trichords belonging to the collection class [016! enter for the first tim e in the third movement's second variation, they are exactly those cho rds hear d before in the second movemen t's opening part (ex. 29d ).

The opening of the third variation signals its similarity to the first movement by being the only variation to employ mirror-synunetrical phrases. '5 On a deepe r strnctural level, the connections betw een variat ions thre e, four, and five and th e first movement arise from aspec ts in th eir unde rlying designs (ex., 28). The symmetrical phrases of the third variation and the first movement's A section are based on the same hexachordal areas yielding the slurred/nonslurred dyads of thema phrase A and th e motivic dyads of thema phrase B. The fourth variation and the first movement's middle s ection are based on row chains formed from kn 2-rela ted row pairs. 16 The fifth variation and the first movement's A' section are punctuated by a return of the rows of the tbema.

Example 30 illustrates the vivid manner in which the associations between the first moveme n t and the third variatio n 's opening phrases are emphasized by regj.stral connections. Examp le 31 th en shows the manner in which the opening of the culminating , the fourth, variation prominently invokes the climax of the first movement's middle section : at these moments the row -pair chains feature th e same row, and the associations are emphasized by surface composition. The sense of return in the fifth variation and in the first movement's A' section as \\ell as their structu ral similarities have been pointed ou t and discussed by Lewin (1987, 183).

"'wason presents the idea that the third varia tion grew eventually il'.lto the firs t movement/ ' by pointing out similarities in the retrograde symmetrical aspects between the third variation and the first movement (1987 , 70, 87) .

161.ewin has discussed the structural similarities of the row transformations of the two chains in the first movement's middle section and iD the third movement's fourth variation (1987, 182).

64 In Theory Only

Example 29. Motivic connections between mvt. III, var. 1-2 and mvt. II: {a) var. 1, mm . 12-13 and mvt. II, end of concluding phras e (m. 2 1); {b) var . 1, con clu ding phras e (mm. 21-23) and mvt. II, opening {m. l ); {c) var. 1, mm. 18 and 21 and mvt. ll middle phrasal element (m. 16); (d) var. 2, tri chords and mvt. II trichords

29a , o@ ~

~-.

J ~ l'f

29b.

ri+. -- - --- __ __ _ kmfO, !aI ~ . +

=-


Example 29 (cont.)

29c.

! "- . --- ------- ---,n@ '

. ~ I . ~ ;._ J . . I

~ IVV'N f-0 . ~

., :i. . 1,

.

Xi&)

~ . '" . r 1'-

29d. mvt. i i: m. 24 26 30(33 31 mvt,ij; m,8 4 9 3

66 In Theory Only

Eltalllple 30. Associat ions betwe en mvt. III, var 3, opening (mm . 33-35) and mvt. !, opening (mm. 1-4)

0 ,__ @ , __ ..,..,. _______

-.

., I ' I '"'

- ' , _ f'- f t'f


The structural similarities between variations one and two and the second movement, and between variations three, four, and five and the first movement, clarify the manner in which the thema lies a t the focal point of a large -scale symmetrical structure. This large-scale structure, as well as the series of nested symmetrical structures within it , dupli cates the tripartit e formal layout of the thema (ex. 27b, p. 63). Hence, as comparison between examples 27a and 27b reveals, the entire work's large-scale formal shaping manifests the dial ectic between the balanced, symmetrical structures and the sense of progression, a quality that charac terizes the work in various spans of time, as well as the thema itse lf.

In this music, the strong sense of progression, interacting with the symmetries, arises from continuous, multilayered accumulation of relationships and events . In the process of hearing the entire work , the thema emerges as the defining moment : it enters at the focal point of a large -scale symmetrical structure, bu t at the same time it crys tallizes the relationships of the two previous movements. This crystallized interpretation then serves as a basis for the varied elaborations introduced in the subsequent five variations . The coda concludes the piece by capturing the relationships of the ,thema through their interpretations in the first and second movements .

The wealth of relationships inherent in Webern's Variations for Piano, Op. 27, a composition that has fascinated musicians for decades, cannot fully be enjoyed without taking into account the interaction between the surface composition and the underlying structures, just as it cannot fully be appreciated without acknowledging the dialectic between its symmetrical structures and the sense of temporal accretion. By inspecting these dialectics, whether between the surface and deeper levels, or between symmetry and temporal accretion, one may learn more about this music than by inspecting any element alone. It is only through this interaction that in such concise idioms of composition as Webern's a piece may become an intensified moment with depth that penetrates all its structural layers .

68 In Theory Only

Refe ren ces

Babbitt, Milton. 11960] 1962 . Twelve-Tone Invarian t s as Compositional Determinants. Musical Quarterly 46: 246-59. Reprin ted in Problems of Modem Mu.sic, ed. P. H. Lang. New York : Norton .

___ . 1987 . Words About Mu.sic. Ed. S. Dembski and J. Straus . Madison : Un iv. of Wisconsin Press.

Bailey , Kathryn. 1991. The Twelve -Note Music of Anton Webern: Old Forms in a New language . Cambridge: Cambri dge Univ. Press.

Hasty, Christopher. 1981. Rhythm in Post -Tonal Music: Preliminary Questions of Duration and Motion. Journal of Music Theory 25/2: 183-216.

Leibov.itz, Rene . [ 1949 ) 1970. Schoenberg and his School. Trans . D. Newlin. Reprint, New York: Da Capo .

Lewin , David. 1962 . A Metrical Problem in Webern's Op. 27. Journal of Mu.sic Theory 6 I 1: 124 32.

___ . 1987. Generalized Musical Intervals and Transfonnations. New Haven, Conn.: Yale Univ. Press .

___ . 1993. A Metrical Problem in Webern 's Op. 27. Mu.sic Analysis 12 / 3: 343 -54.

Mead, Andrew. 1992. Review of The Twelve-Note Music of Anton Webern: Old Forms in. a New Language by Kathryn Bailey. Integral 6: 107 - 135 .

___ . 1993. Webern, Tradition , and Composing wi th Twelve Tones. Mu.sic Theory Spectrum 15/2: 173 ~204.

Morris, Robert. 1987. Composition with Pitch-Classes: A Theory of Compositi.onal Design. New Haven, Conn.: Yale Univ. Press .

Nolan, Catherine. 1989. Hierarchic Linear Structures in Webern's Twelve-Tone Mus ic. Ph.D . diss., Yale Univ.

Schnebel, Dieter . 1984 . Die Variationen fur Klavier Op. 27. Musik-Konzepte: Sonderband Anton Webern 2: 163 -217 .

Koivisto, Th e Defining Moment 69

Stadlen, Peter . 1958 . Seriali sm Recons idered. The Score 22: 12-27 .

Travis, Roy. 1966. Directed Motion in Schoenberg and Webern. Perspectives of New Music 4/2 : 85 -89.

Wason, Robert. 1987 . Webern's Variations for Piano, Op . 27: Musical Struc tu re and the Performan ce Score. Integral 1: 57 -103.

Webern, Anton. 1983. Aus dem Briefwechsel Webem -Steuermann . Musik -Konzepte: SonderbandAnt on Webern l : 23-51.

---

. 1979. Variationen fur !Gavier, Op. 27. Ed. P. Stadlen. Vienna: Universal Edition.

Westergaard, Peter. 1963. Webern and "Total Organization" : An Analysis of the Second Movement of the Piano Variations, Op. 27. Perspectives of New Music 1/2: 107 -20.

__ _ . (1962 ) 1972. Som e Problems in Rhythmic Theory and Analysis. Perspectives of New Music 1/ 1: 180 -91. Reprinted in Perspectives on Contemporary Music Theory, ed. B. Boretz and E. T. Cone, 226-37. New York : Norton.

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koivisto - 1997 - the defining moment the thema as relational nexus

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