C. Catherine Losada - Between Modernism and Postmodernism

57

Between Modernism and Postmodernism:Strands of Continuity in Collage Compositions

by Rochberg, Berio, and Zimmermann

c. catherine losada

This article discusses a group of pieces that can best be understood as musical collages: the thirdmovement of Luciano Berios Sinfonia (1968), the first movement of George Rochbergs Music forthe Magic Theater (1965), and the last movement of Bernd Alois Zimmermanns Musique pour lesSoupers du Roi Ubu (1966). It demonstrates that chromatic complementation and a concurrent sys-tematic process of chromatic saturation provide the logic behind the harmonic, formal and voice-leading content of these pieces, thus establishing an unexpected link between these works andtheir serial predecessors.

Keywords: Berio, Rochberg, Zimmermann, collage, Postmodernism, quotation, chromatic comple-mentation, chromatic saturation, Sinfonia, significant gap, gap-fill

In the last forty years the extensive use of musicalquotation and juxtaposition of contrasting styles has cre-ated an unprecedented level of heterogeneity in the mu-sical language. The musical collage,1 in particular, explicitlysubverts the concept of unity by juxtaposing various frag-mentary quotations from different musical styles within a

single composition.2 Thus, it poses the most stimulatingquestions for the analyst: What is the relationship betweenthe disparate elements in a collage? What are the structuralimplications of combining such a variety of disparate ele-ments? Finally, what theoretical tools should be used to ana-lyze music with such diverse musical idioms? This article ad-dresses these questions within the context of concreteanalytical findings. It discusses a group of pieces that canbest be understood as musical collages: the third movementof Luciano Berios Sinfonia (1968), the first movement ofGeorge Rochbergs Music for the Magic Theater (1965), and

I would like to thank Ellie Hisama, Philip Lambert, Andrew Mead,Catherine Nolan, Philip Stoecker, Joseph Straus, and the anonymousreaders of Music Theory Spectrum for their helpful feedback on earlierdrafts of this article.

1 In this article, my usage of the phrase musical collage refers to reper-toire (written mainly since the 1960s) that conforms to the definition ofcollage found in Burkholder (The New Grove Dictionary of Music andMusicians, 2nd ed, s.v. Collage): The juxtaposition of multiple quota-tions, styles or textures so that each element maintains its individualityand the elements are perceived as excerpted from many sources andarranged together, rather than sharing common origins . . . Elements in

a collage differ in key, timbre, texture, meter or tempo, and lack of fit isan important factor in preserving the individuality of each and convey-ing the impression of a diverse assemblage.

2 Kramer (1995, 12) defines the concept of unity from the twentieth-century modernist perspective as the condition that all parts in a compo-sition have to be related not only to the whole but also to each other.

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the last movement of Bernd Alois Zimmermanns Musiquepour les Soupers du Roi Ubu (1966).

With its unprecedented power to elicit explicit referentialconnotations, this music brings to the forefront the dialecticopposition between referential and absolute meanings inmusic,3 as well as the conflict between formalist and expres-sionist approaches to analysis described by Leonard Meyer.4

Coupled with the difficulties that the incorporation of dis-parate materials poses to the analytical process, the level ofreferential determinacy has created a tendency for analyticalwork on this repertoire to be limited in scope, focused on adescription of the main constituents and the referential con-notations of these works.

Many analyses of Sinfonia, for instance, have confinedthemselves to a listing of sources (an essential first step inany such analysis), coupled with tentative phenomenological,semiotic, or psychological conjectures regarding the motiva-tion and effect of their combination.5 George Flynn (1975)takes this approach to the extreme. He emphasizes the po-etic effect of the heterogeneous musical surface and explicitlyrejects any technical approach to Berios music, claiming thatin listening to Berios music the listener need not chase tonerows, intervals, durational patterns, or otherwise discover

and keep track of precompositional production plans. Suchdenotative activity can only damage the listeners primary,poetic responsibility to the music (393).6 Although analyti-cal approaches that concentrate exclusively on the referentialand expressive aspects of these works can address importantaspects of the composition as an artistic product, they fail toidentify the importance of the choice of a particular excerptfrom a composition as opposed to another and imply that amusical product can be created where the relationship be-tween its constituent elements is primarily defined by criteriaother than specific technical associations.7

My study, following Meyer, posits that in musical experi-ence the same stimulus, the music, activates tendencies, in-hibits them, and provides meaningful and relevant resolu-tions for them (1956, 31). It thus attempts to provide adiscussion of the quantifiable elements of these works, whichso far have not been systematically analyzed. Isolated techni-cal aspects of collage compositions have been discussedmainly within the context of a particular piece.8 Generally

58 music theory spectrum 31 (2009)

3 Meyer (1956) states that absolutists are those that insist that musicalmeaning lies exclusively within the context of the work itself, in theperception of the relationships set forth within the musical work ofart, and that, on the other hand, referentialists contend that musicalso communicates meanings which in some way refer to the extramu-sical world of concepts, actions, emotional states, and character (1).

4 Meyer (1956) explains that the formalist would contend that themeaning of music lies in the perception and understanding of the musi-cal relationships set forth in the work of art and that meaning in musicis primarily intellectual, while the expressionist would argue that thesesame relationships are in some sense capable of exciting feelings andemotions in the listener (3).

5 Hicks (198182), for example, deals exclusively with the referential im-plications of the practice of quotation with a particular emphasis ontextual relationships in Sinfonia.

6 Similarly, Dixon (1992) and Ringer (1966) focus for the most parton how Rochbergs music reflects the composers ideological preoc-cupation with the reevaluation of the musical past and his new aes-thetic of stylistic pluralism, thus bypassing a technical discussion of hismusic altogether. A technical approach, in this context, refers to an an-alytical methodology that seeks to describe patterns and structures thatresult from the purely musical elements of a piece (such as pitch,rhythm, duration, dynamics, texture etc.)

7 Though this is certainly the case for many Dada compositions or worksthat rely heavily upon chance (many works of John Cage, etc.), it couldhardly be applied to a work such as Sinfonia, where almost every singlepitch and its placement are so carefully controlled.

8 Osmond-Smiths (1985) excellent study of Sinfonia identifies the quo-tations contained in the piece and describes isolated technical elements(such as the sharing of common pitches, harmonic basis or melodicshapes) that associate many of the disparate components. LikeOsmond-Smith, Budde (1972) and Altmann (1977) present isolatedexamples of ways in which disparate quotations are connected inSinfonia, within the context of a discussion of the piece in more generalterms. Danuser (1988) examines connections in Rochbergs music and

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between modernism and postmodernism 59

speaking, the technical connections are discussed in a limitedfashion, noting isolated relationships between materials,and the underlying large-scale processes are never clearlyaddressed.

Other approaches to this repertoire have been constrainedin different ways, by concentrating, for instance, on a singlecomposers output.9 Only recently has the practice of bor-rowing been scrutinized from a wider perspective. PeterBurkholder has been instrumental in this respect, setting upa useful typology of musical borrowing that crosses differenttime periods and styles.10 Likewise, works that incorporatemultiple quotations have been subjected to scrutiny as a uni-fied body in the work of Lisa Brooks Robinson (1994), whotraces the influence of Mahler in several collage composi-tions.11 Although isolated technical aspects relating to the

musical function of the quotations with respect to the collagecontext into which they are introduced have been describedby all these analysts, there has been no attempt to describethe large-scale structure of these pieces or to trace structuralfeatures that span different compositions.

The present study will address both of these concerns. Byemphasizing technical aspects over referential implicationsof the practice of collage, it will describe techniques for link-ing disparate elements and features of the musical languagethat transcend foreground events and that are also commonto a variety of different compositions written in this style.12

I will demonstrate that the heterogeneous surface of thesepieces does not reflect a simplistic rejection of deeper con-nections, but instead is governed by a multitude of associa-tions that create unconventional structures and relationships.Taking these relationships as its basis, I will outline a struc-tural model that does not simply ignore the contrasts in themusical language, but instead embraces these contrasts as fun-damental building blocks,13 thus simultaneously subvertingand transcending traditional notions of unity. Furthermore,this article will demonstrate the intimate relationship

and prolonged) and motivic techniques. The only link between theprocesses she describes in her analyses of these different pieces is thereliance on Mahler: Many of the procedures applied to the appropri-ated material represent an exaggeration or intensification of proceduresand techniques found in the works being quoted and/or in other worksby Mahler (1994, 49).

12 Following Meyer (1956, 33) this study assumes that the disagreementbetween the referentialists and the absolutists is . . . a result of a ten-dency toward philosophical monism rather than the result of any logi-cal incompatibility. Thus it does not seek to undermine the referentialapproaches to these works, but rather to provide an alternative andcomplementary methodology that yields interesting insights into themusical language.

13 In this way this study responds to Kramer (1995, 12), who calls for an-alytical approaches that will embrace, rather than deny the postmod-ernist aesthetic of diversity of these works.

elucidates similar relationships in Zimmermanns and Berios music(Danuser 1990, 402-03; from Tillman 2002, 7879).

9 Such is the case with Adamss (1983) study on R. Murray Schafer,Klppelholzs (1981) study of the music of Mauricio Kagel, the insight-ful discussions of the music of Zimmermann by Khn (1978) andKiesewetter (1985), and the discussion of continuities in the music ofThomas Ads by Roeder (2006).

10 See Burkholder 1994 and his two entries in The New Grove, s.vv.Collage, Borrowing. Similarly seeking a broader outlook, Metzer(2003) has focused on how the referential implications of the practiceof musical quotation extend over a variety of different styles. He studiesthe role of quotation as a cultural agent in a variety of twentieth-century repertoires, including the music of Ives, Duke Ellington andBubber Miley, Schoenberg, Berio, Rochberg, Sandra Bernhard andStockhausen, among others.

11 The works Robinson analyzes include the final movement of LukasFosss Time Cycle (195960), the first movement of Rochbergs Musicfor the Magic Theater (1965), the third movement of Berios Sinfonia(1968), and the second movement of Schnittkes Fourth ConcertoGrosso/Fifth Symphony (1968). Applying an approach that blends refer-ential and technical analysis, her analyses of the individual pieces ex-plore intertextual associations, various structural procedures such as ex-pansion, integration, and defamiliarization (a term that refers to theconcept of art as a process through which perception is complicated

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between these structures and the formal and dramatic struc-ture of the pieces, thus uncovering surprising sources of uni-fication and continuity.14

The findings contained in this article shed new light ontwo of the most provocative issues of the postmodern de-bate. The first relates to the applicability of the concept ofunity as a necessary characteristic of a musical language (andhow it can be imposed on a given musical structure when itis heard or analyzed).15 The second relates to the dispute re-garding the prevalence of continuity or discontinuity be-tween modernism and postmodernism.16

Some authors have defined postmodernism as existing inopposition (either as a reaction or resistance) to modernismwhile others question the idea of a break asserting that theword postmodern itself is useful in implying links with

modernism.17 One of the main arguments that this lattergroup invokes (Kaplan 1998, 3) is that resistance is a funda-mental feature of modernism and that most features typicallyassociated with postmodernism have been found in earlierperiods, and most notably in modernism proper ( Jameson1988, 2627).18

A useful concept in understanding the postmodernistbent of these works by Berio, Zimmermann, and Rochberg,is the concept of pastiche. Frederic Jameson (1988) invokespastiche as one of the most significant features or practices inpostmodernism (15). He distinguishes pastiche from parodyby clarifying that parody capitalizes on the uniqueness ofthese styles and seizes on their idiosyncrasies and eccentrici-ties to produce an imitation which mocks the original(1516) while pastiche is a neutral practice of such mimicry. . . without the still latent feeling that there exists somethingnormal compared to which what is being imitated is rathercomic (16). The juxtapositions endemic to the musical col-lage associate the music with pastiche, as opposed to parody,since the very multiplicity of references makes a single normimpossible to establish. The meaning of the work doesnt de-pend upon a single reference point, but instead upon the ef-fect of their combination.

The musical surface of these works purposefully throwsinto question both the notion of individual style and thenotion of an underlying commonality between the differentelements, two fundamental aspects of modernism.19 Thus, in

14 The term unification implies the existence of cohesive relationshipsamong all parts, the term continuity implies a stronger condition wherethe temporal aspect is essential to the structure of the relationships.Kramer (1995) has defined discontinuous music as music that isepisodic in nature and lacking in development (23) however, thischaracterization really only denies the existence of one kind of continuity.

15 Kramer (1995) argues that there is always a handy analytical methodavailable to demonstrate how (if not that) the music coheres. All weneed do is try hard enough, bend the piece or the method sufficiently,or ignore disunifying factors, in order for the piece to come out unified.Both listening and analyzing create as well as discover unity. But is thatunity really in the music? (15). Also [i]t is all too easy to project theperceptual unity of listening back onto the stimulus. The postmodernaesthetic, however, encourages us to separate the two, by conceiving ofthe text-the music-as autonomous . . . the listeners perceptual unity/disunity is not identical to the musics textual unity/disunity. An analy-sis of these collage works, which maintains sensitivity to this perspec-tive, will contribute to a refinement of this discussion.

16 Kramer (1995) states that modernism includes the progressive andoften atonal music composed after approximately 1909 (20). Jameson(1988) adds that modernist aesthetic is in some way organically linkedto the conception of a unique self and private identity, a unique person-ality and individuality, which can be expected to generate its ownunique vision of the world and to forge its own unique, unmistakablestyle (17).

17 Foster (1983) is a scholar who sees postmodernism as anti-modernist;Kaplan (1988, 1) is one who questions a break between modernism andpostmodernism.

18 Jameson (1988, 15; 28) and Kaplan (1988, 35) go on to discuss the con-cept of postmodernism as being related to the new social/production/consumption contexts that arose in the new 1960s, as much as to thecontent of a work of art in itself .

19 Harvey (1989, 45) posits the rejection of meta-narratives as one im-portant factor that sets (postmodernism) apart from modernism.Kramer (1995, 21) argues that the great meta-narrative in music is or-ganic unity. Thus, the rejection of organic unity, which the surface of

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concrete technical terms, it seems that these collage workswere conceptualized as a reaction to modernism (and are thustheoretically allied to a postmodernism of reaction). Thefindings described in this article reevaluate this assertion,demonstrating that the links to modernism are as importantto the structure of these works as the elements of resistance.

chromatic saturation and the significant gap

Although it has not traditionally been discussed in refer-ence to this repertoire, the relationship between aggregatecompletion and musical structure is essential to many otherstyles of composition. These include atonal works in addi-tion to pieces that incorporate twelve-tone compositionaltechniques and even more specifically pieces that exploitcombinatorial relationships of various types. Charles Rosen(1975) has stated that the saturation of musical space isSchoenbergs substitute for the tonic chord of the traditionalmusical language. The absolute consonance is a state ofchromatic plenitude (4748; quoted in Straus 1995, 230).This view attaches special significance to the moment wherethe musical space is fully saturated and invokes the conceptof expectation in this context, which is in accordance withWeberns remarks on aggregate completion: In short, a ruleof law emerged; until all twelve notes have occurred, none ofthem may occur again. The most important thing is thateach run of twelve notes marked a division within the piece,idea, or theme (1963, 51).20

The principles of chromatic completion and gap-fill pro-cedures in more recent music have been discussed at length

by Straus with reference to the melodic process of RuthCrawford (Straus 1995, 816; 41).21 These principles are di-rectly applicable to this study. In the compositions by Berio,Zimmermann and Rochberg which are examined in thisstudy, the disparate quotations that are juxtaposed or super-imposed are related by chromatic complementation.22 The con-cept of chromatic complementation postulates that the pitchcollections presented by the different quotations interactwith one another not on the basis of their similarity or inter-section, but on the basis of their difference and the mannerin which they combine to create progressively larger collec-tions. Thus, disparate elements are brought into relationshipwith one another in a manner that seeks to build upon,rather than vanquish the dissimilarities between them. Thecomplementation relationships result in a process of chro-matic saturation, in which the musical space is completelyfilled in through the appearance of each one of its con-stituent members. In these pieces, the musical space consti-tutes a pitch (in the case of Berios and Zimmermannspieces) or pitch-class (in the case of Rochbergs piece) subsetof the chromatic collection. The different elements that con-tribute to the process are not necessarily presented simulta-neously, but must be bound by common membership in agiven musical structure (for example a phrase, or a larger for-mal section of a piece). The conjunction of chromatic com-plementation and a concurrent systematic process of chro-matic saturation provides a model for the harmonic, formaland voice-leading content of these pieces.

these collage works invokes explicitly, is another aspect that has earnedthem the designation of postmodern.

20 Various theorists have recently argued for the significance of the mo-ment of presentation of the complete chromatic in classical works byHaydn, J.C. Bach, Mozart, Beethoven, and others (see Baker 1992;1993, Burnett and ODonnell 1996 and Burnett 1998).

21 Straus introduces many concepts that are relevant to the current discus-sion, such as the process of chromatic completion as an element withcadential function and as a factor than can create connections acrosssectional boundaries. He also provides embryonic examples of otherprocedures that involve chromatic completion and gap-fill, includingprocesses that structure the pitch organization on various levels (estab-lishing a sense of hierarchy), that provide large-scale connections be-tween formal sections, and that exploit the full aggregate.

22 This idea resonates with Roeders (2006) discussion on the importanceof voice-leading parsimony in the music of Thomas Ads.

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The expressive potential of such a model is realizedthrough the significant gap: in which the musical space is de-marcated implying that it will eventually be saturated.23, 24

This concept extends Meyers (2000) essentially melodicconcept of gap-fill25: The relationship is one in which theincompleteness created by a gap implies subsequent com-pleteness through a fill; and, generally speaking, the largerthe gap, the stronger the sense of incompleteness and theimplication of fill (163). According to Meyer, the mind...expects structural gaps to be filled; but what constitutes sucha gap depends upon what constitutes completeness within aparticular musical style system (1956, 44).26

To arrive at what constitutes completeness within thismusical style I will invoke Meyers concept of a soundterm, which he defines as a sound or group of sounds(whether simultaneous, successive, or both) that indicate,imply, or lead the listener to expect a more or less probablyconsequent event (1956, 45).27 One of the ways in which

the practice of collage composers differs from Crawfordspractice lies in that the boundaries of the operative tonalspace are often clearly stated, and the space itself is subse-quently emphasized through various means. RochbergsMusic for the Magic Theater, for instance, incorporates amultitude of twelve-tone lines throughout the work, whileBerios Sinfonia makes extensive use of the chromaticcluster as one of the works most important gestural com-ponents. Through these and other devices, the beginningsof all three pieces discussed in this article establish thefilling in of chromatic space as a crucial sound term forthe piece.

For instance, two of the most structurally importantsections of the third movement of Berios piece,28 the intro-duction and recapitulation, start with the quotation of con-trary motion chromatic lines from Schoenbergs FnfOrchesterstcke, Op. 16, No. 4 Peripetie (presented here inExample 1) and a chromatic cluster from G3 to E5 that ver-ticalizes and saturates the space opened up by the first twochords of the same piece (given in Example 2).29 Above thiscluster, there is another layer, which consists of notes from23 Meyer (1973, 110) defines an implicative relationship as one in whichan eventbe it a motive, a phrase, and so onis patterned in such a

way that reasonable inferences can be made both about its connectionswith preceding events and about how the event itself might be contin-ued and perhaps reach closure and stability.

24 To emphasize the sense of process and the dramatic potentiality of theexplicit delineation of the space to be filled I have chosen the terms chro-matic saturation and significant gap (as opposed to the more neutral termgap-fill and the more goal-oriented term chromatic completion).

25 Significantly predating these authors, Riemann (1895, 1819) explicitlyinvokes the filling up of a gap as an important determinant of melodicstructure and harmonic progression. In the context of harmonic progres-sion, he especially recommends the use of steps of a minor second.

26 Although Meyers concept of gap-fill does not invoke chromatic spaces,in the following discussion I will demonstrate how his concept can beextended beyond the tonal realm in a manner that is consistent with hismethodology.

27 Meyer (1973) asserts that most of the time a pattern can be fully com-prehended and its internal relationships analyzed only by seeing what fol-lows from it (113). Meyer also points out the dangers of implied eventsresulting from statistical probability, given the fact that the realization of

an implication can be significantly delayed. To circumvent this dangerhe urges that it is necessary to stipulate as precisely as possible whatthe antecedent events are understood to imply. For the more preciselythe organization of each parameter in the consequent event is specified,the less likely that event matching those specifications is the result ofstatistical distribution (117). Thus, the clarity of presentation of thesound terms employed in these pieces and the exact coincidence of therealization of the implications with important structural moments inthis piece are essential aspects of this analysis.

28 The ways that Rochberg and Zimmermann establish the sound termwill be discussed later.

29 Berio clearly distinguishes the separate components of Chord A and Bthrough reference to Schoenbergs original instrumentation. As inSchoenbergs original, Chord B is given to the brass and Chord A isgiven to the strings, while the percussion, strings and woodwinds chro-matically saturate the gamut.

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the C Major/minor scale (the tonality of the Mahler Scherzo)and extends to the pitch E7 (Example 3). The beginning ofthe third movement of Sinfonia thus establishes the system-atic filling in of chromatic pitch space as an axiomatic soundterm (both through the use of chromatic scales and chro-matic clusters).30

Meyer states that the existence of both similarity and dif-ference between musical events is a necessary condition forpatterning of any sort (1973, 26). The juxtaposition of a clus-ter and a more open texture at the beginning of the piece pre-sents an incomplete pattern which establishes a structural gap.Meyer also states: Once a sound term has been established asa coherent, though not necessarily as a complete or closedunit, then part of the series taken by itself will, generally

speaking seem to be incomplete, particularly if the fragmentoccurs in the earlier parts of the total work (1956, 129).Furthermore, a shape or pattern will, other things beingequal, tend to be continued in its initial mode of operation(1956, 92).31 The ensuing quotations, with their complemen-tary pitch contents and the continual reappearance of chro-matic clusters continue the process of chromatic saturation.

As we have seen, the filling in of chromatic spaces is op-erative in serial music, the music of Crawford and even sometonal music. However, differing from tonal works and incontrast to Crawfords music, where chromatic completionresults from a continuous melodic process, the element oftonal juxtaposition is of paramount importance to theprocess of chromatic saturation in these collage works. Thecomplementary pitch/pitch-class relationships between thequoted passages create tonal contrasts that call into questionthe structure of the tonal space which will be employed inthe work, thus emphasizing the significance of the processand the moment of its saturation. Through this process, thepresentation of the complete chromatic in these works has a

30 As will be discussed later, these pieces also invoke this sound term byreferring and responding to the normative structures of modernism.

31 Elsewhere he states: The law of good continuation (which he appliesmainly to melodic processes) is relevant and applicable to other musicalprocess as welle.g., harmony, instrumentation, texture, form and soforth. Any aspect of the musical progress governed by probability rela-tionships, whether these relationships are products of learning or theresult of relationships created within the context of the particular work,establishes preferred modes of continuation (125).

38 38 38

38

38 38

Trumpet in C 1

Trumpet in C 2

Trumpet in C 3

Trombone 1

Trombone 2

Trombone 3

example 1. Chromatic scales from Schoenberg,Fnf Orchesterstcke, Op. 16, no. 4, measure 2

A B C

example 2. First three chords from Schoenbergs Fnf Orchesterstcke, Op. 16, no. 4 Peripetie

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completely different effect than it has in a piece where thechromatic material is fundamentally integrated into themain tonal fabric.32 Thus, the compelling expressive strengthof the structural gaps is unique to this repertoire. As Meyerstates: A structural gap, then, creates a tendency toward fill-ing in. And if this tendency is delayed, if the completion ofthe pattern is blocked, affect or the objectification on mean-ing will probably follow (1956, 134). Much of the expressivecontent of Sinfonia, for example, results from the incorpora-tion of contrasting quotations which invoke different tonaluniverses and the occasional reemergence of MahlersScherzo, events that interrupt the process of gap-fill.33

The process of chromatic saturation in these pieces isnon-serial and takes different forms along a continuum ofcomplexity. The discussion of the movement from BeriosSinfonia will demonstrate how the technique can operate inpitch space and serve to articulate large-scale formal structure.The discussion of the other pieces will show that the tech-nique is more widely applicable. Rochbergs Music for theMagic Theater will illustrate how the same technique functionsin pitch-class space and how significant gaps can define

voice-leading on a local level. Zimmermanns Musique willdemonstrate how the expressive potentiality of the signifi-cant gap can be exploited.

berio, sinfonia

The techniques of chromatic saturation are adapted topitch space and include every pitch of the composition in thethird movement of Berios Sinfonia, which, as PeterBurkholder tells us, is considered by many the prototype of amusical collage (New Grove Dictionary of Music andMusicians, 2nd ed, s.v., Borrowing). This piece is looselymodeled on Mahlers Symphony No. 2. The explicit corre-spondences between the third movements of both pieces arestriking.34 The outer form of the third movement of Sinfoniafor the most part conforms to the structure of Mahlers

32 Baker (1993) states: Chromaticism may serve to enrich, expand, sur-prise, and confuse, but ultimately, as both Schenker and Schoenbergagreed, its purpose is to confirm the tonic (259).

33 Meyer (1973) writes: Only when a pattern proves to be problematic dowe tend to become consciously aware that it is implicative (114).

34 However, it is possible to extend the concept of modeling beyond thethird movement. Both pieces are in five movements and borrow fromnumerous musical sources. Furthermore, there are explicit connectionsbetween the corresponding movements. For instance, the fourth move-ment of Sinfonia begins with an overt reference to the fourth movementUrlicht of Mahlers Symphony. The four voices state the two openingpitches of the solo alto line in the same register. Furthermore, the con-ceptual organization of the fifth movements of both pieces is closelyrelated: both pieces contain extended quotations from the previousmovements, a feature that Berio develops within his collage aesthetic toincorporate simultaneous layering of previously presented material.

Significant Gap from E5 to E7Represents a chromatic clusterwithin those boundary pitches

example 3. Significant gap from E5 to E 7 through reduction of the opening sonority in the third movement of Berio, Sinfonia

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Scherzo. The latter is utilized like a cantus firmus throughoutmost of the piece, and provides the underlying rhythmic anddurational framework for nearly all of the remainder, even inthe absence of actual thematic presence. Quotations are gen-erally layered over the Scherzo so that they coincide with oreven emphasize important subdivisions. Thematic referenceto the Scherzo at the points of subdivision, through a resur-facing of the dominant thematic material (the reprise), isprevalent. Thus, the apparent discontinuity of the surfacecontrasts of the piece is somewhat abated by the clarity ofthe underlying ABACABCA formal structure of the Scherzo.

Within this framework, however, the thematic material ofthe Scherzo is fragmented so that it sometimes disappears al-together from the texture, while at other times it is juxtaposedwith other fragments. On top of this, commentary from thecomposer is added, in the shape of added layers, clusters,chromatic lines, distortions of the thematic material, numer-ous fragmentary and stylistically distinct quotations from therepertoire, and even occasional deviations from the dominanttemporal framework (especially through two large insertionsduring the course of the piece). The commentary tends to pe-riodically obliterate the tonal language of the Scherzo and thesense of process implicit in its thematic organization on aforeground and middleground level.

The voices participate in this process by creating varyingdegrees of distance from the musical surface through an arrayof techniques that range from yelling to singing, with manyintermediate stages, including the rendition of fragments ofsolfge. Furthermore, they explore the gamut of distance be-tween composer, performer, audience, and philosophicalcommentary in a theatrical fashion, alternately being an inte-gral part of and commenting off-handedly on the piece. Thiscommentary often deals with surface details, such as words ortitles that clarify the particular quotation that is being heardat that time. For example, the reference to chamber musicduring the quotation of Hindemiths Kammermusik (rehearsalA14, measure 23), to a violin concerto (being played in theother room) during the quotation from Bergs Violin Concerto

(rehearsal C14, measure 56), to Daphne et Chloe under-neath the quotation of Daphnis et Chloe (rehearsal D23, mea-sure 88) and many other instances. However, the text rangesthe gamut from surface irony to philosophical questions. Theclimax of the piece is introduced by a text by Berio that ques-tions the very significance of the work of art: And when theyask, why all this, it is not easy to find an answer. For when wefind ourselves, face to face, here, and they remind us that allthis cant stop the wars, cant make the young older or lowerthe price of bread . . . (Berio 1968, Home Forum Page). Infact, one of the most important roles of the voices is how theycomment on the most important structural idiosyncrasies ofthe piece. In this way, the voices explicitly refer to processesintrinsic to the act of composition.

Though the present discussion will not attempt to dealcomprehensively with the text, it will refer to ways in which itis intimately linked to both the structural and dramatic contentof the piece. One of the most significant instances of textual re-currences in the piece is that of the vocalists fragments Wherenow? When now? and Keep Going which are overwhelm-ingly associated with sectional divisions and especially the im-pending reprise of the initial scherzo material and the simulta-neous resurfacing of Mahlers Scherzo.35 In the passage that

35 Keep Going appears for the first time in the middle of the first state-ment of the initial theme (measure 17), where it signals the impendingcontinuation of the phrase. It appears later in the piece overwhelminglyrelated to the reintroduction of the Scherzo material. For instance, it in-troduces the second section of the initial scherzo (W, rehearsal C18and C21, measures 60 and 63), the impending return of the initialtheme in that section (rehearsal D22, measure 87), the scherzo repriseafter Trio I (rehearsal G13, measure 143), Trio II (rehearsal R22, mea-sure 368), and at the end (rehearsal EE1, measure 550). The other threeoccurrences refer to impending or aborted attempts to return toMahlers thematic material: after the theme that acts as an interruptionin the initial scherzo (rehearsal D12, measure 77), at the beginning ofTrio I (rehearsal E7, measure 102) where the soprano attempts but isunable to reestablish Mahlers text) and to introduce the transition toTrio II (rehearsal J4, measure 199), cementing the struggle betweenMahler and Stravinsky that occurs at that point.

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corresponds to the second scherzo reprise (rehearsal S, mea-sure 375), this association is exploited in an extremely com-pelling fashion, which demonstrates the integral role of thetext to the structure and dramatic content of the piece.Having established a pattern of correspondence between theemergence of Mahlers thematic material and the occurrenceof the scherzo reprise, Berio breaks with both expectationsfor a highly effective dramatic effect. During the retransitionthat precedes the passage, the reintroduction of the scherzoreprise is prepared through the gradual reemergence of mater-ial from the Scherzo (beginning at rehearsal R11, measure 358,but especially after rehearsal R23, measure 369), by means ofthe descending chromatic motive that introduces the scherzoreprise (rehearsal R28, measure 374) and the simultaneous ap-pearance of the text so frequently associated with the reestab-lishment of Mahlers text (Keep Going, rehearsal R22, mea-sure 368). However, Berio obliterates the scherzo reprise with awrenching quotation from the drowning scene in Wozzeck,which carries the tension build-up far beyond its originalbounds. The effectiveness of this moment lies in the listenersexpectation of a decrease in tension (through the reestablish-ment of the Scherzo) and the substitution for a quotation thatnot only maintains, but also increases the tension graduallyand steadily to a level almost beyond endurance. A literal bat-tle between Berg and Mahler ensues, represented by the voicesurging alternately to Stop and Keep Going.

The reliance on Mahlers Scherzo therefore constitutesonly one layer in the analysis: the outer form of the piece.In spite of the numerous ways in which Berio emphasizesthe characteristics of Mahlers piece, there are also importantstructural moments unrelated to the Scherzo. The mostimportant example on the large-scale level is the inserted re-capitulation immediately preceding the climax of the move-ment, a move that has no basis in Mahler. This divergencefrom Mahlers scheme is extremely significant to the struc-ture of the piece, as will be discussed below.

On a localized level, the interplay of disparate elements,musical languages, and musical styles (including that of

Mahlers Scherzo) creates pitch associations that encompassand interact with the dimly perceived tonal vestiges ofMahlers piece. As a result, they create a formal structure oftheir own, which subsumes the structure of the Scherzo. Therelationship between these disparate elements thus consti-tutes yet another layer of analysis, that of inner form, whichis of primary concern in this analysis.

The conflict between these two formal aspects is never re-solved in this piece. Instead it is an integral aspect of its ex-pressive power. The different quotations in Berios piecethrow the tonal space of the piece into doubt, thus creatingambiguity. Of course, the longer doubt and uncertainty per-sist, the greater the feeling of suspense will tend to be. Thestimulus situation creating doubt and uncertainty must, ofcourse, be progressively intensified if suspense is to be main-tained or increased (Meyer 1956, 28). The Mahler Scherzoserves such a role. It periodically emerges and temporarilysimulates resolution of the tonal conflicts established by thepiece. However, this feeling of resolution is subverted everytime as the Scherzo disappears from the musical surface,yielding to more tonal contrasts which heighten expressionas they urge towards resolution.

The apparently disparate musical layers are related in avariety of ways, including pitch relations of exclusion (whichbecome a paradoxical source of unity through the concept ofchromatic saturation in pitch space).36 Excerpts interact withone another to saturate specific pitch-space chromaticgamuts. This relationship is significant because for the mostpart the quotations are presented unaltered and untrans-posed. In this view, the pitch content of a given quotation,and the manner in which it complements the chromatic con-tent of the excerpts surrounding it, determine the exact

36 Significantly, the concept of chromatic saturation is related to one ofthe most characteristic techniques of the musical text on which themovement is primarily based. Chromatic proliferation constitutes anessential feature of Mahlers developmental and variation techniques inthe figuration of the Scherzo.

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choice of the quotation to be used and its placement at anypoint throughout the movement. This structural model thusoffers an explanation for the choice of quoting a particularexcerpt from a composition.37

Examples 4 and 5 demonstrate how chromatic comple-mentation works on a foreground level. Example 4 presentstwo excerpts that are juxtaposed in Berios piece. The circledpitches in the oboe and flute are abstracted in Example 5 inorder to explain how the quotation from Berliozs SymphonieFantastique at rehearsal E12E13 (measures 10708), providestwo previously unheard pitches, A5 and B5, which registrallyconnect the space opened up by the preceding excerpt fromDebussys La Mer.38 Through the saturation of a givengamut, each section of music is governed by a sense of struc-tural completion, the weight of which coincides with thefunctional importance of its formal boundaries. Although in

nearly every section there are pitches that do not constitutepart of the foreground saturated gamut, these pitches be-come integral to gamuts at higher structural levels.

Example 6 demonstrates the process of chromatic sat-uration of the Trio I excerpt that contains the material ofExample 4, subdivided into its initial two subsections. Theinitial subsection (rehearsal E6E15, measures 10110) pre-sents a fully saturated gamut from E3 to C6. Significantly,the F3 that is provided by the misquotation of Mahler at re-hearsal E9 (measure 104) provides the only appearance ofthat pitch in this section, suggesting that Berio uses distor-tions of the original material not only to signal the degree ofdistance from it at the given moment, but also to adapt it tohis structural scheme. The pitches outside of the chromati-cally saturated gamut in the lower register outline the pitchboundaries of the middleground structure (D2) and thebackground structure (E1) respectively, while the gap createdby the missing C6 in the upper register signals that the sec-tion is not yet completed.39

The following subsection complements this scheme insignificant ways. The chromatic scales that appear within thesecond subsection (rehearsal E15E25, measures 11020)both emphasize the gamut of the initial subsection by reiter-ating the pitches E3 and C6 (Example 7), and saturate themiddleground gamut it outlines in the lower register (downto the pitch D2). Simultaneously, quotations from Ravels LaValse (No. 19) provide the C6, missing in the first subsection,and outline a middleground upper boundary (a significantgap) to the pitch A6. The eventual saturation of the gamut

37 As I stated earlier, other authors, such as Osmond-Smith, have offeredcompelling explanations as to why a specific piece is referred to at anygiven time in the composition. These explanations are based on the ref-erential connotations obtained by quoting from a specific piece at anygiven time, and how they relate to the text or dramatic content of thepiece. However, they often fail to identify why a specific excerpt from agiven piece is chosen as opposed to any other.

38 The columns in Example 5 represent measure numbers. The rows inthe example represent pitches laid out chromatically in pitch-space,with the lower pitches appearing at the bottom and increasing by asemitone with each successive row. The numbering system that I haveused is that in which C4 represents middle C; the shaded areas repre-sent the measure where a specific pitch first appears in the excerpt andthe patterns indicate which quotation provides the particular pitch. Thelayout of Example 5 is similar to the charts that Bernard employs tograph his operations in pitch space (see Bernard 1981; 1986 and 1987).It is also similar in some ways to Clendinnings Range Graph (seeClendinning, 1995, 236). The difference between my example andClendinnings graph is that while her graph includes only pitches actu-ally sounding at any given time, my graph focuses on the first appear-ance of a particular pitch and then graphs that pitch as something thatremains in effect conceptually throughout the rest of the section, even ifit is not actually sounding.

39 The importance of outer boundaries, which are stressed in my analysisand which represent the lowest and highest points attained in thecourse of particular passage are essential aspects of Bernards approachto the music of Varse; many of his structures depend upon total spaceoccupied over a period of several measures (Bernard 1981, 10).Clendinning (1995, 252) also remarks on the importance of outerregistral boundaries that are conceptualized as operating over a wholesection of music in her analysis of Lontano.

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38

38 38 38

38

38 38 38 38

Flute 1 & 2

Oboe

English Horn

Clarinet 1 & 2

Violin I

Violin II

Viola

Cello

Double Bass

104

pizz.

alla punta

Pont.quasi niente

Debussy, La Mer II, 19 Berlioz, Symphonie Fantastique II, m. 122

example 4. Berio, Sinfonia, III, r. E9E15 (measures 10410) excerpt, in concert pitch. Copyright 1968 by Universal Edition A.G., Vienna. renewed. All Rights Reserved. Used by permission of European

American Music Distributors LLC, sole U.S. and Canadian agent for Universal Edition.

MTS3101_03 4/16/09 6:46 PM Page 68


up to this new upper boundary pitch provides structuralcompletion to the whole section that contains this excerptand introduces the first scherzo reprise. Although local sec-tions of music saturate gamuts, the combination of struc-turally linked local sections is required to achieve the satura-tion of a middleground significant gamut. Thus, rarely does alocal section contain a chromatic gamut equal to that of thesection as a whole.

Through the significant gap, the pitch organizationreaches a high level of sophistication. The expectations ofcompletion achieved through the presentation of a specificpitch or the saturation of a given gamut permit the concep-tualization of distinct structural levels. These structural levelsare based on a hierarchical system intimately connected topitch space and range. The premise is that smaller saturatedgamuts tend to organize foreground events while largergamuts constitute background structures. The dramatic roleof notes in both registral extremes, which will be discussed inwhat follows, supports this conceptualization by positing thatsignificant gaps which extend into registral extremes havemore dramatic potentiality, and thus more of a structuralweight when they are filled, than gaps within the middlerange. The system offers an explanation for large-scale

coherence in terms of pitch content and elucidates the struc-tural import of the different sections of the movement.

The interaction between the pitch structures and the for-mal organization of the third movement of Sinfonia on alarge scale demonstrates both the depth of the formal re-liance on Mahlers Scherzo and the importance of the in-serted recapitulation, which constitutes the major formaldeviation from it. The graph in Example 8 summarizes thestructures formed by chromatic saturation and the significantgap and their function on three different structural levels.40

Example 9 provides a key to the notation in Example 8. TheABACABCA formal structure of Mahlers Scherzo and theinserted recapitulation constitute the main subsections in thelarge-scale pitch organization of the movement. The signifi-cant gaps and chromatic gamuts within these sections consti-tute pitch relationships that substitute for the obliterated andtranscended tonal language of Mahlers Scherzo in creating in-nate links that give depth as they interact with the superficialstructures created by thematic recurrence. Simultaneously, the

40 Each level emphasizes the operative boundary notes of progressivelylarger sections of music.

Debussy La Mer II, no. 19

Berlioz Symphonie Fantastique II, m. 122

104 105 106 107 108C6B5B5A5G5G5

example 5. Chromatic complementation in the oboe and flute lines, r. E9E13 (measures 1048)

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example 6. Chromatic Saturation of Trio I excerpt, r. E6E25 (measures 10120)

A Altered Mahler quotation

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 A6G6G6F6F6E6D6D6C6C6B5A5A5G5G5F5F5E5D5D5C5C5B4A4A4G4G4F4F4E4D4D4

Mahler's Scherzo

Berlioz, Symphonie Fantastique II, m. 122

Ravel La Valse, no. 18, m. 10

Debussy, La Mer II, no. 24 m. 2

Debussy, La Mer II, no. 19

Ravel La Valse, no. 18, m. 7

Chromatic Lines in Keyboard

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 C4C4B3B3A3A3G3F3 AF3E3E3D3D3C3B2B 2A2A2G2G2F2E2E2D2D2C2B1B 1A1

:F1E1

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pitch structure of the piece emphasizes the dramatic outlinesof its large-scale directed tension spans through chromaticexpansion of the boundaries.

Formally, the background graph (extracted as Example 10),illustrates how, in this view, the complete saturation of the sig-nificant gap from E7 to A7 constitutes a dominant structureof the piece. The systematic presentation of each of the en-compassed pitches as background upper boundary notes,

culminating with the presentation of E7 as the backgroundupper boundary in the recapitulation of the movement, com-pletes the process of saturation.

The pitch E7 appears briefly during Trio I (B) in a chro-matic scale that saturates the background gamut to theboundary pitch A7. Similarly, it constitutes part of a chro-matic scale in the second scherzo reprise, which saturates thegamut to the boundary pitch F 7. Not until the reprise of

38 38

38

38

Piano

E. Harpsichord

Pno.

E. Harp.

113

116

example 7. Berio Sinfonia, III, r. E18E24 (measures 113119); range E2C6 with gaps. Copyright 1968 by Universal Edition A.G., Vienna. renewed. All Rights Reserved. Used by permission of European

American Music Distributors LLC, sole U.S. and Canadian agent for Universal Edition.

MTS3101_03 4/16/09 6:46 PM Page 71


I

II

III

( )( ) ( )

( ) ( ) ( ) ( ) ( )( ) ( )

( )

( )( )1 2 11 19 33 45 57 58 62 74 98 101 104 140 146 181 188 210 228 230

233255 266 308 342

Intro. AInitial Scherzow w '

BTrio I

A1st Scherzo Reprise

CTrio IIx

trans.

z

( ) ( ) ( )( )

( ) ( )

A G

( )

( )( )

example 8. Structures formed by chromatic saturation and the significant gap in the third movement of Berios Sinfonia

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( )

( )

( )( )( )( )

( )357 375

395423413 488457 496 502 575559

568

A2nd Scherzo

trans. BReprise

Trio I

CTrio IIx

C (cont.)

CLIMAX

RECAPITULATIONReprise

AFinalReprise

( )

( )

F F E

I

II

III

example 8. [continued]

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Significant Gap

35.Represents a simultaneouslysounding chromatic clusterfrom G3 to E5.

a) b)

E Moment when gap is filled Missing pitch ( )A E Missing pitch appears

Represents a space that is staurated byall pitches within a section. The space isoutlined by the boundary pitches Dand B

c) d)

Chromatic Extension of the boundary notesA A

e)

example 9. Key to the notation in Example 8

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Trio II, where it contributes to saturate the gamut to theupper-boundary pitch F7, does the pitch E7 appear indepen-dently of a chromatic scale. By this time, its appearance con-firms the existence of large-scale scheme through which thegap from E7 to A7 (first extended by a semitone to A7), isgradually and systematically filled in by successive chromaticpitches appearing as background upper boundaries (G7 fromthe first scherzo reprise through Trio II, F7 during the secondscherzo reprise, and F7 during the reprise of Trio I and TrioII). This scheme reaches its culmination in the recapitulation.At this point, the gap from E7 to A7 of the beginning is re-stated, but is immediately followed by the pitch E7. Thispitch thus takes up its post as the background upper bound-ary through a literal semitonal extension of the previouslyoperative E7 and the significant gap from E7 to A7 is finallysaturated on a large scale.41

Meyer says that a feeling of harmonic completenessarises when the music returns to the harmonic base fromwhich it began or moves to one which was in some wayimplicit in the opening materials (1956, 150). The recapitu-lation of this piece achieves both levels of completeness as it

first restates and subsequently fills the significant gap thatwas presented at its beginning.42

Foreground and middleground details highlight the E toA gap. For instance, throughout the first section of the move-ment, which corresponds to the introduction and the initialpresentation of the scherzo (A), the gap from E7 to A7 isfilled with the exception of the pitch E7. Thus, the significanceof the appearance of this pitch and the concurrent saturationof the initial gap are established and replicated on a fore-ground level. Throughout this section, the registral and pitchspecific structural gaps are emphasized by textural and coloris-tic treatment. The A7 initially appears as a sustained harmonicthat is separated in color and texture from the main body ofthe piece. Beginning with the music at rehearsal A20A24(measures 27-31), the sonority expands chromatically into aharmonic cluster that progressively absorbs the pitches G7,G7 and F7. Thus, the gap is further emphasized by color andtexture considerations. When the gap is finally filled later inthe piece, these textural distinctions disappear as well.

The background lower boundary notes also emphasizethe essential structural function of the recapitulation. In theopening section of the movement, a gap from F1 to C1 is set

42 The law of return appears to operate most effectively where the givensound term is left incomplete. Since the sound term is a Gestalt which setsup forces toward a particular kind of closure, the only way it can be closedis by repeating it with a new and more final ending (Meyer 1956, 153).

41 Significantly, as can be seen in Example 11, there is a parallel sym-metrical process through which the middleground boundary notesrise chromatically from C7, C7, D7 and finally reach the E7 of the re-capitulation.

example 10. Large-scale upper register significant gap (level III of Example 8)

m. 1 101 146 210 375 423 457 488 568

A

( )( ) G F F E

A B A C A B C AInitialScherzo Trio I 1st Scherzo Reprise Trio II 2nd Scherzo Reprise Trio I Reprise Trio II Reprise Recapitulation Final Scherzo Reprise

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up. This gap remains unsaturated until the transition to thesecond scherzo reprise (which is an important structuralboundary in Mahlers Scherzo, signaling the moment whenall the main components of the movement have been pre-sented). The gap is finally filled in by the presentation of thepitches D1 and E1 (Example 11) in the four measures thatprecede this important juncture,43 where the reprise of the

scherzo is subsumed by a quotation from Wozzeck, as was dis-cussed above. In the recapitulation, this structural process ispresented in a condensed form by an F1 to C1 chromatic mo-tion in the bass (Example 12), which constitutes an importantgesture that connects the recapitulation to the reestablishmentof Mahler for the climax of the piece and the reestablishmentof C1 as the principal lower boundary note.

43 The lower boundary pitch of a given gamut is often reinforced throughits appearance as a bass note at the distance of an octave. For instance, inthe initial section of the piece (Section A), the background lower bound-ary note C1 is reinforced through the foreground lower boundary noteC4, and the implication of middle-ground lower boundary pitches C3and C2, by chromatically dense spaces above them. Similarly, large-scaleand middleground upper boundary notes are often separated by an oc-tave from the foreground sectional gamuts that they contain. For ex-ample, throughout the first subsection of the initial scherzo (W), theupper boundary notes of the clusters are E6, an octave below themiddle-ground upper boundary pitch E7. Likewise, the second section ofthis initial scherzo has an upper boundary pitch A6, an octave below thebackground upper boundary pitch A7. Similarly, the first scherzo reprisepresents a foreground upper boundary pitch G6, which is an octavebelow the background upper boundary pitch, G7. Bernard (1987, 65;1994, 234) and Clendinning (1995, 24041) discuss the similar role ofoctave doublings in the music of Varse and Ligeti, within the context ofanalytical models that are based otherwise based on pitch space.

example 11. Large-scale significant gaps, upper and lower registers, with parallel motion from the middleground upper boundary pitches

( )( )

m. 1 101 146 210 375 423 457 488 568

A B A C A B C AInitialScherzo

Trio I 1st Scherzo Reprise Trio II 2nd Scherzo Reprise Trio I Reprise Trio II Reprise Recapitulation

( )( )C1

F1

Final Scherzo Reprise

8

example 12. Gesture that connects the recapitulation with the reestablishment of Mahler for the climax of the piece,

r. AA13BB1 (measures 5002). Condensed filling in of theLower Register Significant Gap from F 1 to C1. Copyright

1968 by Universal Edition A.G., Vienna. renewed. AllRights Reserved. Used by permission of European American

Music Distributors LLC, sole U.S. and Canadian agentfor Universal Edition.

83

83

Cello

Double Bass

Sounds an octavelower than written

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Immediately following the recapitulation (rehearsalAA1AA14, measures 488501), the harmonic rhythm ofthe movement slows to an unprecedented degree as theprocess of saturation of a gamut extends over larger portionsof music. As in other sections of the piece, the text com-ments on both the structural and dramatic content of thepiece in a very explicit way. The increasing disintegration ofthe texture, which leads to the final dissolution of the mo-mentum, is accompanied by the text He is barely moving,now, almost still (rehearsal EE7, measure 556). The senseof completion achieved by the recapitulation is illustrated inthe timing of the saturation of its gamut. The outlined C1-E7 gamut is not completely saturated until the final scherzoreprise. Thus, the recapitulation provides large-scale closureto the piece as it fulfills the structural expectations set up bythe pitch structure of the initial sections, while it introducesboundary pitches of a gamut whose gradual saturation coin-cides with the ending.44 In this way, the recapitulation clari-fies and resolves the large-scale structural implications ofthe piece in a manner that is analogous to processes thatoccur in tonal music. The realization, during the recapitula-tion, of implications set up at the opening of the piece(often reiterated in fact by the restatement of the materialfrom the opening) is an important device (Meyer 1973,14344).

Each of the structural background boundary notes A7 andC1 is expanded by chromatic motion of two semitones in thecorresponding direction during the course of the piece. Thepitches B0 and B0 extend the gamut of the piece as a whole inthe lower direction as do the pitches A7 and B7 in the upperdirection. With the exception of the pitch A7, none of thesepitches function as middleground or background boundarynotes. Thus, it is only by viewing the piece as a whole thatthey fit into the pitch structure of the piece and achieve their

function. The range from B0 to B7 constitutes the total chro-matically saturated gamut for the piece, and this gamut wouldprovide the ultimate reduction of the background structure ofthe piece. Since these chromatic extensions of the backgroundgamut have no middleground function, I shall examine theirsignificance to the background structure of the piece.

Significantly, the appearances of these background chro-matic extensions of the gamut correlate to important goals inthe directed motion and spikes in the dramatic contours ofthe piece. The gradual build-up of tension that occurs fromthe beginning of the piece through the initial appearance ofTrio II is accompanied by the chromatic extension of thebackground upper-boundary note from A7 to A7. The tem-porary dissolution of built-up tension during the course ofTrio II, which leads the piece to its nadir point, is accompa-nied by a large insertion of material and the chromatic exten-sion of the lower-boundary pitches by two semitones to thepitch low point of the piece.45 The textif this noise wouldstop thered be nothing more to say . . . the show is over; all isover, but where then is the hand, the helping hand . . . its a longtime comingmakes explicit reference to the dramaticfunction of the music at that point. Finally, in a move that in-creases the significance of these chromatic extensions, imme-diately following the structural completion achieved by therecapitulation in Berios piece, the climax is reached through aquotation of Mahlers climax, which extends the upper-boundary note for a final time from A7 to B7, the highpointof the piece. Evidently, the dramatic contour of the piece isemphasized by its pitch structure through the concept ofchromatic extension.

The most striking element of the movements pitch orga-nization involves the distinct structural levels possible toachieve by means of the significant gap. Thus, though on a

45 The B0 appears in the contrabassoon as part of the cluster (rehearsalM15, measure 269). The B0 appears in the same instrument at thelocal climax created by the Ravel La Valse quotation (rehearsal O9,measure 303).

44 Meyers apt discussion of how conjunct and disjunct patternings, andtheir interactions, generate implicative relationships on different hierar-chic levels (1973, 131) supports this argument.

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background level the structural pitch organization of themovement is defined by the gap from E7 to A7 and the ex-pectation of the saturation of that gap through the presenta-tion of the pitch E7, as described above, the subsections withinthis music also demonstrate completely organized pitch struc-tures that compellingly illustrate the correlation betweenstructural completeness and the saturation of a significant gap.

For instance, as I discussed with reference to Examples13, the first subsection of the initial scherzo (W, measures161) is governed by a significant gap in the higher registerthat is presented in the first chord of the movement

(Example 3). The final saturation of the gap from E5 to E7,with the presentation of the pitch C7 (in a quotation in thesolo violin from Bergs Violin Concerto at rehearsal C15(measure 57), coincides with the high point that prepares theending of the first half of Section A of the Scherzo (Example13; Example 14 provides the Berg excerpt). The manner inwhich the excerpt arpeggiates up to the pitch C7, thus subtlyreaching into the upper register as the section ends, makes thechoice of this excerpt particularly satisfying to the listener. Thesaturation of the initial significant gap of the movement coin-cides with the end of the first major subsection. The E7 is the

example 13. Middleground significant gap: Initial section of the opening scherzo

( )

( ) ( )

( )( ) ( )

E Intro A

Initial Scherzow

Significant Gap

II

I

(missing pitch)C* Arrival of Missing Pitch C7

w'

m. 1 11 19 31 33 42 43 57 58 62

Themes a a b a

MTS3101_03 4/16/09 6:46 PM Page 78

demonstrates the essential technical role of a particular ex-cerpt and its placement within Sinfonia.

The compelling structural power of this system is demon-strated by the existence of sections where more than two lev-els of structure occur simultaneously. The most important ofthese sections is the passage starting at rehearsal I7 (measure188) that achieves the transition between the first scherzoreprise and the second trio. True to its nature as a transition,the passage both literally provides structural completion tothe previous section while it sustains a significant gap that isto be saturated in the next section.

As the graph in Example 15 (which is extracted fromExample 8) shows, the first scherzo reprise (starting at re-hearsal G16, measure 146) presents three different boundarynotes, G6, C7 and G7. These boundary notes are forcefullystated and emphasized by the chords that end the scherzoreprise (quoted from Stravinskys Le Sacre). The most localgap, which achieves completion in the transitional sectionthat follows, is the gap up to G6. The saturation of this gap isachieved by the presentation of the pitches that are missingfrom the scherzo reprise, B5 and F6, as the last pitches in thetransitional section; thus, the transition can be seen as a struc-tural extension of the scherzo reprise, which culminates whenthe gamut to the upper boundary of G6 is finally filled.

Above it, the middleground gap up to C7 is initially re-ferred to in the last chords of the scherzo reprise. This C7 is


upper boundary note of a significant gap operative in themiddleground structure.

The graph in Example 8 suggests a correspondence be-tween the saturation of a significant gap and importantstructural boundaries that continues throughout the move-ment. As in the example discussed above, it is often the casethat the particular missing pitch is presented by a quotationthat is inserted towards the end of the section.46 The correla-tion between structural completeness and final saturation ofa gap through the presentation of a specific pitch thus

46 Other examples abound; for instance, in the second part of Section A (W,rehearsal C20E5, measures 62100), the Ravel La Valse quotations andMahler Scherzo material open up a gap to A6, which is filled by the pre-sentation of F6 within the quotation from Debussy La Mer at rehearsalE2 (measure 98) in the last few measures of the section. Similarly, thebeginning of the piece can be even further divided through the con-cept of the significant gap. At rehearsal B5 (measure 37), theHindemith excerpts expand the cluster that appears at B (measure 33)in the upper direction. Except for the C7, they eventually saturate thespace up to the D a major seventh above the previous limit (D7, seethe foreground graph of Example 23). Thereby, the upper registerspace opened up by the first sonority of the piece is for the first timepartially subjected to chromatic saturation. The reference to and par-tial saturation of the initial gamut coincides with the end of the repeti-tion of theme a in the Mahler Scherzo and introduces the section ofcontrasting material.

example 14. Sinfonia, III, (measures 5558). Quotation from Bergs Violin Concerto (I, measure 169). Copyright 1968 by Universal Edition A.G., Vienna. renewed. All Rights Reserved. Used by permission of European American

Music Distributors LLC, sole U.S. and Canadian agent for Universal Edition.

3 8 55 ! ! ! !

!

! ! !

* Pitch C7

Solo Violin

MTS3101_03 4/16/09 6:46 PM Page 79


emphasized as a sustained note (which is quoted fromMahlers Scherzo) throughout the transitional section thatfollows. The gap it outlines is literally and immediately filledwhen it becomes the upper boundary of the chromatic clus-ter that occurs at the beginning of the second trio. The finalgap presented in this first scherzo reprise is that up to thepitch G7, which constitutes the background upper boundaryfor this whole section through the second scherzo reprise.

Thus, the chromatic saturation of a given gamut providesthe motivation behind the combination of excerpts that do nototherwise relate in an obvious way through motivic or pitchsimilarities. The gamuts and boundary notes of these chords inadjacent sections interact to create important structural rela-tionships that emphasize the formal and dramatic structure ofthe piece. Because of the emphasis placed on pitch-space, themethodology employed in this analysis relates in interestingways to analyses that have dealt with other works that em-ploy pitch space as opposed to pitch-class space systemati-cally to delineate structure. These include works by Varse47,

Lutos awski48 and Ligeti,49 among others. The previous dis-cussion implies that the emphasis on pitch space, as opposedto pitch-class space relationships is a crucial characteristic ofmuch twentieth century music, and especially of music that

example 15. Middleground upper register significant gap: First scherzo reprise and transition

( )( )G

G

C

m. 146 188 210 308 342A (Scherzo Reprise) Transition C (Trio II)

47 As is evident from previous references, many of the analytical premisesof the current approach overlap with those that Bernard has developedto approach the music of Varse (1981; 1986 and 1987). The emphasison pitch space, as opposed to pitch-class space results in the followingassumption: If the vertical dimension is to serve as the primary scale ofreference, then the partitioning of vertically defined space will take oncrucial significance (Bernard 1981, 3). Moreover, criteria of absolutesize and distance, in the vertical sense, must form the basis of structure(Bernard 1981, 4). My approach distinguishes itself from Bernards in

that instead of employing the operations of projection, rotation, expan-sion and contraction (see Bernard 1986, 218), which take symmetry asone of their fundamental characteristics, it emphasizes the full satura-tion of the pitch space as a fundamental aspect of structure.

48 Stucky 1981 and Rae 1999 have discussed how the completion of chro-matic aggregates disposed in pitch-space assumes an important struc-tural role in Lutos awskis late period (Stucky 1981, 114). These aggre-gates create harmonic fields that articulate the formal structure throughcontrast (see for instance the discussion of harmonic structure in Jeuxvnitiens by Stucky (1981, 13441) and Rae (1999, 7984). In othercases the full presentation of the aggregate can serve as a climactic goalpoint, constituting the culminating point of a process (Stucky 1981, 114,119). Furthermore, these aggregates can be disposed as chromatic clus-ters that are gradually filled over a section of music in ways that are remi-niscent of those discussed in the current study (Stucky 1981, 12122).Thus, both Lutos awskis music and Berios these processes the involvepitch-space relationships are capable of creating large-scale relationships.

49 Ligeti himself has commented on the importance of pitch space in hisoutput: It is no longer primarily the intervals that constitute the struc-ture but relationships of density, distribution of registers and variousdisplacements in the building up and breaking down of the verticalcomplexes (Ligeti 1958, 56, quoted in Bernard 1987, 208). Bernardnotes the importance of volumes of sound of varying density accordingto schemes based on vertical span and symmetrical considerations(Bernard 1987b, 220) in Ligetis output from 1965 to 1970. He also

MTS3101_03 4/16/09 6:46 PM Page 80


was composed after the late 1950s, an idea that will be takenup again at the end of this article.

rochberg, music for the magic theater

Rochbergs Music for the Magic Theater is modeled onMozarts Divertimento in B flat, K. 287: the first and secondmovements quote extensively from this work. The firstmovement constitutes a prototypical example of a musicalcollage. It is composed of numerous successive short sectionsof music that are set off by textural, stylistic, tonal juxtaposi-tion or rests from the surrounding components. These sec-tions correspond to fragmentary quotations from a variety ofpieces, interspersed and superimposed with original com-mentary by the composer (sections of music that are newlycomposed and relate in a myriad of ways to the quotations).The layers of commentary incorporate a broad range ofstyles and textures, from freely atonal lyrical passages in thesolo flute, to strident, hocket-like passages in the upperwoodwinds and brass that are aggregate based and thus em-ulate twelve-tone rows (but are not used serially). Likewise,the distinct musical languages of the incorporated quotations(from Mahler, Mozart and Varse) contribute to a highlydisjunct musical texture. Furthermore, though quotationsand commentary recur in different guises throughout thepiece, there is no distinct formal scheme in the recurrence. A

general effect of discontinuity and fragmentation resultsfrom the successive juxtaposition of very distinct textures andmusical languages.

In this movement, the technique of chromatic saturation isfor the most part realized in reference to pitch classes and doesnot operate in the realm of actual pitch space (as it does in theother pieces discussed in this essay). It plays a primary role inenhancing the sense of structural completion of many sectionsthroughout the piece, in creating links between sections, andmost significantly, in clarifying pitch relationships betweensuperimposed and juxtaposed disparate quotations, thus func-tioning on a multitude of levels of musical structure.50

Gap saturation procedures also influence many of thevoice-leading tendencies of this work. Glenn Watkins notesthat the disparate elements in this piece are unified by theirmutual use of the [012] chromatic trichord.51 The concept ofgap saturation and the use of the chromatic trichord arestrongly related because the chromatic trichord is the prototyp-ical filled gap. The expectations created by the pervasive use ofthis trichord enable the composer to use the outer pitch-classesas a gap with strong voice-leading implications that are realizedat the moment that the gap is chromatically saturated.

The movement is generally composed of numerous shortand contrasting sections separated by rests or distinct breaksin the rhythmic momentum from the surrounding music.The most straightforward examples of chromatic saturationin this piece involve cases where aggregate completion artic-ulates formal units. Example 16 presents a reduction of thefirst section of the movement (the introduction). It consistsof original material by Rochberg and is clearly articulated asa separate entity by a fermata rest in all instruments exceptthe first horn, which sustains the pitch C through the begin-ning of the following section. As the example demonstrates,

notes the importance in this music of voices based on their spatialpositions-that is, on their literal functions as upper and lower bound-aries of occupied pitch space (Bernard 1994, 231). Bernard considersthese pitch space relationships to be more essential to the way themusic is perceived that the inaudible technique of micropolyphonywhich Ligeti described as his compositional process (Bernard 1987b,209). Clendinning (1995, 22930) makes a similar point and labelsLigetis technique by the term microcanon. Similarly, in this analysis ofBerios piece, the tonal contrasts of the different quotations are sub-sumed by relationships created by upper and lower boundaries inpitch space.

50 Lambert (1997, 17; 8188), discusses the importance of this techniquein the music of Ives.

51 According to Watkins (1994b), this feature was first pointed out byRochberg himself.

MTS3101_03 4/16/09 6:46 PM Page 81


example 16. Music for the Magic Theater I. Aggregate completion in the introduction to the movement (newly composed by Rochberg). Score in C.

#

167167

167167

167

167167

167

167

167

'

(

'

) (

* +, '

-

,

,

-

, .

, ,

, .

.

.

= 144152/

*'

Act I: in which the present and the past are all mixed up and its difficult to decide or to know where reality is0 !

1z3

0

!1z3 stab the air!

= 724

555

5

5

55

5

5

5

1z3 6

1+ 0 + 7 07

1z3 6 1 1z3 6 !1z3 1z3 6 1

+ + 071z3 6 1

1z3

!!

!1z3 8!

brilliant, make piano ring Complete the aggregate

!

88!floating, veiled, barely perceptible88

Pitch classes in order of appearance

7 8 E 1 2 0 94 3T65

Strings

Piano

Tuba

Trombone

Trumpet in C

1

2

Horn

Woodwinds

07

floating, veiled, barely perceptible

MTS3101_03 4/16/09 6:46 PM Page 82


the presentation of pitch-classes E and A within the lastchord of the section completes the aggregate, thus signalingclosure of the formal unit. The elements contained in thisisolated section are set off from those in adjacent sectionsthrough the sense of structural completion thus achieved.The occurrence of this structural process at the beginning ofthe piece and in other sections (see, for instance, rehearsalnos. 910), establishes a sound term for this piece. In otherwords, it imbues the process of chromatic saturation with afunctional role that is exploited throughout the rest of thepiece.

For instance, chromatic saturation of the aggregate func-tions as a link between adjacent sections. This is the casewhen a single pitch is withheld and provided at the appropri-ate place in the following section. Example 17 demonstratesthis process. At rehearsal 11, a hocket-like, rhythmicallyfree passage in the woodwinds and horn is followed by aquotation from Mozart s divertimento. The only withheldpitch-class in the rhythmically free passage is pitch-class F,which appears prominently as the first and uppermost pitch

of the tonal quotation that follows.52 The function of ag-gregate completion in this example is to structurally linkthese adjacent sections of music which feature strong con-trasts of texture, instrumentation, rhythm, meter and pitchorganization.

One of the most important usages of chromatic satura-tion in this movement occurs in the sections which featurethe superimposition of commentary over a quotation.Example 18 presents a reduction of the music at rehearsal

52 Numerous other examples of this occur in the piece. For instance, thequotation from Mahlers Symphony No. 9, IV (measure 14) that startsa couple of measures before rehearsal 2 and is played interspersed withcommentary through rehearsal 3 presents all pitch-classes of the aggre-gate but F. F is withheld throughout this section and finally occursprominently as the fortissimo first note of the Varse quotation at re-hearsal 4. Similarly at rehearsal 20, all the pitch-classes of the aggregateare presented between the Mozart Divertimento I (measures 6066)quotation and the added layer of commentary with the exception ofpitch-class G, which appears prominently as the first pitch-class of thenext section, a rhythmically free lyrical passage in the solo flute.

example 17. Music for the Magic Theater I (r. 1112), reduction. Chromatic saturation as a link between highly contrasting sections.

43

43

Completes the aggregate

Cello and Bass

31

8

Rhythmically free hocket-like passage in the woodwinds and trumpetsover sustained notes in the cello and bass

Fl.

11

ca.5

5612"

Tpt.0 ca.1/21"

5

5poco1 6Ob. Cl.

5

ca. 1"

5 poco177: 8 8( )( )( )

Beginning of quotation fromMozart,mm. 624

Divertimento K. 287, I

12

Allegro

8


0 4 8 2 3 6 T 9 1 7 5E

Bsn.

MTS3101_03 4/16/09 6:46 PM Page 83


12. The F major triad from Mozarts Divertimento, K. 287 isliterally suspended as an arpeggiated figure in the piano andwoodwinds is interpolated. This figure complements thepitch-class content of the quotation. The presentation of thecomplete aggregate with pitch-class A both ends the inter-jection, and creates a feeling of arrival that prepares the re-sumption of the quotation.

Example 19 demonstrates how aggregate completionplays a major role in the interaction of disparate layers at re-hearsal 13. This time both layers are superimposed. Thelower layer continues the tonal quotation from Mozarts di-vertimento, while the upper layer presents piercing pitches inthe woodwinds and trumpets. These pitches generally occurin a higher register than those in the underlying quotation,

example 18. Music for the Magic Theater I (r. 12). Aggregate completion relates the Mozart Divertimento I (measures 69) quotation and the interpolated layer of commentary.

;

43

43

43

43

+ +

+

,

( )

( )( )

Piano &Woodwinds

Violin I

Violin II

Viola

Cello &Double Bass

6

71 espr.

Completes the aggregate

Interpolated layer of commentary

Allegro = 1444dolcissimo8dolcissimo8

dolcissimo8

1

1

1

1

66

6

Mozart quotation is suspended Mozart quotation resumes


5 3 2 0 4 9 1 E 6 87 1T

12

MTS3101_03 4/16/09 6:46 PM Page 84


example 19. Music for the Magic Theater I (r. 13). Aggregate completion relates the Mozart Divertimento I (measures 924) quotation to the strident superimposed commentary. All pitch classes are provided by the added commentary,

except for pitch-class B, which is provided by the ostinato bass and the Mozart melody line.

;

43

43

43

43

43

+ +

,

+ +

0

+ - +

+ ++ -

+

+ +

+ +

+ - + + ++ -

+

+ +

-

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