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Structuring in Luciano Berio’s Sequenza IV Pauls, Cheryl Irene 1997

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STRUCTURING IN LUCIANO BERIO'S sequenza IV CHERYL IRENE PAULS B.A., The University of Winnipeg, 1986 B.Mus., The University of Manitoba, 1988 M.Mus., The University of British Columbia, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF MUSICAL ARTS in THE FACULTY OF GRADUATE STUDIES School of Music We accept this thesis as conforming toJhe.reqjttired standard THE UNIVERSITY OF BRITISH COLUMBIA August 1997 © Cheryl Irene Pauls, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^ I T ^ a / f t X SUdjU.d , <9 H M ^ - , The University of British Columbia Vancouver, Canada Date DE-6 (2/88) II ABSTRACT This paper explores structuring in Luciano Berio's sequenza IV. The analytic inquiry draws on the methodology of music theory, on Berio's writings (which generally take the form of philosophic reflection), and on the physical necessities and traditions of piano playing. Issues of form - as presented in segmentations of similar durations, syntactic relations, and gestural language - inform discussion of the place of the player in tracing, interpreting, and forming the music's structure and statement. The form of sequenza IV is created most explicitly through the gestures of playing the piano, specifically, those of playing the piano's most idiomatic expression, chords. Chords fragment and reform into various types that provide a tangible means of distinction throughout the piece. Chords are the typical expression of harmony, and accordingly Berio constructs the piece from specific harmonies. Harmonies also fragment and reform into particular sonorities; however, the correlation typical of chordal gestures and harmonic content is continually disengaged and reformed. Harmonies thus become decontextualized, assimilated into the texture rather than providing distinct contrasting entities within the form. Despite the continual redefining of distinctive harmonies, the listener is constantly aware of multiple events and processes, that is, of a form constructed in polyphonic layers. Polyphonic layering is introduced into the piece tangibly through the timbral distinguishing of material sustained in the sostenuto pedal from surface material, that is, from material with dry articulation. However, the capacity of the sostenuto for harmonic expansion through sympathetic resonance draws these timbrally distinct elements together and causes this aspect of formal distinction also to be continually in flux. i i i The following analysis presents several approaches to defining the structure of sequenza IV. Firstly its form is described in reference to traditional idiomatic expressions and formal devices applied to essentially similar pitch materials. Secondly, form is explored as a linear structure of both sections and phrases according to chordal types, symmetric proportion, and cadential gestures. These general descriptions treat pitch only insofar as it supports the delineations between phrases. Graphs of individual parameters represent the piece's structure according to independent and accumulated intensity levels. Thirdly, pitch content is addressed and defined as a polyphonic layered structure. A tendency is observed for these layers to assimilate each other's characteristics, which suggests that pitch structure can also be understood as a comprehensive shape with varying registral and pitch densities. Graphs portray both this structure and that of the acoustic resonance of pitch content in local sostenuto harmonies. The role of that complicity throughout the piece is then discussed in local contexts so as to define the structure dramatically. Each chapter thus presents a way of structuring sequenza IV, and each is in itself a layer of a multiple-layered construction. i v TABLE OF CONTENTS Abstract ii Table of Contents iv Preface v Introduction 1 Chapter 1 Form as Gesture 6 Chapter 2 Form as Successive Sections 19 Chapter 3 Form as a Succession of Phrases 52 Chapter 4 Form as Harmonic Polyphony 63 Chapter 5 Dramatic Form: Sostenuto Structure 72 Summary 92 Bibliography 93 Appendix 1 95 V PREFACE The reader is advised to keep the score of sequenza IV on hand for reference. Copyright permission for quoting excerpts of Universal Edition 30137 has been granted by European American Music. All quoted examples and references to the score are of the 1993 edition. In this edition most of the obvious pitch and rhythmic errors of the 1967 original have been corrected; also a substantial amount of filigree type (non-metered continuous rhythmic values) are rhythmically specific, although still continuous. In both editions, dotted barlines are used when the material is continuous, that is, with no eighth pulse. These barlines, however, are real ones. Several abbreviations are used throughout this paper. Material to be played by the right hand and left hand are abbreviated to "r.h." and "l.h." respectively. The abbreviation "pc" refers to a pitch class, that is, the set of all pitches with the same letter name, to be differentiated from a pitch, which is always register specific. 1 INTRODUCTION It is commonly understood1 that the pauses between the notes, the player's releasing and regathering of physical energy - be it muscular motion or breath -most clearly define for the listener the entities and differentiations constituting a piece's structure. This understanding relies on the perception of a structure as a coherent whole, for pauses become meaningful only when they define a place for the segments they separate within a directed or proportioned shape. This notion also assigns a high value to the role of the player in defining a structure. It is contingent on a hermeneutic model of the player situated and able to interpret from outside of the structure. The following discussion inquires whether such a place separating cognition from expression is available to a performer of sequenza IV, and how the player is involved in the "formation of form."2 This question is in part posed in response to current critical theories that call into question internally coherent paradigms. Primarily, though, the question is practical. It assumes that the performance of a work, from the vantage point of player or listener, is the privileged means of musical contemplation and a distinct singular event with beginning and end. The question is thus whether the player can incorporate traditionally acquired skills of listening and pacing3 when the structure seems intended to break the norms of its own constructions and language, and, how the piece is structured according to those aspects. The immediacy of the gestures of sequenza IV suggest a form of transparent simplicity. These gestures, or manners of playing the instrument, create a constantly evolving form that in the end proves to be cyclic. These gestures are 1 Piano virtuosos who trace their lineage to the nineteenth century, such as Artur Schnabel and Vladimir Horowitz, proclaim personal superiority in similar almost legendary statements, "The notes, these anyone can play, but the pauses between the notes that is where the artistry lies," or," the rests, these I play better than anyone else." 2 Luciano Berio, "FornV'in John Beckwith and Udo Kasemets, eds., The Modern Composer and His World (Toronto: University of Toronto Press, 1961), 142. Berio quotes Paul BQee in advocating a manner of listening which is always reevaluating prescriptive tendencies. 3 The issue or pacing by the player is in many respects similar to that of structural processes of progression and recession, discussed in Wallace Berry, Structural Functions in Musk (Englewood Cliffs: Prentice-Hall, 1976), 294. 2 based on the piano's capacity to sound large amounts of harmonic material as single events in various forms of chords. Chords are presented and transformed in well-known styles of fragmentation and arpeggiation. After the gestures form into ones that least clearly articulate pitch content, clusters and ametric filigree, chords reappear. There is extensive overlapping of textures; each seems to evolve from, and then preclude the preceding one. Formal transparency is also expressed through a low density of texture in many aspects. The plenitude of rests and long pauses, the brief melodic voice-leadings and registers introduced but not sustained, the absence of an articulated regular pulse, and the infrequency of dynamic progression or recession, thus, the relative infrequency of characteristic means of creating sustained musical thought, serve to create a structure of momentary, ephemeral events. The absence of slur markings and the abundance of rests within sequenza IV give the question of pacing of the seemingly elusive surface-level structuring both acute practical importance and aesthetic relevance. The question is not only of which events to relate but of how pronounced the gestures of connection or differentiation should be. The practical aspect of this question will be addressed in this analysis through discussion of form as discrete segments - sections, phrases, and in some instances harmonies - that have directed motion, contrast and symmetry. The aesthetic aspect involves abstraction, an awareness that similar events, lines and pulses are experienced because the listener creates them from the materials provided based on prior knowledge of musical form, and not because the piece's structure or the player's gestures convey them. This aspect will be addressed initially as a principle of structuring, one on which many of the structures discussed subsequently are dependent. The analysis that follows thus presents two means of defining structure 3 within sequenza IV. Both assume that the form is multi-dimensional, possibly contradictorily so. The first chapter discusses how the structure of sequenza IV can be understood as commentary on many of the traditions of musical structure. Berio refers to his compositional style as writing not in forms but in metaforms, thereby suggesting that a particular form does not define a piece, but that aspects are significant in light of various historical formal models.4 As such the piece is about a structure, and about the breaking of interdependencies of the gestures and events constituting a piece's structure. The term metaform can also be used to refer to constructions in sequenza IV, both generic types such as linear voice-leading, and unique types such as sequences of particular harmonies, neither of which are presented in a linear manner but are understood on account of presuppositions that cause or allow the listener to create a structure in abstraction. Metastructuring thus does not exclusively define a piece as devices and referential meanings, but also forms it as the accumulation of individual aspects understood apart from their local contexts, thereby providing temporal continuity. In this way, various parameters that in themselves do not serve to delineate particular events articulate the shape of the piece. The second means of defining structure, presented in chapters two through five, extends the latter notion of metastructure. Each of these chapters presents a way of viewing the piece as a totality, whether by a general description of prominent features and processes, or by a comprehensive visual representation of a particular aspect. Chapters two and three present two aspects of sequenza IV's successive form, sections and phrases. These segmentations govern local contexts, but ignore many of the connections established between like or similar constructions. Chapter two concludes with graphs that chart intensity levels of seven formal components, all of which are traditionally regarded as secondary, or 4 Philippe Albera, Luciano Berio and Jacques Demierre, "Entretiens," in Contrechamps (Paris: L' Age D'Homme, 1967): 66. 4 accompanying gestures to the formal structure of a piece. These are thus removed from contexts in which they function syntactically, and viewed as independent elements within a larger context. Osmond-Smith has suggested that pitch is the only pre-compositionally structured aspect of sequenza IV, and that the work is experimental, dependent on rhetorical gestures for its comprehension.5 While it is with pitch that the listener can most easily abstract and remember entities and thereby form connections, as an accumulation of intensities these other parameters form a structure on their own terms in addition to the rhetorical gesturing of local contexts. The final two chapters look at pitch structure, firstly in isolation and secondly in reference to the effect of the sostenuto pedal. Chapter four discusses the piece as a polyphony of harmonies distributed seemingly at random in varying contexts throughout the piece. The lack of articulation of these harmonic layers, or sequences, as well as the continual gestural fragmentation of chords causes a great deal of overlap in the perception of harmonies. Thus the perspective assumed in the graphs that conclude this chapter is that pitch is a single continuous layer on which independent entities fade in and out, creating various densities of registral space and particular pitches. Pitch thus becomes an aspect of texture, within which certain combinations on occasion build to and fragment from particular harmonies and time points, but that primarily forms a spectrum with various single pitches or harmonies that serve as focal points during their durations. The final chapter looks at pitch according to the harmonic structure generated by acoustic resonance. Specifically, the pitches that are acoustically resonant with those held in the sostenuto pedal - partials or fundamentals of a pitch in the sostenuto - are considered to extend harmonies that contrast with those pitches that are not sympathetically resonant. The form of sequenza IV is then considered according to 5 David Osmond-Smith, Berio (New York: Oxford University Press, 1991), 40. 5 the effect of the sostenuto within local contexts, as a metasonata whose contrasting entities are initially independent, developed in opposition, and reconciled. According to the composer, the entire piece is generated from the opening two chords - harmonic ideas - that are expressed in various melodic forms throughout the piece.6 This suggests that materials and structures within sequenza IV can be traced to an originating source, and that harmony is expressed in elongated gestures, creating various structures of a linear dimension. The following analysis presents several such linear constructions. 6 Luciano Berio, comments following a colloquium presentation, University of Ottawa, 1986, quoted in John MacKay "Aspects of Post-serial structuralism in Berio's Sequenza IV and VI," Interface, Vol. 17(1988): 227. 6 CHAPTER ONE FORM AS GESTURE Berio suggests that the listener does not come to music with a tabula rasa, rather, that experience always informs the listening process.7 However, he militates against meaning or expectations being predetermined, and berates the listener who wants only the immediate effect of artifices of formal suspense.8 He advocates structuring, whether in composing, playing, or listening, in terms of gestures. Berio defines a gesture as an entity that is so-named because it carries a trace of historical significance, but that is applied so as to defy codification, and instead conflicts with the known nuances of a particular gesture.9 Even though he continually redefines their expressions, Berio considers content and function to be operative and distinct terms. He suggests that the same entity can be presented in a unifying or opposing relation to other entities, depending on the manner in which materials are deployed, not on the materials in and of themselves.10 Form in sequenza IV can be understood to be about the establishing of relations through the gestures of traditional musical constructions. The function that relates similar events is not necessarily operative elsewhere in the piece, or, that function may be assimilated into different types of materials. Also, sequenza IV is not necessarily temporally constructed around similarly constructed events. Similar structures form the piece primarily in the abstracted gathering of scattered parts by the listener. The discussion that follows is not comprehensive, but features several of the gestures encountered in sequenza IV within dimensions of pitch, rhythm, gestural notation and repeated entities. 7 Osmond-Smith, 37. 8 Berio, in Beckwith and Kasemets, 142. 9 Berio, "Du Geste et de Piazza Carita," in Contrechamps (Paris: L'Age D'Homme, 1963): 45. 1 0 Berio, quoted in Dalmonte, R., Lorenzini, N., Assaroni, L., Frasnedi, F. ll Gesto Delia Forma (Milano: Arcadia Edizioni, 1981), 187. This opinion is expressed in sequenza FV in both gestural and pitch content. 7 Figure 1 shows several disjunct structures that can be understood according to linear voice-leading. In part a, dynamic shape and metric placement dictate a directed gesture in m m 48-9 that is not consistent wi th the shaping of pitch content. The distortion of a familiar structure through pointill ism and a metric and dynamic goal that is not part of the line obscure the direction of linear voice-leading shown by slurs. That is, the accented chord on the downbeat of m.49 does not include the expected B ^ , and the E^ attacked at the midpoint of m.49 beat 1 is the reassertion of a pitch introduced in m.48 and is heard apart from this directed gesture. Figure 1 (a rhythmic reduction) m.48 m.49 8 Part b, based on mm.120-22, is an example of another common gesture, that of unequally opposing pitches that are chromatically adjacent. The beginning of m.120 introduces the pitches and F#4 j n close succession. An extended jgf/F^is also followed by F#4; the latter occurs at the strongest metrical point of any of the pitches in the flourish in which it is situated making it sound like a chromatic resolution, but the difference in their respective durations is so great that this voice-leading relation can scarcely be perceived. Part c traces a line found in the lower register from mm.1-19. The irregular presence of the pitches in the line makes it a structure that supplies cohesion but neither generates expectation nor determines the player's gestures. In all of the examples a certain structure is understood because of the voice-leading expectations of the listener, not because these are emphasized in the music. A common process of the 12-tone tradition is that of aggregate completion. Chromatic aggregates consistently occur within relatively short spans in sequenza IV; however, they rarely correlate to musical gestures. (For the most part Berio advocates a non-serialized approach to form, suggesting instead the destruction of initial material.11) Figure 2 shows several of the instances in which aggregate completion corresponds to single gestures. In Figure 2a and c the l.h. completes an aggregate of which the r.h. states most of the pes, and in 2b an aggregate is expressed in r.h. alone, along with D'' in the held sostenuto pedal. Berio's reference to forming the piece around what is essentially a harmonic discourse is expressed in sequenza IV in the incorporation of harmonic gestures that resemble those of traditional musical structures. For example, the interval of the third, the predominance of which unifies the first section, can be regarded as a gesture, because it recalls triadic harmony. 1' Berio's anti-12-tone attitude in the 60's, as made explicit in the article "Aspect d'un artisanat formel," precludes ordering as form-defining. This does not prevent him from making use of the less tangible properties erf structuring common to 12-tone writing. 9 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London The gestural status of certain intervals is particularly significant in the dramatic gesture of a tritone and its immediate inversion in mm. 131-4 as shown in Figure 3. This inversion is climactic in being the only really obvious depiction of compositional process within the piece,12 and so seems to call into question Berio's professed formal dialectic as a discourse. 1 2 Adding to the perception of climax is the occurrence of this inversion at the golden mean as calculated in measure numbers. 10 Figure 3 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed AH Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London In several passages structures can be understood according to tonal functions. For example, closure in the final few measures of the piece is created by several tonally idiomatic events, as shown in Figure 4: semitone motion ascending to the tonic and a bass descent by fifth (or ascent by fourth). These two events do not resolve to the same harmony, nor in either case is the resolution final. C#2 0 f m.213 moves to D2 in m.214, root of the expected "tonic" harmony of the piece, that is, the first chord of the piece. This chord, however, is not understood as a resolution for long since the m.213 chord is held in the sostenuto pedal and thus outlasts its successor. This C # 2 can also be understood to resolve to F#l in mm.214 and 215, although again the C# sounds beyond its resolution. These tonal functions thus provide relations, but as gestures of historical allusion and not structural principles due to both the infrequency of occurrence and contradictory aspects of their settings. Figure 4 m.213 m.214 m.215 • \* 7 0 • ^ — i 1 • 1 y _ z — • i i Pitch structure is frequently regarded as fundamental to the form of a piece. This traditional role is not maintained throughout all of sequenza IV. In the central section of the piece, pitch acquires the role more commonly attributed to texture, lending an overall coherence but depending on other criteria for its sense of motion and direction. The gesturing at the beginning of the piece draws attention to pitch in that many similar chords occur in close proximity, with only minor changes such as stepwise voice-leading and octave transfer, so that individual voices are understood. As the piece progresses the texture becomes much more continuous through both cluster formation and ametric filigree; consequently pitch is not differentiated into distinct ideas and becomes a background texture. Also, there are many passages in which changes of articulation and chordal type, not the pitch content, provide contrast. For example, in m.80, as shown in Figure 5, the proximity of pitches of the staccato chord, grace arpeggiation, and sostenuto chord renders the harmonic distinction of these individual events to be less than elsewehere in the piece. Rather, pitch content can be understood as if it were a continuum that can be extended by stepwise movement or by the harmonic 12 extension of like intervals, in and out of which pitches move. Figure 5 m.80 Jl ~ - i ^ \ SOSt. * ^ ~f 4 Meter could also be a gesture, but while sequenza IV is written in metric notation, its meter is rarely articulated. The only pulsed passage is mm.76-88, where eighth-note pulses and many duple subdivisions of it are prevalent. The regularity is expressed in a measured tremolo F^-D^ with frequent, irregular stress accents. This gesturing of the regular traditional pulsing seems to be a comment on its banality; Berio thus invokes historical gestures not only as materials, but also to critique traditional structures. Another aspect of gestural reference is made clear by the notation. Consider, for instance, the broken chords and ametric filigree that comprise the gestures of mm.145-161. They are notated differently; that visual distinction is not necessarily audible, but can be if the player interprets them according to the historical traditions of these gestures. Broken chords appear frequently in eighteenth and nineteenth century piano music at climactic points, accentuating through temporal extension material that represents a singular entity. Ametric filigree, in contrast, is a typical modern expression in which the possible (harmonic) connections amongst pitches are multifarious and secondary to the presentation of scattered bits. In juxtaposing these two types, there is both a certain blurring of distinction between these 13 contradictory historical expressions that exist simultaneously within contemporary artistic expression, as well as structural contrast. Repetition as a formal principle is probably the most common gesture of form-definition within musical tradition, in terms of both durations and similar or motivic entities. Berio refers to repetition as the new "diabolus in musica,"13 suggesting that it is not to be used as a means of structuring, but incorporated as an ornament of tension within a structure otherwise defined. Repetition is generally considered a significant factor in the articulation of musical structure. Similarity of both proportions and specific materials allows for a factor of recognition, and for the play of subtle difference. In Berio's music, however, the repetition of individual pitches and pitch combinations seemingly appear at random within differing gestural contexts. For instance, throughout sequenza IV Berio "repeats" vast amounts of pitch material. On one level, the continuous derivation of material from preceding, particularly the first two, chords suggests that every event in the piece is a repetition of sorts. Beyond that, there are several passages in which repetitions are easily identified. Figure 6 lists the corresponding pitch successions. These repetitions are altered by subtle changes of voice-leading and octave transfer within a complete reworking of the durational and dynamic aspects, that is, of the gestural context and shape. While the beginning of some repeated pitch segments coincide with the beginnings of sections otherwise defined, sectional 1 3 Luciano Berio, "Aspect d'un Artisanat FormeL" in Contrechamps (Paris: L'Age D'Homme, 1981): 17. Figure 6 Original Statements mm.1-10 m.64 mm. 55-63 mm.104-153 Repetitions mm. 65-70 m.94 mm.95-103; mm. 154-158 mm. 159-201 • 14 lengths do not similarly correspond. Berio advocates the inclusion of recognizable relations wi th which the listener can construct a structure, thereby elevating the role of the listener wi th in the defining of form. He refers to a certain redundancy of content as an essential formal principle. This general reference does not suggest that repeated materials signify formal functions, but rather that there be enough similarity to prevent chaos from destroying al l the possible relationships. 1 4 In sequenza IV redundancy of content in itself offers moments of recognition of what seem to be fixed pitch units; this factor wi thin the piece tends to be more one of disassociating a given event from its role wi th in local context than of defining form, since recognized or similar sonorities do not appear with regularity in time or context. This is not to say that repeated materials are never emphasized. Occasionally repetitions do stand apart from the local texture. For example, the sfjk chords in mm.65-8 are those that are repeated from the opening of the piece. However, this repeated element does not form a structure of the same weight and duration as its initial statement, but is abbreviated, truncated and imbedded within a new structure, even if dynamically distinct. According to Osmond-Smith, gestures are incorporated into Berio's music without becoming motivic forces,1 5 that is without setting precedent for grouping and accent elsewhere i n the piece. This need not imply that relations are always negated, but can also be understood as a process in which the means of motivic relation gradually become so multifarious that the motive loses specificity. The two chords in m . l , as shown i n Figure 7, state a motive that exemplifies this process. The fol lowing discussion w i l l show how, over the course of several measures, the motive-like quality of a two-chord succession is initially concretized 1 4 Berio, in Beckwith and Kasemets, 145. 1 5 Osmond-Smith, 37. 15 and then dissipated. Figure 7 1 P t Sust. ped t Ic 1 © Copyright 1967 by Universal Edition (London) Ltd., London ® Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London The question of motivic connection between these chords arises from the perspective of the player, who must decide whether to let go of energy during the rests between staccato chords, or to connect gesturally and then release, wi th the necessary subtle dynamic differentiation. To connect the first two chords and then release implies that a new idea begins at m.2, in keeping wi th a traditional understanding of metric placement. There are reasons besides metric placement to consider the first two chords as a motive. Harmonically, the r.h. of the second chord extends the upward stacking of the first, while the l.h. of the second fills the registral space between the entities in each hand of the first, as shown i n Figure 8. Five of the six pes of the second chord are repeated from the first, including one without registral transfer. The motive can thus be understood as the fragmentation of a single harmony. Also, the placement of the second chord as the last subdivision of a quintuplet renders its execution more precarious than that of the first chord, which occurs at the beginning of the beat of the first beat of a measure. The difficulty in counting the quintuplet l ikely results i n a physical holding of the silence to this point, which 16 makes its placement a release, and of lesser accentual weight than the first chord. Figure 8 m.l A The grouping of chords in m.2 does not follow as neatly as i n m . l , that is, as a harmonic continuity, although the similarity of contour and of l.h. registral placement to m . l suggest a parallel motive. The placement of both chords on notated beats argues both for and against motivic connection. Articulated pulses provide a relation between events, but also equalize them, albeit on strong and weak beats. The assigning of a specific type of chord (the second chord of m.2 is a transpositionally altered form of the second chord of m. l ) to a certain place, that is, as the second and upper chord i n a two-chord unit, suggests the stabilization of a motivic shape. The sostenuto to surface chord in m.3 suggest a structure analogous to the previous two measures in terms of registral and metric placement. Only two pes are the same i n these two chords, the least number possible for the density of pitches; thus, minimal sympathetic resonance is generated. In mm.3-4, l.h. surface chords sound connected through tonal harmonic reference. The first is a D major root-position triad; the second is easily understood as the second inversion of this same entity, wi th some of the space between pitches filled in. In associating these two chords motivically, metric placement becomes weak to strong, as opposed to the strong to weak contour in al l the preceding 17 motivic instances. In m.6 separation of sostenuto and surface structuring is made more explicit in that the final chord of m.5 recurs on the surface, that is, without having been altered in content by the intervening sostenuto chord. The literal construction of the surface chords is unaffected by the sostenuto; however, perception is. In m.6 a densely-spaced harmony moves out i n contrary motion to a more sparsely spaced chord. Almost all of the latter chords pitches resonate sympathetically wi th the prevailing sostenuto harmony. 1 6 The two surface chords of mm.6-7 act as their own motivic unit. They are not differentiated i n pitch content, but in dynamics. The dynamic shape of weak to strong is supported metrically. The dynamic differentiation as is established i n mm.6-7 is similar to the structuring of a repeated chord in mm. 7-9 where a particular chord occurs three times, at pp, then sffz, and finally ppp and held i n the sostenuto. Thus this motive is not for long definable by particular relations of contour or interval of pitch, or of temporal interval, but is a small-level expression of a core idea of the piece. Sequenza IV presents itself initially as an exploration of fragmenting harmony, and of bui ld ing harmonic connections. The presentation of the initial two chords establishes both pitch, intervallic, and harmonic materials from which the piece is derived, and relations of harmonic fragmentation and continuity; however, its specific two-chord motive gradually becomes indistinct. Pitch and metric constructions, styles of notation, and repeated and motivic segments, all of which can be termed traditional formal components, thus provide a reference to gestures that relate materials within local contexts of sequenza IV. However, these relations do not similarly connect materials i n other passages, and cannot be traced independently in order to define the form as a whole. 1 6 This can be seen in the graphs at the end of Chapter 4. 18 To understand Berio's sequenza IV according to gestural reference is to place it in line wi th a prominent aesthetic of the 60's (and since), that of decontextualization of distinct identities. The process is similar to that of several contemporary Italian works i n other art forms. For example, Federico Fellini's f i lm 8 1/2, Italo Calvino's novel / / on a winter's night a traveller, and Umberto Eco's novel The Name of The Rose are all works i n which the process of constructing the work is an essential aspect of content. In all three works the mode of understanding the structure is teleological; however, that structure is not presented in direct linear sequence. This aesthetic offers a contemplative interpretation of form i n sequenza IV. What requires sensitivity in performance is the decisions of when to direct a traditional gesture, and when to distance a similar structure as a vague reminiscence. Berio describes virtuosity as historical knowledge of all styles, and the capacity of a player to move back and forth quickly amongst styles and ways of defining form. 1 7 Sensitivity and virtuosity thus define the role of the player as essential to the structuring process. Berio states, 'The composer furnishes the interpreter wi th starting points, with general lines of action, wi th proposals and suggestions to which the performer must react in a constantly renewed way." 1 8 Thus while gestural references within identities, processes and formal components compel the listener to understand sequenza IV as an external, abstract structure, these same devices offer the player paths into the creative process of presenting that same structure as a temporal continuity. The following chapters identify several ways in which that continuity can be formed more cohesively. 1 7 Berio, quoted in Albera, "Introduction aux neuf sequenzas," in Contrechamps (Paris: L'Age d'Homme, 1981): 91. 1 8 Berio, in Beckwith and Kasemets, 144. 19 C H A P T E R T W O F O R M A S SECTIONS Six successive sections form sequenza IV into sequences of similar length. 1 9 Each section is distinguished from surrounding ones by textural coherence, that is, by its most prevalent chordal fragmentation style, and by the processes or materials that define its harmonic interaction. Other parameters frequently support this segmentation and w i l l be represented in this discussion by graphs of intensity levels. The graphs, whether viewed independently or together as an accumulation of intensity levels, are referred to in the discussion below only insofar as they illustrate other processes that specifically define a section. Sections are not necessarily distinguished by variation within the same parameter. For example, Section 3 is characterized most obviously by a pitch-specific dyad i n a particular gesture (tremolo), but coherence i n Section 4 is achieved by structural opposition within a variety of parameters, including pitch, harmony, interval, dynamics and register. Nevertheless, the relative similarity of overall duration makes this segmentation significant. Sections are demarcated by clear divisions i n which cadential gestures complete one section and distinct changes announce the next. Yet the materials surrounding each junction frequently l ink adjacent sections by a k ind of elision as the material that w i l l be prominent in the upcoming section appears as a dependent or accompanying gesture i n the preceding section. This allows the form of the piece to sound as a continuous transformation of ideas. Several sections derive from a particular pitch relationship that is presented within the opening sonorities of the piece, not necessarily l imited to the first two chords. This process draws on the particularly Beethovenesque technique of a 1 9 David Burge, Twentieth-Century Piano Music. (New York Schirmer Books, 1990), 164. Burge claims that the original score was written on 7 oversized pages, each but the sixth concluding with a cadence; I have not seen this aspect taken into account in other sources, nor have I found the six sections to be of equal length. 20 motto harmony - a short motivic idea at the beginning of a piece - that expands into much larger formal structures throughout the piece. The six sections distinguished by important cadences and textural change are mm.1-34, mm.35-64, mm.65-94, mm.95-136, mm.137-186, and mm.187-217. There is a close correspondence i n the lengths of the first three sections,20 wi th an increase i n length in Sections 4 and 5, followed by a much shorter sixth section. The form of the piece as understood i n sections thus conforms to a traditional arch-shaped dramatic model. The first section, mm.1-34, is characterized by a homo phonic texture expressed primarily i n chords. Berio has stated that his compositional premise within all the Sequenzas is a melodic presentation of an essentially harmonic discourse. 2 1 The defining of harmonic discourse by chords continues even when the texture transfers to a more consistent arpeggiation, and the attack densities vary greatly wi th in individual voices. In mm.21-28 voices continue to progress as if a regular harmonic rhythm were still coordinating them. H i g h and low dynamic peaks in each hand continue to occur simultaneously, as do rests. A n affinity of the arpeggiated material i n mm.21-28 to chords is also maintained through a similarity i n the spacing between voices and a lack of rhythmic profile. For example, as seen in Figure 9, the last two beats of m.23 (excluding the final l .h. grace note, D^ , which can be understood as harmonically connected to the following measure) span a ninth in each hand, and a diminished octave between the hands, and are thus similar to many of the chords in the opening material. 2 0 The piece consists of many tempo changes and some variation in the number of beats per measure (three is the norm); I have not calculated sections in terms of constant durations because I think the piece is structurally gestured with the measure as a unit to be understood and compared. 2 1 Berio, quoted in Entretiens avec Rossana Dalmonte, 129. 21 Figure 9 m.23 l^Brn J — m.l f In addition, Section 1 is unified by a consistent harmonic density of two chords per measure.22 For example, m.18 appears to be a broken rapid arpeggiation of a single entity extending much beyond the range characteristic of previous chords. However, it segments easily into two parts, or as two arpeggiated chords, one at p and the other at f-jf. Consistency of intervallic structuring within the chords is another means of coherence in Section 1. The initial chordal gestures consist of primarily tertian harmonies. Figure 10 a) m.l m.2 m.3 m.4 m.5 l i t * m.6 \1 * 1 l l hi I \>» b) \yTZJi 2 2 This density does not produce a regular harmonic rhythm because of the changes of tempo and meter. It seems that despite changes in literal time span, the notated measure suggests the amount of material included in a single gesture, which in this section is consistent. 22 Figure 10a shows the r.h. parts of mm. 1-6, (except for the first chords in mm. 2 and 3 and the third in m.5), in which vertical thirds clearly predominate. Figure 10b shows a way of hearing voice-leading connections in these chords. As the section progresses some voices slowly subdivide and simultaneously move in two directions, progressing towards cluster-type structures. While thirds consequently become less prominent in the rest of the section, the voice-leading frequently maintains a link to those later chords that most closely resemble their tertian sources. Tertian sonorities are also suggested by some of the horizontal structuring. For instance, in m.13, the descending top voice as beamed in Figure 11 expresses the right hand of the first C major chord of the measure. However, the harmonization of this triadic arpeggiation does not prolong C major. Figure 11 Pn5 -1* Several widely spread chords, such as the l.h. of the sostenuto chord in m.3, as shown in Figure 12, can be understood as tertian sonorities in which the middle element has been transferred up an octave, that is, still in terms of triadic harmony.23 The second chord has been altered from the triad by chromatic alteration and octave transfer. Figure 12 ~ „ v m.2 m.3 — 2 3 Several of these observations are reliant on the separation of the hands of a simultaneity, not unlike how two tonalities frequently are understood independently in bitonal music. 23 Compound intervals expressing thirds are also emphasized i n non-adjacent voices of simultaneities. In m.6, and frame what is closer to a cluster than a tertian chord; these same pes form a focal point at the beginning of the arpeggiated section, m.21. As shown i n Figure 13, the specific melodic interval of a third, B^-D 6 , recurs as the upper voice of adjacent chords i n mm.7,15, 22-3, and 28-9, acting as an almost motivic presence i n otherwise different harmonies. Figure 13 m 7 i i— mJ 5 H I K mm. 22-3 mm.2S -9 g H > | % 7— i r I * — V \0 } 1 v— —\ 2 Specifics of the derivation of pitch material in this section w i l l be shown in Chapter Four, including altering chords via voice-leading, octave transfer, transposition, and adding or subtracting voices, all of which produce chords that are obviously similar to, or hybrids of those that precede. These processes are immediate i n effect and ad hoc i n distribution; they do not establish longer units of material or rates of motion, but are understood i n connection to prior, similar sonorities. Several climactic elements mark the end of the section. There are several accelerations: the tempo increases to ,h=104 in mm.33-4, a specific motive, G ^ - A ^ , which was presented in a very slow rhythm previously, is greatly diminuted in 24 m.30, and in mm.29-33 the pacing of the alternation between chordal and arpeggiated gestures increases. The accelerations lead to the end of m.34, where for the first time the damper pedal is down as notes are attacked, thereby enhancing the dynamic emphasis. Figure 14 shows how right and left hands present dramatic ascents to and respectively; these pitches recall the outer right hand voices of the initial chord and thereby help provide closure.24 Figure 14 i i v ' ' v v f e ) i The beginning of Section 2 is marked by clear changes. The tempo of J>=60 is reintroduced at m.35; this tempo predominates throughout Sections 2 and 3. The chords of Section 1 appear infrequently; instead, the texture of mm.35-64 is characterized by two-part polyphony with relative equality in the density of material of each hand, but few common articulation points. Also, as is clear in Figure 29, the rate of change and variety of durations employed is greatest in Section 2. Rapidly changing rhythmic durations produce a disjunct texture, establishing more distinct rhythmic profiles. Certain gestures such as trills, tremolos and clusters, all of which evolve from two pitches, emerge and begin to blur pitch distinction. Linear melodic voice-leading is limited to extremely brief references, and many gestures become isolated events in and of themselves. Section 2 is also the only one in which specific rhythmic and contour shapes recur. Such similarity can be seen in the comparison of mm. 39-41 and 46-8, as 2 4 The sustained Dflat4 extending from m31 and throughout section 2, is an example of an entity or layer existing independently and in contradiction to section breaks. 25 shown i n the circled events i n Figure 15. Figure 15 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London Section 2 contains the strictest derivation of pitch units of anywhere i n the piece, aside from exact repetition. The presence of a set of pitches in various configurations ties Section 2 together. This set begins as a distinct harmonic/melodic idea, a succinct motive of two chords that appears in mm.31-2, close to the end of the previous section.2 5 Together these chords state all but E^ of Several of the pitches of these chords are introduced prior to that, for example, the r.h. pp materials in m.27. 26 the complete aggregate. These chords first fragment in m.35. The fragmentation directs itself toward EM> at the beginning of m.36, completing the chromatic aggregate. In this fragmentation al l step-related pitches preserve the melodic ordering of the mm.31-2 statement, as shown by the lines in Figure 16. Figure 16 The process of pitch derivation relating much of the material in this section is akin to 12-tone composition, not so literally that a particular ordering of the 12 tones is maintained, but that certain relationships within the aggregate are explored for unifying effect. Throughout this section, dyads from these chords become decreasingly associated with the aggregate and increasingly fixed in their independent effect. The presence of these dyads maintains the perception of fragmentation of the chordal source. Figure 17 shows the presence of dyads and trichords i n mm.35-7, 39-41 and 53 that are similar to those i n close proximity i n mm.31-2. Also , the presence of independent entities does not preclude their occurring subsequently i n "original" form; note that m.53 is more strongly similar to m.35 than many of the intervening statements.26 2 6 This cyclical dimension superimposed on a transformative process has bearing on a sense of phrase, as is discussed in Chapter 3. 27 Figure 17 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London 28 Another pitch consistency in this section is the accentuation of provided from a series of complete aggregate presentations that all begin with that pc. These presentations incorporate several different transformations, as shown in Figure 18 - octave transfer in m.39, pitch inversion in m.40, and contour inversion in m.41.2 Figure 18 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London Although chords rarely occur in this section, there is nevertheless a consistency of prominent intervals that creates coherence, some of which can clearly be traced back to one of the opening chords of the piece. The intervals of greatest prevalence in this section are p4s, p5s, and tritones. Figure 19 shows how the second chord of mm.31-2 can be understood to be derived from the first chord of m.2.28 2 7 There are several other instances of B-flat throughout these measures; as is common within the piece, the focusing of processes according to a certain principle does not preclude the simultaneous presence of other patterning of the same material. 2 8 Other of the elements in mm.31-2 have more immediate roots, for example, the E5-Bfla t5 tritone of m.31 occurs in m29. These two pes occur in close proximity frequently, including within the first chord of the piece. 29 Figure 19 m.2 m.32 It' i if &e » t • J til • There are several instances in which a very high density of these intervals occurs, as shown in Figure 20. M.40 retains about the same number of tritones as in the mm.31-2 chords but extends the p4ths and tritones. Tritones are featured at the end of the section. In m.59 a tritone occurs in every pc combination. Figure 20 m.40 m.59 Many of the processes of derivation appear without accentuation from accompanying gestures or directed shapes. However, occasionally the inception of a new idea or the elevation of a subsidiary idea is conveyed emphatically. In m.41 there is a sudden «/outburst where a decrease in intensity is expected; this expectation is based on the relative strength of the event on the metrical downbeat of this measure - a dotted eighth with a tenuto indication. The breaking of this expectation adds emphasis to the inversion of p4s to p5s, and of the dyad Bflat-A 30 from a descending to an ascending interval. The p5s that appear in the l.h. here consist of the same pes as the p4s in mrn.32 and 35. P5s subsequently become more prevalent within the texture. The fixing of specific pitch dyads as well as of a few trichords, along with the freeing of these from association with the complete set, is enhanced by gestures that detract from larger harmonic and melodic contexts, such as trills, tremolos and clusters. For example, Figure 21 shows that all of the independent entities in m.43 were proximate in mm.35-6, with p4s inverted to p5s, (except E^-A'', which did not occur as a p4 previously, but only as a distant p5 in mm.35-6). The dyad E-D, which previously was melodic, is now a verticality. Figure 21 m.35-6 m.43 W a b c d e a b c d e The emergence of clusters is another important process in this section; clusters are increasingly prevalent as pitch material becomes associated with dyads. This process begins in Section 1 with voice-leading that simultaneously moves by step in two directions from a single pitch. In mm. 21-28, where the fragmentation can be understood as broken chords, independent voices thicken into bands of seconds through static neighbour motion. However, actual notated clusters appear only after chords clearly fragment into dyads, and frequently the outer pitches of the clusters can be traced to earlier dyads. For example, the first cluster, which occurs in m.40, OJ-Y^, is a pc equivalent of the dyad C^-F^ that occurs in mm.32 and 35. 31 Clusters occur frequently throughout Section 2, and on occasion throughout Sections 3-5. Following a high density of clusters in m.59 beat 2 - m.60 beat 1, comparatively larger linear and vertical formations return; this return helps articulate the shape of the section. The re-establishing of intervals similar in size to many of the chords in Section 1 occurs in the combining of smaller clusters. For example, in m.57 the F#2-E3 cluster is a combination of F#2-B2 from m.57 and B^-E3 from m.60, as seen in Figure 22.29 A sense of closure to the section is provided by the extended pause in rnm.62-4 that follows ten measures of extreme dynamics, pitch density (especially of clusters), and continuous rhythmic activity. During this pause pedals are lifted, effecting a thinning of resonance. A fermata in m.64 further enhances the dissipation of motion through quiet, ascending arpeggiations. The reappearance of the opening sonority in its original form at m.65 marks the beginning of Section 3, mm.65-94. The strength of the sense of return is created by its preparation at the end of the preceding section. Figure 23 shows how the pc content and register of the first sonority of the piece are gradually reconstituted beginning in m.59. Figure 22 m.57 As occurs frequently in sequenza IV, this process is not presented in linear sequence. 32 Figure 23 m.59 m.60 m.61 m.65=m.l First, which earlier is presented as an independent identity (mm.30 3 0 and 33, then i n 42 and 51 as the upper note of a cluster) attaches itself in a cluster to A ^ , spanning the r.h. interval of the opening sonority of the piece. This cluster is then transposed down an octave twice i n the next two measures, reaching the original register in m.61. Next appears a broken chord that shares many pitches wi th the m . l chord; its l.h. consists of the pc content of the original transferred up an octave, with the lowest note played alone just prior to this chord. Several of the other pitches of this reformed chord are focal points i n the preceding material. For example and F^ occur as a tr i l l i n mm.53 and 59, following which E ^ is the upper and lower limit of clusters. F#, which occurs as the lowest voice in two chords of m.61, returns to F#3. This preparation for the return of earlier material through its reformation out of material that has become independent is analogous to the process i n tonal music of turning a dominant as a local tonic into an extended dominant seventh as a function of, and just prior to a return to, the tonic. The reprise in m.65 actually extends beyond the reformation of the opening chord. Mm.65-68 include a truncated presentation of five of the opening chords of the piece played sffz, wi th the vibrations upon release held in the damper pedal. 3 0 M.30's notated B 7 (1993 edition) should be a G 7 ; G 7 appears in the 1967 edition. 33 Several of the original chords have been omitted but the ordering of Section 1 recurs intact.31 These sffz chords form a dynamically and articulatively distinct layer within the texture. The reprise or quotation of chords from the beginning of the piece that signals the opening of the third section is carried out in polyphony with the gradual reconstruction of the chord at the end of m.64 as separate chords, one on the surface and the other in the sostenuto. Figure 24 two distinct these elements. The "extras" are materials that will be developed in the subsequent passage. Figure 24 Progression reprised from mm.1-6 m.68 Sost. m.65 m.66 m.67 . ^ 4 Surface m.67 m.69 "Extras" m.70 _/ ^  It H dm ft <l • The reprise of the opening extends to recall other events of Section 1. For instance, the texture at m.71 recalls that of m.21 in its presentation of a continuous, quasi-arpeggiated r.h. with a l.h. of single notes, which together complete chromatic aggregates and are interrupted by staccato chords. However, like the reprise of the chords, this textural reprise is abbreviated. Moreover, these repeated chords and textures are not as homophonic as the opening: the chords in Section 3 are interspersed with events that make them seem, by contrast, substantially greater in density and dynamic. Also, the more meandering gestures of the arpeggiated 3 1 The third chord is altered by the addition of E^; the fourth has no direct precedent, but is similar to aspects of both of the chords on the first beat of m.5. 34 materials in Section 3 do not reduce to verticalities as easily as the similar material in Section 1. Thus a heightened sense of polyphony is suggested by the incongruity of dynamics and density, and by the interpolation of new material. These repeated elements do not pervade the whole section, but only introduce it. The central figure in this section is a repeated tremolo between F^ and D5, which prior to this occurs only sporadically. The first appearance of the tremolo between these pitches in m.35 leads quasi-tonally to a pc goal, EK32 The dyad recurs briefly in m.67, and then in m.76 as a grace figure, as conveyed both in notation and in function - on beat 1 it leads to E ^ , and on beat 3 it leads to E ^ , similar to the gesture in mm.35-6. However, in m.77 it achieves more substance notationally, and becomes itself embellished with grace figures. The subsequent notation indicates both a central and an embellishing function to this tremolo; other than a brief departure in m.78, the embellishments lead only back to itself. Its centrality is apparent in the texture that dominates Section 3, a two-voice polyphony that contrasts the FD tremolo with a counterpointing line. This polyphonic texture becomes obvious already at m.71. The two different roles of the FD tremolo in Section 3 demonstrate a common procedure within sequenza IV - the freeing of a gesture from a formal function. The procedure generally works as follows: a gesture is introduced within or as a function, and then becomes motivic, that is, it becomes the central idea to which even the pitch structure is embellishment. Here, specifically, the traditional role of the gesture of a tremolo is to intensify a harmonic climax point, or, when it occurs in the midst of a phrase, to accompany a melodic idea. As with other repeated textures, the traditional tendency of tremolos is to recede dynamically once established. In Section 3, however, one cannot clearly distinguish a melodic from an accompanying voice. Certainly one idea is more melodically progressive and 3 2 Throughout Section 2 short tremolos occur frequently, but, only in the capacity of filling in some of the temporal space of a singular verticality that earlier consisted of rests. 35 the other more static, but the dynamic indications and stress accents are such that neither part is clearly differentiated from the other; rather, one seems ever to be trying to obliterate the other as they vie for attention.33 Both parts are a simultaneous variation on the same theme at different rates and to different extents, that is, a variation on the tremolo. The repeated FD gesture acquires the function traditionally attributed to melodic material as it takes shape with variation in the rhythmic subdivisions, accents, and dynamics. The part that more closely resembles melodic material can also be understood as an augmented quasi-tremolo. It frequently returns to a few pitches as points of reference and is without progressive direction. This part includes short spans of voice-leading - in m.76 for example, as shown in Figure 25 - or of implied harmonic progression, as seen in the p5 descent of C#3-F#2 o n m e downbeats of mm.77 and 78. However, these patterns have little relevance beyond their immediate context.34 Meandering stepwise lines in mm.71-2 r.h., 73 l.h., and 78 beat 2 also convey this hybrid effect of directed line and tremolo. „ . „_ m.76 Figure 25 s~ i r # = z The prevalence of the F-D dyad emphasizes the M6th interval. The pervasive presence of the sixth in this section is not analogous to the centrality of 3rds and 4ths in the previous ones since it simply recurs, and does not transform surrounding material into similar intervallic structures. Section 3 is also distinguished by having the most continuous pulsed motion 3 3 Neither type of material is associated with a particular hand, as the types alternate between the hands. 3 4 This is how I have characterized many of the structural patterns of the piece as a whole; they are not categorically different here, but brought into sharper focus. 36 of any part of the piece. The regularity of the rapid pulse in the FD tremolo is reproduced at a much larger scale in the other voice.35 In mm. 763-8 a common articulation of eighth and sixteenth pulses emerges in the left hand. A rhythm of two eighths or sixteenth-eighth is also presented in mm.83-8 at the beginning of almost each of these equal-length measures. Even prior to the introduction of rapid pulsing in the FD tremolo, a particular pc is stated in regular pulses. In mm.71, 72, 73 and 76 pc C occurs on the downbeat of the measure, each time at the same dynamic. The pulsing also articulates the eighth pulse in mm.72-3. This additional pulsing of Cs establishes a metric context for the more rapid tremolo gesture. A notated comma in the l.h. part at the end of m.90 indicates a caesura; this is followed by the inwards motion from a fairly lengthy chord in the outer registers of the instrument. This motion can be understood cadentially, and is extended with an ascending grace figure covering the registral span of the second chord, whose resonance subsequently is held in the sostenuto. Together they provide closure to Section 3. Several after-effects - m.94's quiet, ascending, arpeggio-like figures, like the analogous material in the m.64 cadence - enhance the conclusion. The fourth section, mm.95-136, consists of a less polyphonic texture. Throughout this section both hands are involved in registrally expansive single gestures with extremely quick wide leaps. The tremolo of the last section is extended here to wide-ranging gestures, many of which are clusters, with the occasional reminder of single-note trills and tremolos such as those in mm.98, 101-2. Section 4 consists of seemingly even less sustained directed motion than 3 5 Regular rhythmic accents are used in conjunction with limited pitch content, and thus do not serve as a means of clarifying a pitch idea, but as a way of isolating the rhythmic idea. Individual elements are isolated in various sections throughout the piece, what must be remembered is that the limiting of pitch has the inverse effect on other dimensions to what the limiting of other dimensions have on pitch. Limiting pitch content makes other parameters more apparent, but limiting other parameters also dulls the perception of pitch, which is more articulate through greater differences in other dimensions. 37 Section 3. The constant change of direction stifles a sense of forward motion, especially when the tremolo gesture does not result in the recurrence of like entities. The intensity of the changes of direction arising from the loud wide-ranging leaps becomes an intensity of opposition within other musical parameters: dynamics, density of material, harmony, intervals, and chromatically altered pitches.36 As successive groupings of material become segregated, oppositional contrasts are established. Most notably, long single notes are contrasted with dense articulative activity in which there is a lack of cadential repose. For example, F^ is sounded at the end of m.120 and heard alone until the articulation of a flurry of 32nds in the second half of m.122. The latter's pp dynamic is the only closural aspect of this gesture. The explosion of the single notes provides release as though the absence of activity in the held note were building energy or tension in its lack of differentiation. The time interval between these events, and thereby the drama of the expression, increases throughout the section. Section 4 reaches a climax in mm.131-4 with a drawn-out tritone that is further elongated with a fermata. Figure 26 shows that of the l.h. tritone extends the sustained material into a chord that strongly recalls the first chord of the piece. This sostenuto chord itself is assembled from preceding surface materials; thus, as in Section 2, this section ends by regathering of pitch elements of the initial chord. 3 6 These are articulated in detail in Chapter five as accentuations of the sostenuto/surface differentiation that is also in direct opposition in this section. 38 Figure 26 m. 130-2 m.l Y — i — * I r - i - , i > ^ t f H T _ f f l T (Sust. ped.) © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London Once this chord has faded back into the surface, closure is provided by a string of cadential gestures like those that close the previous two sections. The flurry of activity in mm.134-35 compensates for the most extended low attack and registral37 density gesture of the piece, the mm.131-34 tritones, and continues to gather together the harmonic material that had been opened or extended within 3 7 Registral density refers to the number of different pitches that are sounded within a given time span. 39 the passage. The arpeggiations on the last two beats of m.136 provide an extra release of activity, and then move by voice-leading and decrescendo directly into m.137, seemingly dissolving into its initial harmony. Although these features are not strongly cadential in isolation, in this context - being the final and most dramatic presentation of stasis vs. intense activity, and just prior to significant textural changes - a cadence is evident. The fifth section, mm. 137-186, opens with a distinct change of timbre. The expressive indication dolce and much of the pitch content associate the broken chord at the downbeat of m.137 with the slow ascending cadential arpeggio in mm.64 and 94. This gesture of continuous fragmentation becomes the basis of Section 5, in which stability - asserted by broken chords held in the sostenuto pedal - is contrasted with the indistinctness and detached fluency of surface material notated as ametric filigree. The lack of rhythmic profile in either gesture produces a texture in which contrast is provided only by varying degrees of imprecision within essentially similar types. On several occasions dynamic surges within the ametric filigree pull this material into the forefront, challenging the gestural hierarchy. Starting at m.154 the contrast of sostenuto and surface as simultaneous layered entities moves on to contrasting successive textures, those of chords and ametric filigree, both sustained in the damper pedal. Following this there is a slow reemergence of chords as verticalities out of the arpeggiated texture. The return to chords is not achieved merely through restating them, but by gradually regathering pitches until all members of specific chords coincide temporally. This is illustrated by Figure 27, which highlights the more prominently accented pitches of mm. 170-81. The sostenuto chord in m.177 slowly builds from about m.170, and then continues transforming into the chord held in the sostenuto in m.181. These materials continue to build past the end of Section 5 towards the return of the 40 opening sonority of the piece, in m.194 wi th all but one pitch, and eventually complete in m.214. Figure 27 m A climax and cadence for Section 5 occurs at m.184 with a sudden increase in tempo to J)=104, followed by a descending figure and a fermata. There is no clear change of texture or material immediately following the cadence, as at previous sectional divisions. Rather, mm.187-9 present an elision between Sections 5 and 6. The chord at the beginning of m.187 can be heard as a goal point since it is an arrival of clarity of chord, not a resolution of other pitches. Its span is stated in clusters at t h e / chord in m.185, and various of its pitches are stated i n m.186, thus leading towards its return. This chord also can be heard as a beginning, i n the sense that it sounds like the beginning of a tonal prolongation following a caesura, 3 8 a different process than that of gathering pitch material for a chord. The figures in both hands at the end of m.188 also present an elision. The tempo of J)=104 has begun by this point, yet the dynamic shape indicates a tapering, a slight ritard of closure. The return to chords that are similar to those at the opening of the piece, both in gesture and harmonic content, suggests that the sixth section can be heard 3 8 This is discussed in Chapter 5, p.94. 41 as a reprise or coda. Many of the chords are more strongly symmetrical in register than those from which they originate, with their symmetrical properties brought into sharper formal focus. For example, the final chord in the sostenuto, sounded in m.213, is very similar to the first chord of m.2, except that a few pitches have been omitted, so that the structure now has m6s as outer intervals, and only p4s between. The final surface chord, mm.214-16, consists of augmented triads in each hand; it can be understood as having transformed into a combination of the second chords of mm.l and 2, and of 202-5, as shown in Figure 28. Figure 28 m.I m.2 m.202 m.203 m.214 b b 1 a 1 aVb 1 This section differs from the opening not only in greater symmetry of particular chords, but in the duration of segments that exhibit coherent processes. There are longer spans of continued contour; for example, mm. 195,196, 201-2 convey a longer gesture in that each has three or four chords in succession through which the bass continues to ascend. Mm.213-7 provide closure both rhythmically and tonally. As discussed in reference to Figure 4, cadence is experienced within several typical gestures. A series of tempo decelerations and a decrescendo of a repeated chord very clearly direct this passage to closure. The analysis above consists primarily of a description of prominent features 42 within sections whose segmentation is understood by internal cohesiveness within a variety of structural parameters and cadential gestures of delineation. The following graphs, Figures 29-35, comprehensively represent the intensities of seven structure-defining parameters of sequenza IV in isolation. These parameters are durations, dynamics, articulations, attack density, registral density, pedal resonance, and tempo. Figure 36 graphs the cumulative intensities of these seven parameters, portraying a shaping of sequenza IV apart from its pitch content, suggesting that dimensions other than pitch are not merely employed to articulate pitch structuring. Of course, as stated in the first chapter, these are frequently gestured specifically to redefine that structuring; however, the effect of continual recontextualization is of a gradual independence of the pitch structure and its articulating gestures. This separation of content and form suggests a quasi-isorhythmic independence of parameters. These are not ordered or serialized, but nevertheless contribute significantly to the perception of a multiple-layered structure. These graphs measure intensity according to the eighth-note pulse in which sequenza IV is notated. While this pulse is not immediately accessible to the listener, it provides a frame of reference for the player; the graphs thus are indicative of the intensity levels of the player's concentration. Assigning intensities on a per beat basis acknowledges the relatively low accessibility of articulated pulses in not differentiating on- or off-beat placement.39 There are eight levels of intensity in each of these graphs. Distinct values are indicated in a code on each Figure respectively; these values are rated in intensity from one to eight. The height of the graphs thus indicates both a distinct and a comparative intensity value. Values have been assigned according to the simple 3 9 Consequently the graphs also do not literally represent the temporal spacing between events; however, such representation would not alter overall shapes significantly. 43 assumption that more is greater.40 The cumulative graph, Figure 36, charts the sum of intensities and the amount by which each intensity level differs from the previous beat, that is, the intensity of change. In the summing, the weighting of these seven parameters is equal; recurrences of particular values within any of these, unlike the recurrences of specific pitches and collections of pitches, do not result in recognizable unique events. Also, each level of change is worth half the value of an intensity level. The accounting for change in intensity level is based on the principle that the effect of change enhances the intensity of a particular value; however this particular rating is arbitrary, chosen to evince the large-scale shape as presented in Figure 36. Values that are slightly more or less than those indicated on the grids are represented by darker or lighter shading respectively in the individual graphs, but are normalized in the summing of the cumulative graph, since the difference they would produce is minimal. The cumulative graph indicates an overall intensity shape for sequenza IV. The piece opens with a slow increase in intensity that proceeds to relatively consistent high intensities, (mm.40-103), with a few dramatic decreases. Extreme intensity changes then become much more prominent, (mm.104-139), and are followed by intensities of mid-range consistency, and finally closure through a decrease in intensity. Section delineations as described earlier in this chapter are indicated on this graph with arrows for reference. Some section divisions occur at low intensity points, such as those in mm.64 and 94. Others, such as those in mm.136 and 186, occur at places of change in the overall intensity level. 4 0 The rating of intensities of articulations, as shown in Figure 31, does not strictly fit this assumption; these values have been assigned according to two criteria: sharpness of attack and duration length. 4* O) i 1 I 52 CHAPTER THREE PHRASE SHAPE Another way in which sequenza IV can be understood as a temporal continuity is through segmentation into phrases. In a piece where each parameter of musical construction is presented with a certain individual distinctiveness and a tendency towards independence, a concept of phrase structure may seem incongruous, or at least irrelevant. A phrase generally suggests a coincidence of parameters in the presentation of what can be construed as a single complete thought, with three definable parts or roles - a beginning or place of stability, a climax or place of contrast, and a reconciling gesture or cadence. While Berio's predilection for broken gestures may make it difficult to define these parts, the piece can be understood in phrases, including the requisite parts. Wallace Berry states that the "... delineation of such formal units as phrase, motive/and others purely by cadential, overt punctuation, and by associable recurrence is often in effective contrast and functional opposition to other, especially metric structures."40 While I would not, accordingly, suggest that a phrase structuring is more than one of many methods of defining rhythms and accentuations, it is an important one because it offers a dimension that the player can easily hold in focus. Particularly in the first half of the piece, phrases are articulated by various cadential gestures approximately every ten measures, establishing a common length, with each including phrase members and a device of closure. These members suggest not only internal grouping, but also the typical functions of statement, diversion and closure. A phrase structure of quasi-regular proportions in which each phrase conveys a directed thought lends coherence to this portion of the piece, where the means of defining sequence become increasingly diversified. 40Wallace Berry, Structural Functions in Musk (Englewood Cliffs: Prentice-Hall, 1976), 322. 53 The first phrase, mm.1-10, is established by the change of texture (to a quasi-arpeggiation) and a return to a tempo of J>=72 at mil l . Within the phrase four changes of tempo, each of which is announced with timbral distinction - the introduction of a sostenuto chord at m.3, the second sostenuto chord at m.6, and a sffz chord with damper pedal collecting random resonance after release at m.8 -immediately give the impression of four phrase members. The durations and harmonic differences between these members are progressively minimized, which helps to convey continuity within the phrase. Each member features a pair of chords;42 in the first two members the chords are distinguished by changes in pitch, but in the third the same chord is repeated with a change in dynamics. This change in parameter in the third member provides contrast, and allows the phrase to be understood according to the typical phrase model wherein a climax occurs towards but not at the end of the phrase. Also, this repeated chord is not a new harmony but the same as the last chord of m.5, thus altering the gesture by beginning with the former member's second chord. The fourth member, with tighter voice-leading and relatively constant contour, particularly in the upper voice, acts cadentially. A sense of closure to the phrase also emerges from a slow rising chromatic line from that extends into the following phrase and combines with a descending line from E^, as shown in Figure 37. This slow ascent contains something of the tension of a similar linear ascent in tonal music, such as might appear over a dominant pedal at the end of a development or episode section just prior to the return of a theme. The comparison is not of similar segments; however, the effect of this device of closure is similar, and dictates that the extended rests in the middle of the bar43 are a notated rallentando. This renders m.ll's fragmentation not only a categorical change, but a resurgence of energy - a 42In mS a three-chord motive appears, although the syncopated rhythm causes perception to still be of a two-part contour. These pairs of chords often occur in addition to sostenuto entities. 4 3 Granted, silence is not experienced with these rests due to the continuity of some sound in the damper pedal; however, the absence of articulated points is still experienced as suspended tension. 54 new phrase. Figure 37 mm. 8-11 J=±f •' i ! j ii N4=* 1 p 9 1 There is no change in the sostenuto structure between phrases one and two, like the ones that accompany changes of tempo44 between smaller units within the first phrase. The continuity of sostenuto and voice-leading over the phrase break gives the player a context in which to situate the material at beat 2 of m.l l , thereby preventing an accentuation of this change, which would be inappropriate to the fluidity created by overlapping processes of continuous chord derivation. By not accenting beat two, the player can affirm a traditional reading of metric placement in which a rest on the first beat of a measure carries poignance and allows what follows to be heard as an idea already in motion. The second phrase cadences at mm. 19-20 with an arrival at via various lines of voice-leading, some local and direct, others less so due to sporadically-placed elements and dynamic shifts. As shown in Figure 38, tonal closure is suggested with the use of "dominant" affirmation of G as tonic in the twoppp chords in mm.19-20. Within this phrase four successive units can be identified by differences in texture: broken material, mm.11-12; chords, mm.13-16; a sustained chord, m.17; and a descending scale to a specific goal, mm.18-19. 4 4 These tempo changes are likely inaudible to the listener due to the lack of articulated pulse points. They articulate units of gestural distinction for the player that transmit to the listener. 55 Figure 38 m.19 m.20 o o The beginning of the third phrase (m.21) coincides with a change of tempo to J>=104, and of texture to primarily arpeggiation. The length of this phrase is ambiguous since there are no obvious cadential gestures prior to m.37. Nevertheless, the musical materials of mm.21-37 consist of two different types, rendering two phrases plausible. The third phrase, mm.21-30, consists of a series of arpeggiated fragments related in pitch content, each with chord al punctuation. The fourth phrase, mm.31-37, begins with the succinct presentation of a two-chord gesture in mm.31-2, as gathered from some of the pitch materials from arpeggiations in mm.21-7; this gesture then unravels. The unity of mm.21-30 as a phrase is supported by the presence of the A ^ - G ^ motive, which no longer acts cadentially as in m.19, but instead as a melodic motive. Again there are four phrase members. The first two members are arpeggiated gestures that end with or are interrupted by chords. The first of these chords is in opposition to, and the second a likeness of, the prevailing sostenuto chord. The third member is disruptive in that the sostenuto drops out and each voice almost concurrently rises a semitone (m.28), as shown in Figure 39. Figure 39 mm.26-28 m.28 I 56 The fourth member, mm.29-30, is at a dynamic of ppp and consists of a repetition of two chords from the first phrase interrupted by a presentation of A ^ -SO diminuted as to be little more than a brief trace of this idea. The tapering off and moments of reminiscence are not unlike a coda in cadential function. The brief dynamic outburst on the third beat of m.30 breaks the cadence abruptly, and in so doing ushers in the next phrase. The cadence of the fourth phrase at mm.37-38 is easily discernible. The rallentando into a fermata and a brief slowing to a tempo of «h=40 function as closure; this role is supported by the gesture in the pitch materials. The independent voices, that is, the material in each hand, meld together for a cadence.45 In m.37, the r.h.'s internal structure of 4ths and 7ths extends down into the pitches of the l.h. material. The l.h. here reaches up to the r.h. structure in stating the tritone, E^-A^, in mm.36-7, as seen in Figure 40. Figure 40 m.37 ;>A4 r > P4 3 This tritone provides closure in the l.h. passage alone in that it states the intervening pitches between those with which it is presented in mm.36-7; the obvious transposition operation thus frees this interval from pc specificity.46 The tritones between which it intervenes, D-A^ and E-B'', previously had been 4 5 This is a characteristic device of closure with historical precedent in polyphonic writing. (The comparison again is limited; this is not a directly imported function.) In contrapuntal forms cadence frequently is marked by voices abandoning independent ideas in order for the voices to comcide temporally in a particular harmonic gesture. Here the coincidence is not only in time but of precise pitch material. 4 6 This process in the l.h. is not in itself cadential, but in being coincident with cadential devices it enhances the cadence. 57 transferred down two octaves from their placement in mm.31-32 and 35; by filling in the pitch space between them the E^-A tritone unifies the phrase. This fourth phrase can be divided, like the third phrase, into four members. The first member, mm.31-3, owes its continuity to a steady dynamic increase, with an ending marked by a sudden opening to extreme registers. The r.h. of the second, m.34, consists of a continuous arpeggiated figure whose crescendo-decrescendo shape directs brief voice-leadings to pc G (recall the similarity to m.20); this flourish occurs together with two short independent gestures in the l.h., both of which suggest directed motion to their final pitches. Dynamics most strongly set apart the phrase member in mm.35-6 beat 2 from that in mm.36 beat 3 - 38, dividing at the rest in the r.h. of m.36. Designating mm.31-8 as a phrase contradicts some obvious aspects of closure at m.34, including the section segmentation as discussed in the first chapter. However, the weight of the cadence at mm.37-8 does not allow for a new phrase beginning at m.35.47 The third member, mm.35-6 beat 2, fits the role of contrast within the phrase; its dynamic of ppp and the number of dimensions in which it acts as an upbeat represent it is an inner focusing within a phrase rather than as a new idea. The final member begins by emulating the dynamic shape of the third, and then is extended with a decrescendo. The fifth phrase is articulated notationally at mm.49-50 by a fermata and slowing to a tempo of J>=40. There is no actual articulation of this pulse; however, its marking is significant for the player who will observe it as a cadential sign. Closure is demarcated, as it was in phrase two, through a coordination in the materials of the two hands. The r.h. grace figure just before the final C#4_G#4/ which gathers from the preceding pitch materials, leads pointillistically to each of 4 7 It could be argued that this pause is also too great after just three measures into a section; however, it is phrases that I am more consciously describing as constructed or delineated by the player, while sections are more defined by pitch processes and gestural types. 58 the l.h. pitches. Recall Figure la, where previously static pitches form lines just prior to these two pitches. Some parallels to earlier material in rhythm, contour, and intervals suggest additional or superimposed rhythms within this phrase. M.43 is similar to m.36 in that both are preceded by a 32nd-note cluster tied over the bar while the other hand presents the articulation of the first and third subdivisions of a triplet followed by the latter half of a 16th duplet. The similarity continues with the articulation of the second part of a triplet and repeated melodic contour in the first beat of the following respective measures. However, while it is common to define phrase beginnings at the place of initiation of similar rhythmic material, nothing in these gestures is in itself initiating; these repeated portions are thus understood within otherwise defined phrases. Contours in mm.46-8 similar to those in mm.39-42 again appear to indicate a phrase division. These passages can be heard as parallel on the basis of their many shared rhythmic patterns, melodic shapes and intervals, although not pitch - or interval - series. Recall Figure 15. Also, the material in both hands melds together in mm.44-5, a gesture directly comparable to that of the phrase ending at mm.37-8. To hear a phrase ending at m.45, however, would throw the quasi-regular phrase lengths off, since there is a clear phrase ending at m.50. Certainly some degree of repose will be experienced at m.45, but little, since this gesture is not elongated with a fermata as it was in m.37. Instead, a fermata occurs in m.46, where the dramatic expansion of register following m.45's gestures of closure does not suggest repose. This is an event of dramatic expansion, and suggests suspended energy. That this fermata does not represent the end of a phrase is clear in the lack of coincidence of devices of closure. This passage can best be understood as a cadence formula that becomes 59 disassembled and imbedded within the texture and so no longer signifies a cadence. It is part of a process by which cadences, and hence phrases, become so assimilated into the texture that they no longer clearly articulate segments. The cadence to the following phrase, mm.51-64, has already been described as bui lding towards Section 3 beginning at m.65. Prior to this grand cadential gesturing there is a phrase of generally high dynamics and pitch density. Changes i n gestural contour during this phrase divide it into four members, although, since ideas become more continuous rhythmically, segmentation is less clear than in previous phrases. The first member, m.51, consists of several gestures with voice-leadings i n contrary motion. Mm.52-4 is unified i n its stating of material similar to that i n m.35; 4 8 clusters in both hands near the end of m.54 conclude this member. 4 9 The third member, mm.55-58 beat 1, is the climax of the phrase, as is made clear through the tremolos' intensification of attack density and the dynamic increase to jff. The fourth member, mm.58 beat 2-61, is characterized by a heavier concentration of pulses; for example, the beginning of almost every beat receives a stress accent. A directed pulse is created by the accented l.h. pc Bs, each with r.h. activity completing the beat, on beats 2 and 3 of m.60. Mm.62-64 form a cadential extension; m.64 contains an accumulation of standard cadential gestures including three distinct units (one on each beat), of primarily ascending contour in varying styles of arpeggiation, all at a pp dynamic. The gesture of the middle arpeggiation is slowed down by a fermata and dolce instruction. The expanse of time and of cadential gestures is such that cadence becomes an event i n itself, independent of the preceding phrase and of its functional identity. The next phrase, mm.65-75, ends with characteristic repose as is indicated by 4 8 Mm.53 and 35 are both incorporated within phrases according to the above designations. The repetition of material that becomes so obvious at m.53, however, causes an interruption in the linear sequence, and tends to sound as a new phrase. M.35 also starts a new idea, as I designated the beginning of Section 2 at this point. Thus, there is an obvious overlapping of means of segmentation. 4 9 There are several similar cluster presentations within the following member. In the first instance clusters function to add intensity, while in the following passage they are the material to which other functions apply. 60 a fermata. The clearing of much of the resonance upon the release of the sostenuto pedal and of all but three notes from the chord sounded at the end of m.74 prepares for this closure. The voice-leading into the chord at the end of m.74 also enhances a sense of arrival, a blending of surface elaboration, chord sequence, and sostenuto. This blending provides closure in linking events that were kept separate in mm.65-70 through timbral distinction of sostenuto and surface material. Recall Figure 24, which outlined four distinct layers of harmonic events. This phrase designation seems to defy the obvious break dictated by a change of texture and of tempo at m.71. While these changes create a division, there is nothing in the tonal or rhythmic structuring to allow for cadence. The tenuto on C.3 at the beginning of m.71 may seem to indicate a new start, and in fact a specific pitch and pc idea is initiated here; however, the pitch connections and chord-building are most clearly heard within a phrase extending over these textural changes.49 The next phrase is seventeen measures long, mm.76-92. Its texture of two-part polyphony, continuous motion, and FD pitch dyad is interrupted in m.80 by a staccato chord and a grace figure leading into the next sostenuto chord. The resumption of the same texture in m.82 followed by a phrase of regular proportions renders, in retrospect, the material in mm.76-80 to be a false start. The rest of the phrase, mm.82-92, is relatively continuous, yet it too can be understood to consist of four members. The first two end with trills (within mm.83 and 85) the third lasts until the end of the insistent-FD tremolo and duple rhythmic subdivisions, m.88 beat 2, and the fourth lasts from there until the notated comma in the l.h. at the end of m.90. This comma provides a slight release (r.h. and pedals are sustained) prior to the the inward motion of suspended outer register entities that can be understood as cadential due to the decrease in articulative activity and change in texture. This cadence continues with an ascending grace figure, covering the 4 9 This designation affects the extent of the player's release from the final chord of m.70. 61 registral span of this chord of resolution, whose resonance subsequently is held as sostenuto. This progression of after-effects is followed by the cadential measure of m.94, as noted in the discussion of Section 4. The following phrase occurs in mm.95-105. There is a fermata at m.99 providing an extended pause within the phrase; this fermata is not cadential is because the gestures surrounding it are similar, and it is placed in upper register. This phrase also offers four distinct members separated by rests. The greatest proportion of direct ascending linear motion occurs in the fourth member, which increases the level of intensity and drives the phrase towards cadence. The divisions between phrase members are as follows: after m.97 beat one, after m.99, and just before the grace notes leading into m.102. The phrase is brought to an end by a change of texture and dynamic with an *^ staccato chord in m.103, followed by various cadential effects - a decrescendo into and throughout a broken chord, m.103, ppp ametric filigree at the end of m.l03, and the slowing to a tempo of J> = 60 for an ascending arpeggiation of irregular rhythmic and pitch density proportions in mm.104-5. Throughout the rest of sequenza IV (approximately the latter half), cadential gestures seem obvious only at the ends of larger sectional units. The gradual increasing prevalence of sostenuto material and its tonal implications create longer units and obliterate a clear sense of phrase division. Finding phrases only in approximately the first half of a large continuous form is common to tonal as well as post-tonal music. Phrases are necessary in the portion of the piece where new materials and processes are established, but may be irrelevant to, or even incongruent with, the portion in which internal connections have become both plentiful and contradictory. Signals of repose occur throughout the second half of the piece (for example, 62 a non-articulated slowing to a tempo of J>=50 at m.I 18) so that shapes can be distinguished, but within a context where harmonic connections are sustained over these divisions. In addition, a gradual progression towards closure suggests that several of these relations are becoming functionally and temporally coincident, and as such self-evident. In m.152 a subito ffand fermata over the cluster followed by a descending contour, release of pedal and ppp dynamic, provide cadence. Closure of the pitch segment in m.153 before the distinct change of timbre perhaps requires a slight relaxing. The player scarcely need direct the closure, for the changes are so apparent that they cannot but be understood. Frequently elisions blur distinctions between phrases. For example, commas at the end of mm.172 and 180 can be understood to demarcate new phrases, but in both cases the break slightly sets apart a chord that has been gathering in the preceding material. This analysis shows that the first half of sequenza IV can be understood in phrases, while the second half consists of too many correspondences for such segmentation to be significant. The following chapters look specifically at pitch structures, and the ways they establish both multiple layering and continuities. 63 C H A P T E R F O U R FORM AS HARMONIC POLYPHONY The infrequency of overt, directed linear processes throughout sequenza IV creates a polyphony that can at best be an awareness of multiple processes, or "virtual polyphony."50 Gartmann sees all the sequenzas as the exploration of the heterophonic possibilities of melody through the pursuit of an ideal of implicit polyphony.51 Fragmented bits presuppose lines and shapes underlying the piece from which various polyphonic threads evolve, only parts of which are revealed in the structure. This underlying structure is the listener's construction based upon the relations that are perceived. Pitch materials create multiple layers that in abstraction are understood as distinct. Pitch layers can be understood to represent harmony defined in three ways. The first is sequences of like and similar chords that can be termed motivic harmonies. Similar chords relate by both traditional processes such as stepwise voice-leading, octave transfer and transposition, and common post-tonal processes, such as the forming of hybrids from fixed units, intervallic symmetry, cluster formation, and significant alterations to the presentation of harmonic and melodic dimensions. These processes occur in irregular, and often simultaneous sequence, with members of particular sequences understood as chosen from a set of possibilities, and not necessarily as part of a succession. The frequent changes in registral density and fragmentation type as well as the extensiveness of overlap amongst chords creates a texture in which distinctions between layers become difficult to perceive. This lack of clearly perceptible distinction allows for a second definition of harmony, which is a collection of isolated pitch prolongations. As such the prevailing harmony transforms 50Albera,92. 5 1 Thomas Gartmann, ...das nichts an sich jetnals volkndet ist (Stuttgart: Verlag Paul Haupt Bern, 1995): 40. He offers no analysis of these possibilities. 64 continually throughout the piece, and is named according to the density and registral spacing of all pitches occurring at each successive time span. Both tonal and post-tonal harmonic and melodic relations obtain among these prevailing harmonies. The third definition of harmony is based on the acoustic resonance of the piano, specifically that created by the use of the sostenuto pedal. Harmonic relations based on sympathetic resonance with local sostenuto harmonies form a harmonic shape and layer that stands in contrast to those pitches that do not similarly correspond. The following discussion outlines several of the ways that sequenza IV is understood in regards to the first definition of harmony, and represents harmonic shape in a graph according to the second. The third definition of harmony forms the basis for the discussion of Chapter Five. The homophonic texture of the first section, as discussed in Chapter Two, can be understood as a polyphony of sequences of motivic harmonies. These sequences operate independently of each other in terms of both the types of variables that differentiate respective members, and the temporal spacing of members, which are in each case irregular. The harmonies throughout the first page of the score (mm.1-15) reveal many similarities to the opening two chords. For example, as shown in Figure 41: a) the second chord of m.2 is a transposition of the second chord of m.l; b) the voices of the l.h. of the second chord of m.2 are related by semitone or common tone to corresponding voices in the second chord of m.3, while its r.h. (with an added voice) similarly leads to the r.h. of m.3, and extends from the first chord of the piece;52 5 2 Voice-leading between non-adjacent chords can be heard due to similarity of construction. Even when the same register is sounded in intervening material, the sequence created of strongly similar chords allows these relations to be understood. 65 66 c) the last chord of m.7 is identical to the second chord of m.l while the lastone in m.15 differs from them by only one semitone; d) the first chord in m.13 differs from the second in m.2 by its lowest element having been transposed down a p5; e) the r.h. of m.4 is a transposition up by semitone of the r.h. of the second chord of m.l, with the lower third filled in; f) the r.h. of the second beat of m.12 is a hybrid of portions of the r.h. of both chords in m.l, while its single l.h. notes, F#l and are registral displacements of two pes from the first chord in m.l; g) initially this material seems to be presenting two sequences; by m.5 it is understood as part of a common stacking of thirds with frequent changes of registral extension, occasionally the l.h. corresponds directly with the thirds or expands to perfect fourths; h) the first r.h. chord of m.9 sounds many of the intervening pitches between each voice in the chords in m.5 and m.8, (a repetition from m.3), then is altered by octave transfer, following which it becomes increasingly similar to the opening sonority; thus while transforming from previous material, it is also transforming back into earlier entities, not necessarily the same ones from which it seems to have derived; i) the relation of the l.h. chords of m.2 beat 2 and m.3 beat 1 show simultaneous octave transfer and chromatic alteration; in hindsight mm.l and 2 are understood as similar. These chords establish a polyphony of sequences stemming from different harmonies, of varying rates of pacing of the same harmony, and of progressions from and towards several frequently recurring entities. These specific sequences are most apparent within this opening passage; however, the processes can be 67 understood to continue throughout the piece. Some chords transform quite substantially immediately and then remain static, while others gradually transform throughout the entire piece. Other analysts have looked specifically at the continuities of sequences based on similarity relations to the chords of the opening section. In each case a sequence is identified as a collection of related items, rather than as a process of relation. Osmond-Smith shows a few representative chords of a sequence related by stepwise voice-leading changes.54 MacKay defines several portions of the piece according to three types of chords each with several subtypes.55 He acknowledges that these types overlap and could be otherwise configured. He does not analyze the form of the piece according to these sequences. Hermann identifies fourteen types of chords, that is, harmonies according to a variety of similarity relation criteria including pitch, pc, and the compression, mean distance and overlap between pitches. These fourteen are generated over the first half of the piece after which transformation operations are regarded as indistinct. He uses these types both to differentiate sequences, showing which occur most frequently and to identify formal functions such as beginnings and ends of several of the chords.56 He limits his discussion to those chords gestured as simultaneities, and does not identify the types of units to which formal functions apply. I likewise have not attempted to analyze the form of sequenza IV according to motivic harmonies, due to the density of overlap of content in these sequences. Similarity relations can be used to establish categorical difference; however, the absence of normative processes or gestures to support this difference means that 54Osmond-Smith,39. 5 6 John MacKay, "Aspects of Post-serial Structuralism in Berio's sequenza IV & VI," in Interface: Journal of New musk Research, (Vol. 17 April, 1988):228 and 233. 5 8 Richard Hermann, "A general measurement for similarity relations: a heuristic for constructing or evaluating aspects of possible musical grammars" (Ph.D. diss., University of Rochester, 1993), 203-230. 68 any part of an entity is not bound to a particular formation. Instead it can form in abstraction with any aspect of any prior formation, that is, devoid of barriers. Harmony, defined as a collection of isolated pitches, each forming its own prolongational structure throughout the piece, is graphed in Figure 42. This graph represents pitch density in three measure spans.56 The depth of shading in each span is indicative of the number of beats during which each specific pitch is attacked.57 The literal spacing of top to bottom of the graphs is that of highest to lowest pitches on the piano. Harmony defined by Figure 42 is a textural continuum. Some pitches occur in high density within short time spans and as such are likely more obviously connected to specific originating and goal harmonies; others are distributed more evenly and do not seem characteristic of particular passages. The perception of pitch is thus understood as a backdrop within which changes of shape are those of shading. Both tonal and post-tonal types of relations form amongst events within local time spans regardless of density; these can be understood as ornamental to a structure defined as a harmonic texture. Figure 42 represents the pitch shape of sequenza IV. In the first two-thirds of the piece, there is an alternation of two different pitch textures. Either a few pitches predominate - such as in the darker areas of the Figure from mm.1-39 and 64-117 -or else pitches are spread out in all registers, such as in mm.40-63 and 118-144. In the last third of the piece, there is both a climactic passage and one of closure. The former is created by both high density of specific pitches and registral extremity, mm.145-186, and the latter by a comparative increase in symmetry, mm.187-216. 5 6 Figure 42 presents a condensed form of Figure 51 (Appendixl), which represents pitch on a per beat basis. 5 7 Figure 42 does not represent the continued presence of sostenuto pitches throughout their duration. This aspect is specifically addressed in Chapter Five, and shown in Figure 45. 70 Figure 42 indicates a wide range i n the respective densities of particular pitches. Those that seem to be the most functionally specific are the two that frame the first chord of the piece, and D^. The density of G ^ is both high and continuous throughout the piece; 5 8 as such it is connected wi th many harmonies stemming from the initial entity. D^ , by contrast, recurs infrequently, and within very limited harmonic contexts. Figure 43 shows all of its occurrences, differentiating the two harmonic settings in which it occurs by whole and quarter notes. These two settings are in fact very similar; their initial presentations, m m . l and 19-20 respectively, consist only of like pes. Figure 43 m.I m. o 19 m .20 m.f il m.65 m.I o 15 m.117 nrm 0 • i <*> ^ ^ — , — MP if k 0— 12 XJR — w =* l? i l i 1 * « » ->&— =# ' r w ~ m.130 m.131 I m sost .149 o m.16 6 1 w-Tr m.194 o 11 m.214 o ~*->t^ r r t O 1 \-— 1 w _ id ! r^* Hr1 1 V • \ 9 —• 4 * * £ 4 V . ^ o i~\ i l 1 - p n / ^ 1 rr ? * • < > — 4* =+ 1 , > o r r ? 1 sost it Ti ^ T B — ) T 8 5 8 An association made early in the piece is the registral transfer of to G 7 . Note that G 7 also is uniquely proliferous. 71 Pitch shape thus describes sequenza IV in two textural forms, one as polyphonic layers of distinct chords, and the other as a continuum with constantly changing pitch densities and registral spans. Both textures incorporate tonal and post-tonal harmonic processes. In the former these are understood to form sequences of like and similar chords, while in the latter these provide directed motion to focal points. 72 CHAPTER FIVE DRAMATIC FORM: SOSTENUTO STRUCTURE A common characteristic amongst all of Berio's sequenzas is the use of idiomatic aspects of each instrument as structural, not merely as secondary timbral dimensions. The pieces are not abstract pitch structures that could be transcribed to another instrument; specific properties of each instrument and manners of playing it - whether traditional or newly-derived - are crucial to the formal structures. The most distinguishing feature of the sequenza for piano is its use of pedal resonance, arising from extensive use of the sostenuto pedal and a very specific use of the damper pedal. Pedal resonance affects not only timbre and duration, but also harmonic structure, due to the acoustical properties of the instrument. In more traditional music, overtones are sounded together with their respective fundamentals. This is true of many of the structures here; however, there also are some events in which partials sound as independent entities, rather than only enriching lower fundamental frequencies. The sustaining of a partial independently of that particular pitch being struck is similar to the activating of a harmonic on a string or wind instrument. The specifics of which partials ring, and of whether or not partials once struck are incorporated into the sostenuto structure, are the elements that vary most amongst pianos. These are dependent on the instrument's size, materials, and how it has been tuned, and are important factors in the subtle adjustments of pacing, tempo, dynamic, and articulation that render each performance unique. The effect of the sostenuto pedal is predetermined by the structure of the piano. Specifically, notes held in the sostenuto decay at the same rate as any chord held without pedal when there is no intervening material. When material is played while the sostenuto is depressed, the reiteration of any of the sostenuto 73 pitches w i l l again sound for a full decay time as if held down, and other pitches that are related to sostenuto pitches by low ratio wi th in the harmonic series w i l l either sound those pitches or cause their upper partials to ring, although less prominently. For example, at the end of m.10, E ^ and C#5 r i n g more loudly than the other pitches i n the chord due to the presence of resonating pitches, those an octave removed, in the sostenuto. In m.35, the rings slightly more than the other pitches because it is a perfect twelfth from the sustained fundamental. In m.51, the decaying are in the sustained chord are reactivated by the attacks of E>2 and G*. A n awareness of the effect of the sostenuto pedal is crucial for the player, who must account for these subtle differences i n voicings from those articulated. Figure 44 shows, for the whole piece, the material that is held i n the sostenuto pedal. These harmonies can be understood to generate a much larger harmonic structure through sympathetic resonance, as shown i n Figure 45. Pitches held i n the sostenuto pedal are charted in black boxes for their full durations. Those pitches that are partials of a local sostenuto harmony, or of which the sostenuto structure is a partial, 5 9 are shown as partly darkened boxes, while those that do not resonate sympathetically are shown as very lightly shaded boxes.6 0 5 9 Sympathetic resonance has been calculated for all but the seventh of the first eight partials. The seventh partial generally does not correspond precisely to the structure of the equal-tempered piano. 8 0 This graph indicates only the resonance generated by the depression of the sostenuto pedal, not the damper pedal. The latter obviously causes all pitches to resonate, dealing with which the player is already well-accustomed. Figure 44 74 1-1 n I; Ci O: >: >: W[ d ni O oi I s s s s s s s Wk ; *W i . . W ' ^ / V A I . si];..'..** • . \ \ \ \ \ \ \ \ \ \ \ \ \ • : • .................... , , / .. y , . , , y >.*.\ N \ \ V','. \ S ' ' ' s \ \ \ \ \ t S f / / • • x : i f ' : ' \ N N N ' \ ' \ \ S -i . . . : . . . : . . - . . . : . . > : _ ; . / V / s s s s s 3» ft X \ \ V . \ * \ 81 One of the most tangible ways in which textural and polyphonic differentiation is established at the beginning of the piece is through the contrast of sustained and staccato chords. Initially sound carried i n the sostenuto pedal acts as a harmonic backdrop, progressing more slowly than the material on the surface. This contrast forms a reversal of the roles of sostenuto and surface; the overall texture thus changes from primarily surface material wi th sostenuto background, to sostenuto material as prevailing with surface elaborations dependent on it. Figure 45 represents this process within sequenza IV by indicating a dramatic increase of extended harmonic formations as the piece progresses. Harmonies extended by the sostenuto are established near the beginning of the piece, mm.9-27, and then are relatively scarce until m.138. In the final third of the piece, the sostenuto is employed almost continuously, and is much more prominent than previously due to both more frequent changes i n its harmony and more sympathetically resonant surface material. The form of sequenza IV can be understood according to a quasi-sonata model. In sonata form two contrasting ideas - key areas, frequently along wi th contrasting thematic material - are presented, the second of which is transformed to become dependent on the first in the latter third of the piece. Al though sequenza IV lacks tonal polarity and thematic substance, it nevertheless has two types of material - surface and sostenuto. These two types of material are initially presented as independent and distinct, following which they are directly juxtaposed and contrasted, and then finally reconciled, wi th the surface material dependent on the sostenuto. Thus, we can discern a sonata-like process to the structure. The following discussion traces this process within the local contexts of the sostenuto progression. The fact that the piece opens with surface material alone establishes the 82 sostenuto structure's first entry in m.3 as a secondary texture, growing out of the surface. The sostenuto initially sounds as a pitched background, frequently echoing the structures and processes of the surface at a slower rate. For example, the first few sostenuto chords are derived from the content and voice-leading of the surface material. The outer two voices of the l.h. of the sostenuto chord in m.3 have ascended by step from the first sonority of the piece, with the middle pitch, retained as in the original. The chord in m.6 can be understood as a combination of triadic structures in each hand, as appear in the surface material in mm. 1,2 and 4, and the process of filling in thirds as begins in m.4. In mm.9-16, the sostenuto structuring is an elongated echo of the progression on the surface in mm.8-9. The chord held in the sostenuto in mm.20-7 establishes more direct interaction with the surface, by way of arpeggiation around and into the sostenuto structure. This chord is very similar to the first chord of m.I, with several pes altered by octave transfer. Another of the most prominent pes of the original chord, G, which in the first instance occurs as the top voice, is now heard in close temporal proximity, but apart from the sostenuto structure. Its placement on the surface allows it to be understood as if it were a local tonic with motion directed towards it (recall Figure lc). The prevailing harmony is thus heard as split between sostenuto and surface, with most pitch activity directed towards the portion on the surface. Another relation between sostenuto and surface becomes manifest through quasi-tonal relations of bass notes.61 The lowest pitch in the sostenuto structure of mm.20-27 is D^, which has occurred previously only as the lowest note of the first chord of the piece. The centrality of G^ is affirmed by the sonority in m.20 with as bass, which gives it a dominant function (recall Figure 38). Thus the sostenuto structure helps define and is subservient to the tonality of the surface. 6 1 There are several instances of quasi-tonal relations of bass notes throughout the piece. These bass notes can be understood as roots of chords, representing harmonies that are not present. 83 The arpeggiation in mm.21-27 consists of several of the pitches being held in the sostenuto as well as those adjacent. Surface motion in and out of the sostenuto structure is made apparent in the chord of m.22 in which all but one of the sostenuto pitches have been transposed up or down by semitone, and the / chord in m.23 whose pes are all octave equivalents of those in the sostenuto. In m.25 the arpeggiation resolves directly into the sostenuto structure. Even though the sound-quality of the sostenuto is more obtrusive than that of the surface its role is still subservient. This is evidenced by the tonal pulls towards the surface in the longer lines, with pc G sounded frequently but not part of the sostenuto structure in mm.20-27, as well as with the prominent l.h. line A^-G-F* in the bass of mm.26-28, during which the sostenuto fades out of the texture. After this point of harmonic connection, the sostenuto layer recedes once more into the background. Any sense of sostenuto harmony in mm.31-49 is generated from only one pitch, and from only three in mm.50-63, as seen in Figure 45. The eight-note chord in mm.61-64, which was analyzed as the culmination of Section 2, preparing the listener for the return of the initial sonority of the piece at m.65, adds durational weight to the reconstruction of the initial sonority. While its capacity to sustain sound allows this sostenuto chord to have a stronger effect than the surface material, this effect is employed to enhance the structure as dictated by the surface. The content in the sostenuto in mm.66-95 is again very sparse and thereby limited in effect. Throughout this passage a single 6-pitch sostenuto chord builds slowly by the addition of one or two pitches at a time. The derivation of pitches of this chord from a specific sonority that appears (in like or similar form) frequently on the surface becomes obvious in the retaining of several pitches from the final 84 sonority of m.74 into the sostenuto. This connects the sostenuto structure with one particular harmonic sequence at a place where the ear is accustomed to several. While the sostenuto chords sphere of influence cannot thereby be limited, this specific association inhibits perception of other associations. Another factor that relegates a secondary role to the sostenuto structure throughout mm.76-88 is the obtrusive prominence of a particular dyad, F^-D^, on the surface. The frequency and accent structure of the reiteration of this dyad, as a tremolo, effects a certain banality caused by the difficulty of hearing this gesture as part of any structures beyond itself. Groupings with surrounding material are formed as only the faintest reference, even though the passage contains many pitches in the same register as the dyad, some only a semitone away, that is, in relations that have been considered melodic or harmonic gesture-defining in earlier contexts. It seems as if this particular item of surface material is vying for the constant, distinct timbral status of the sostenuto structure. Berio's predilection for breaking the gesture of an otherwise characteristic formal role dictates that no particular element within the piece can be guaranteed to retain a unique identity; the attempt of a particular event within surface material to become so fixed as to form a distinct other, almost a different timbre as happens with the FD tremolo, is an example of this process. The reversal of role between sostenuto and structure begins to be manifest in the direct contrast of material in several parameters in mm. 110-66. As shown in Figure 46, the chord that forms in m.110 and recurs as a grace chord in mm.112 and 113 is complementary to the one that forms in mm. l l l and is subsequently held in the sostenuto pedal, providing a direct opposition of harmonic and timbral sonorities.62 The two chords circled in Figure 46 combine to form the chromatic 6 2 Aggregate completion is a factor of form derivation throughout the piece in that the complete chromatic is present with sufficient consistency as to be considered important; however, only in a few places does its completion appear in such a marked gesture-defining manner. 85 aggregate as follows: A = {C#, E ,^ E, F, G, A) and B = {Q D, F#, B^B}. Figure 46 © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London This is the most strongly confrontational opposition of harmonic content of any point in the piece. Since the chords are complementary the second chord provides minimal resonance to the first. Direct opposition of these materials is also conveyed in the extremity of the rate of dynamic change and the manner of gathering the materials of each chord through arpeggiated crescendos, as if each were staking out its own pc or pitch area. The variety of temporal types for these two chords, grace figures, broken chords, arpeggiations, and solid chords, lends an insistence to these particular harmonies. Here the player is no longer a facilitator of information with little or no access to what actually is experienced by the listener, but is instead playing both parts within a direct struggle, one that is about pitch content, timbre and dynamics as kept distinct in sostenuto and surface materials. The opposition of complementary harmonies in mm. 110-13 is followed by an opposition of register, pitch densities, and adjacent pitches, highlighting the creating of resonance. Harmonic resonance is a property of the sostenuto pedal that 86 the surface in the following section (mm.l 15-129) attempts to emulate through these oppositions. Figure 47 Cf- ^_ u m. c 1 i 1 p~ . L j : —i ppp Ped 1 Sust. ped © Copyright 1967 by Universal Edition (London) Ltd., London © Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole U.S. and Canadian agent for Universal Edition (London) Ltd., London For example, according to the dynamics and accelerated motion, the long single pitches of F^ i n m.120 and C#4 in m.123 act as goals. In both cases the single pitch is followed by a sudden increase i n pitch density. F is released i n a flourish i n which extra pitch content balances the F's duration. Recall Figure l b , where F^ lasts for approximately five beats and then leads by stepwise ascent to F#4 within arpeggiated 64ths that last for one beat. A grace figure directs motion to the C#; this pitch expands into a chord at the end of m.124 that subsequently is held in the sostenuto, as shown i n Figure 47. These two pitches, C.4 and F#4, are then placed in m.132 in a tritone that functions as a transposed echo and inversion of the most dramatic reversal i n the piece, the statement of D ^ - G ^ l and its retrograde, constituting mm. 131-134. The low register of the single pitches of the horizontally presented D-G# tritone, the 87 elongated pulse - the tempo has slowed to J>=40 - as well as the accented .^dynamic provide a setting of extreme dramaticism. This statement, however, not only makes obvious this means of material and formal derivation, but also provides a focal point within an area characterized by the inversion of sostenuto and surface, and by the establishing of hierarchical relations rather than equally-weighted polyphonic ones between these. As may at first be assumed, this tritone does not stand apart from the local melodic and harmonic (sostenuto) contexts. The pointillistic ascending chromatic figure at the beginning of m.129, <E^, E, F, F#>, is loosely reversed at the end of the measure - <E, F, E ^ , making the D in m.131 a linear succession. Also, this together with what is currently held in the sostenuto provides a strongly similar harmonic entity to the opening sonority of the piece. Indeed, from mm. 115-30 the pitch materials build towards the return of the opening sonority, which upon arrival is held in the sostenuto.64 After the tritones, the ascending gesture continues in an arpeggiation with many pitches and pes that closely resemble the opening chord, as shown in Figure 48. The chord held in the sostenuto becomes more strongly similar to the opening chord of the piece when the surface material is understood to extend it; this familiarity allows the surface to be understood as part of, and not in opposition to, the sostenuto. Figure 48 6 4 This summation of materials differs from that in m.62 in that it does not bring the surface motion to a halt, but allows the surface motion to continue forming outward from it. 6 5 Returning to a former theme, the regesturing of repetition, the inclusion of or extension to pc G# of the opening sonority in m.132 is the mcorporating of what had been been understood as separate from the opening chord sequence in the polyphony of mm.65-7u. 88 This very explicit continuation of the sostenuto into the surface i n a recognized harmonic entity establishes a precedent of independent surface materials being heard as extensions of harmonies sustained i n the sostenuto. Fol lowing these oppositions and inversions, the gestures become much more continuous, wi th obvious hierarchical differentiation of sostenuto and surface material. Sostenuto material is presented as broken chords, and surface as ametric filigree, that is, arpeggiation without rhythmic specificity. Pitch structuring via tonal processes tends to support the hierarchization of materials i n the latter half of the piece. Due to the reliance on aspects of tonal progression, voice-leading, and structures already familiar wi th in the piece, as the piece progresses many of the sostenuto chord changes are understood as a prolongation or a progression, l inked by a common tonal dimension. A specific pc centre, D , is the focal point throughout much of this material. One of the ways in which resolution into the sostenuto is expressed is to centre the harmonic structure on structures that al low the instrument to resonate naturally. A s low ratio vibrations produce a major triad, the result of natural resonance is tonal relations. For example, the lowest pitches of the sostenuto structures i n mm.145-49 are D3-A ^ - D 2 ; the sense of tonal prolongation suggested by this bass line is supported throughout the passage by dynamic gestures and bits of voice-leading that seem to move away from and back to these structures. Figure 4 9 m.145 m. 187 m.147 m.189 m.149 m.194 Q I ( V ? ) I 89 Also, as shown in Figure 49, the harmonies above these bass notes include a l l the pes of the tonal progression I - -1 , with several of the pes expanded through neighbour motion. Also noteworthy is the replication of the sostenuto chord from m.147 as a grace chord i n m.149, functioning as a dominant that decrescendos into its tonic, D , at the beginning of the next measure. In m.153, 6 5 there is a cluster in the sostenuto that bears little resemblance to a D triad other than that the lowest pitch is an F ^ ; 6 6 however, attention is drawn towards this pc through reiteration in four registers, and the placement of E>4 as the final note of the filigree, and the lowest. Thus, while the D prolongation is not the sostenuto structure, the tonality it has created is the central structure.6 7 In mm.167-86 longer spans of material connect harmonically due to the slow acquisition of notes for the sostenuto harmony; recall Figure 27. The pitch material of mm.154-202 is a large repeated segment, as mentioned in Chapter One. Changes in gesturing from the original structure are generally those that help to move the piece towards closure, and l imit diversity of harmonic structures. Mm.162-65 present the parallel passage to mm.110-13. This passage does not have the appeal of opposition of the first, although there is an obvious differentiating of complementary chords as they alternate as sostenuto and surface structures. These chords, however, have their own temporal and registral places, and are not led to i n dramatic fashion via gestural or dynamic flourishes. The sostenuto material is understood to be at the fore as the surface material introduces and echoes it, and becomes increasingly limited i n content. A similar anticipation and echoing of the sostenuto on the surface occurs in 6 6 The dotted barlines in the score are real ones. 6 6 Pc F# holds the bottom place within sonorities throughout mm.152-155 and 158-9, is an arrival point in mm.171 and 175, and again at the bottom of a sostenuto chord in mm.181-186. It seems that the means of prolongation of the initial chord of the piece throughout this section, and as alluded to in reference to m.l 2, is to drop the bottom voice or pc, D, and to retain a sonority with its next pc vertically, F#, which is the (major) 3rd of a D sonority if thinking tonally. Tonal thinking is crucial to a segment of the piece where the natural properties of the sostenuto pedal prevail. 6 7 The reverse also holds true that although a particular tonality, D, establishes the sense of centre harmonically, by the end, it is the gesture of a sostenuto chord, and not D or the original chord that resonate. 90 mm.187-96, the passage parallel to mm.145-151. This strengthens the D tonality that is again suggested by harmonic content of the chords held i n the sostenuto. A s the piece is brought to a close there are various means i n which the surface enhances the harmony of the sostenuto. Several structures that were presented as oppositions earlier i n the piece appear as unified complete structures. The pitches i n the middle- and upper- register augmented triads of mm.214-17 are combinations of the chords that alternated in sostenuto and surface i n mm.202-7. These in turn derive from the second chords in each of m m . l and 2. In mm.202-5, analogous to mm.110-14, two chords are placed in hexachordal opposition. The latter passage does not have the dramatic effect of the former; this is not only because of the absence of elaborate arpeggiation, but also because of the placing of these chords in an upper register.6 8 Throughout this section much of the prolonged harmonic and tonal sense is built and represented by connections i n the bottom voice that both vaguely retain pitches and follow lines, as shown in Figure 50. Figure 50 m.196 m.198 m.200 m.201 The final system of the piece suggests that it is not a particular tonality but the idea of sostenuto as prevailing that is crucial to closure. The final sostenuto sonority, which begins in m.213, is similar to the chord at the beginning of m.2, (although it omits two pitches, and is thus more strongly symmetrical). A s noted earlier, there is an attempt to resolve from this sostenuto harmony to the initial sonority tonally, through semitone ascent in the bottom voice progression, C#2-r>2. 6 8 Many tonal structures make extensive use of upper registers in Coda material, following the resolutions of the major structural components. 91 This resolution is not definitive, and thus also the D tonality, since the chord or resolution is not sustained. The most directed dynamic closure involves the repetition of the third sonority of m.214, moving until the end of the piece from ntf-p-pp-pppr (the piece uses no mp). In the final measure a resounding of the sostenuto chord followed by a chord that rings as upper resonance since all of its pitches resonate with the sostenuto. This final gesture conveys a sense of sound being generated by, or motion from within harmonic structures, and affirms the reversal and bringing together of sostenuto and structure that has occurred. It also reminds of the means of structuring within sequenza IV - harmonic fragmentation and construction. 92 S U M M A R Y This analysis suggests that the gesturing of sequenza IV, both its language and structure, are drawn from and comment on prior musical styles. These expressions are placed within idiomatic gestures of piano playing. A n awareness of traditional gestures as structural components allows the player to incorporate familiar means of creating form - whether as contrasting or continuous entities -that are particular to various historical styles. The notion of gestural structuring within sequenza IV also involves the freeing of motivic harmonies and contours - recognizable entities - from a central function, so that similar materials can be explored as both structural events and textures. Principles of construction are extrapolated from specific gestural forms. A motive w i t h a distinct shape and harmonic connection transforms into various configurations of extended and fragmented harmonies. The effect of the sostenuto pedal is likewise transformed from providing a background layer to harmonic continuities amongst layers. Simultaneous but non-corresponding sequences of repeated and similar harmonies provide a coherence of materials throughout the piece. Its form as a temporal continuity can be described apart from reference to these sequences in both discrete sections and phrases and as an arch-shaped continuum of intensity levels. Registral and time span pitch densities also form the piece as a temporal continuity, one i n which specific pitches provide focal points to which surrounding materials relate. A l l of these processes require the attention of the player, who is an integral component wi th in the structuring of sequenza IV. B I B L I O G R A P H Y 93 Albera, Philippe. "Introduction aux neuf sequenzas." Contrechamps. Paris: L A g e d'Homme, 1981: 90-122. Berio, Luciano. "Aspect d'un artisanat formel." Contrechamps. Paris: L A g e D'Homme, 1981: 10-23. Berio, Luciano. "Du gesteet de Piazza Carita." Contrechamps. Paris: L A g e D'Homme, 1981: pp.41-45. Berio, Luciano. "Form." The Modern Composer and His World. John Beckwith and Udo Kasemets, eds. Toronto: University of Toronto Press, 1961: 140-45. Berio, Luciano. "Meditations sur un cheval de douze sons." Contrechamps. Paris: L A g e D'Homme, 1981: 46-50. Berio, Luciano, Philippe Albera and Jacques Demierre. "Entretiens." Contrechamps. Paris: L A g e D'Homme, 1981: 60-66. Berio, Luciano, sequenza IV. London: Universal Edition, 1965. Berio, Luciano, sequenza IV. revised ed. London: Universal Edition, 1993. Berry, Wallace. Musical Structure and Performance. N e w Haven: Yale University Press, 1989. Berry, Wallace. Structural Functions in Music. Englewood Cliffs: Prentice-Hall, 1976. Dalmonte, Rossana. Luciano Berio. Entretiens. Trans. Mart in Kaltenecker. Paris: J C Lattes, 1983. Dalmonte, R., Lorenzini, N . , Assaroni, L . , Frasnedi, F. II Gesto Delia Forma. Milano: Arcadia Ediz ioni , 1981. Gartmann, Thomas. ...das nichts an sich jemals vollendet ist: Untersuchungen zum Instrumentalschaffen von Luciano Berio. Stuttgart: Verlag Paul Haupt Bern, 1995. 94 Hermann, Richard. " A general measurement for similarity relations: a heuristic for constructing or evaluating aspects of possible musical grammars." Ph.D. diss., University of Rochester, 1993. MacKay, John. "Aspects of Post-serial Structuralism in Berio's sequenzas IV & VI." Interface: Journal of New music Research, 17: 223-39, A p r i l , 1988. Magnani, Francesca. "La sequenza I de Berio dans les poetiques musicales des annees 50." 14 Analyse Musicale. Jan.1989. pp.74-81. Osmond-Smith, Dav id . Berio. N e w York: Oxford University Press, 1991. 95 Appendix 1 21 § CM OH in j CD l-i bp: in ! <u • - 4 - < : O i c \ ^ \ u C i tfl i -5 O : C i <u i is! C ! o i at i X i o : U5 • <u i C 45 • f-t : w ; <X> • JZ : U : 96 97 99 100 r r r r r r r m - r m m n r r r n ) I 1 m 11 m - i - T r i THE UNIVERSITY OF BRITISH COLUMBIA SCHOOL OF MUSIC Recital Hall Sunday, August 24,1997 8:00 p.m. DOCTORAL RECITAL* CHERYL PAULS, piano Sonata, Op. 34, No. 2 (1795) Adagio—Allegro con Fuoco Presto Muzio Clementi (1752-1832) Sonatina Canonica Su "Capricci" di Niccolo Paganini (1943) Allegretto comodo - Allegro moko misurato Largo - Vivacissimo Andante sostenuto Alia marcia; moderato Luigi Dallapiccola (1904-1975) ...sofferte onde serene... (for piano and tape, 1976) Jacqueline Leggatt, mixer Luigi Nono (1924-1991) - I N T E R M I S S I O N -Bagatelles, Op. 126 (1824) Ludwig van Beethoven (1770-1827) Andante con moto Allegro Andante Presto Quasi allegretto Presto - Andante amabile e con moto \ 102 Shiraz(1977) Claude Vivier (1948-1983) Etudes, Op. 18 (1918) BelaBartdk A H i (1881-1945) Allegro molto Andante sostenuto Tempo giusto * In partial fulfillment of the requirements for the Doctor of Musical Arts degree with a major in Piano Performance. Reception to follow in the faculty lounge. 


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