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Sans fin sans (endlessness): for guitar, seven wind instruments and double bass Amort, Joseph Scott 2009

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sans ĕn sans (endlessness) for guitar, seven wind instruments and double bass by Joseph Scott Amort B.B.A. (Hons), Wilfrid Laurier University, 1994 B. Mus (Hons), Wilfrid Laurier University, 1999 M. Mus, University of British Columbia, 2001              Doctor of Musical Arts in      (Music) e University Of British Columbia (Vancouver) August 2009 © Joseph Scott Amort, 2009 Abstract sans ĕn sans (endlessness) is a ĕeen-minute musical composition scored for solo guitar, seven wind instruments (Ęute, oboe, clarinet, bassoon, trumpet, horn, trom- bone) and double bass. Although the work is in one continuous movement, it con- sists of seven distinct sections, each constructed from fragmented pieces of a pre- composed originating structure. InĘuenced by the prose of Samuel Beckett, sans ĕn sans is an exploration of non-linear time and the Deleuzian notion of art as abstract machine. ii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Why this piece now? . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 InĘuences, Materials & Resources . . . . . . . . . . . . . . . . . . . . . 4 2.1 Form & Conception . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Samuel Beckett . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1.1 Lessness . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1.2 (end)Lessness . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Gilles Deleuze and Félix Guattari . . . . . . . . . . . . . . . 7 2.1.2.1 Immanent Difference . . . . . . . . . . . . . . . . 7 2.1.2.2 Abstract Machine . . . . . . . . . . . . . . . . . . 8 2.1.2.3 Art and Philosophy . . . . . . . . . . . . . . . . . 9 2.2 eoretical Foundations . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Algorithmic (Computer-Assisted) Composition . . . . . . . 9 2.2.1.1 Fractals . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1.2 Lindenmayer Systems . . . . . . . . . . . . . . . 11 2.2.1.3 Turtle Graphics . . . . . . . . . . . . . . . . . . . 14 2.2.1.4 Musical Interpretation . . . . . . . . . . . . . . . 15 iii 2.2.2 Spectralism . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.2.1 Spectral Harmonic Structures . . . . . . . . . . . 17 2.2.2.2 Harmonic Space . . . . . . . . . . . . . . . . . . 17 2.2.3 Musical Time . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.3.1 Non-linear Musical Form . . . . . . . . . . . . . 20 2.2.3.2 Duration and Rhythm . . . . . . . . . . . . . . . 21 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Pre-compositional Work . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1 Pitch Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 omlsystem: An OpenMusic library . . . . . . . . . . . . . . 25 3.1.1.1 Turtle Graphics Interpretation . . . . . . . . . . . 25 3.1.1.2 L-system Processing Engine . . . . . . . . . . . . 26 3.1.1.3 Harmonic Space Mapping . . . . . . . . . . . . . 27 3.1.2 endlessness . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.1 Musical Material . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Analysis: sans ĕn sans . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1 Becoming-music . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Interruptive Polyphony . . . . . . . . . . . . . . . . . . . . 41 4.1.2 e Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.2.1 Rhythm . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.2.2 Pitch . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.3 Timbre and Form . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.3.1 Musical Material . . . . . . . . . . . . . . . . . . 50 4.1.4 Tempo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 iv A omlsystem Source Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 A.1 turtle.lisp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 A.2 lsystem.lisp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 A.3 pitchspace.lisp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 B Pitch-Fields in sans ĕn sans . . . . . . . . . . . . . . . . . . . . . . . . 71 C Musical Score of sans ĕn sans . . . . . . . . . . . . . . . . . . . . . . . 75 v List of Tables 2.1 Ordering of Sentences in Lessness . . . . . . . . . . . . . . . . . . . 6 2.2 Available Turtle Graphics Commands . . . . . . . . . . . . . . . . . 14 2.3 Pythagorean Intervals in 2-limit Harmonic Space . . . . . . . . . . . 19 3.1 Turtle Graphic State Evaluation . . . . . . . . . . . . . . . . . . . . 26 3.2 Available Intervals in 5-limit Harmonic Space . . . . . . . . . . . . 29 3.3 Random Funnel Sequence in sans ĕn sans . . . . . . . . . . . . . . . 34 3.4 Large-scale Formal emes in sans ĕn sans . . . . . . . . . . . . . . 36 3.5 Tensions of Musical Parameters in sans ĕn sans . . . . . . . . . . . . 36 4.1 Location of Group I Fragments . . . . . . . . . . . . . . . . . . . . 42 4.2 Large-Scale Form of sans ĕn sans . . . . . . . . . . . . . . . . . . . . 43 4.3 Ensemble Combinations . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 Tempo Map of sans ĕn sans . . . . . . . . . . . . . . . . . . . . . . . 57 vi List of Figures 2.1 A Mandelbrot Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 A Feedback Machine . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 First Stages of a Koch Curve . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Rhythmic Ratio Sequence . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Example of a Random Funnel series . . . . . . . . . . . . . . . . . . 22 2.6 Measures 1–4 of Ferneyhough’s Terrain . . . . . . . . . . . . . . . . 23 3.1 An omlsystem Koch Curve . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 ‘Crystal’ Structure of 5-limit Harmonic Space . . . . . . . . . . . . . 30 3.3 Musical Mapping of a ĕrst-stage Koch Curve . . . . . . . . . . . . . 30 3.4 An omlsystem Randomised Quadratic Koch Curve . . . . . . . . . . 32 3.5 Basic Durational Sequence in sans ĕn sans . . . . . . . . . . . . . . . 33 3.6 Rhythmic Processes in sans ĕn sans . . . . . . . . . . . . . . . . . . 35 3.7 Scordatura Tuning of the Guitar . . . . . . . . . . . . . . . . . . . . 37 3.8 Sketch of Group I, mm. 1–4 . . . . . . . . . . . . . . . . . . . . . . 38 4.1 ‘Sentence’ Ordering in sans ĕn sans . . . . . . . . . . . . . . . . . . 41 4.2 Sample Group I Fragments . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 OpenMusic Rhythm Patch . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 sans ĕn sans, mm. 32–35 . . . . . . . . . . . . . . . . . . . . . . . . 46 4.5 sans ĕn sans, mm. 83–85 . . . . . . . . . . . . . . . . . . . . . . . . 49 4.6 sans ĕn sans, mm. 8–11 . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.7 sans ĕn sans, mm. 19–23 . . . . . . . . . . . . . . . . . . . . . . . . 51 4.8 sans ĕn sans, mm. 40–43 . . . . . . . . . . . . . . . . . . . . . . . . 52 4.9 sans ĕn sans, mm. 74–78 . . . . . . . . . . . . . . . . . . . . . . . . 54 vii 4.10 sans ĕn sans, mm. 98–101 . . . . . . . . . . . . . . . . . . . . . . . 55 4.11 sans ĕn sans, mm. 132–133 . . . . . . . . . . . . . . . . . . . . . . . 56 viii Chapter 1 Introduction All sides endlessness earth sky as one no sound no stir. —Samuel Beckett, Lessness Sans ĕn sans (endlessness) is a ĕeen-minute musical composition scored for solo guitar, seven wind instruments (Ęute, oboe, clarinet, bassoon, trumpet, horn, trombone) and double bass. Although the work is in one continuous movement, it consists of seven distinct sections, each constructed from fragmented pieces of a pre- composed originating structure. InĘuenced by the prose of Samuel Beckett, sans ĕn sans is an exploration of non-linear time and the Deleuzian notion of art as abstract machine. e composition of sans ĕn sans represents my confrontations with a variety of musical and non-musical sources. At its core, it is my attempt to placemymusical ac- tivities within a larger philosophico-aesthetic framework, as well as a continuation of my compositional interest in exploring unusual musical forms and non-traditional instrumental sound production techniques. It is also an attempt to utilise mathe- matical phenomena—including prime numbers, fractals and L-Systems—to generate compelling musical material. e title of the work stems from a French translation of ‘endlessness’, ĕn sans ĕn, literally ‘end without end’. ese words were then inverted as both a play on the title of a prose work by Samuel Beckett, called Lessness, or Sans in its original French; and, as a reĘection of the partly random construction technique which allows for any number of potential outcomes. 1 e unusual ensemble found in sans ĕn sans was chosen deliberately for its tim- bral potential, ability to produce wide dynamic contrasts and rare use. e choice of guitar for soloist also reĘects my predilection for underused, non-orchestral in- struments. Despite a limited presence inWestern art-music—early examples include John Dowland’s lute works—the early 20th-century saw composers such as Manuel de Falla and Heitor Villa-Lobos bring a newfound legitimacy to the instrument. No- table contemporary works for solo guitar include Luciano Berio’s Sequenza XI, Tris- tan Murail’s Tellur, and Brian Ferneyhough’s Kurze Schatten II. Ferneyhough has also prominently featured the guitar in his recent opera, Shadowtime, based on the life of German philosopher Walter Benjamin. e second scene, Les Froissements d’Ailes de Gabriel, is scored for solo guitar and large chamber ensemble, and Ferneyhough’s compositional focus on fragmentation and random ordering provided a strong in- Ęuence on sans ĕn sans. Each of these works push the guitarist’s technique to new limits and introduce a variety of innovative methods for sound production, many of which are utilised in sans ĕn sans. Following a brief discussion of themotivations behind sans ĕn sans, this disserta- tion spans four chapters: 1) InĘuences, Materials & Resources; 2) Pre-compositional Work; 3) Analysis: sans ĕn sans; and, 4) Conclusion. Supplemental materials, includ- ing computer source code, harmonic reference material and the full score of sans ĕn sans, can be found in the appendices. 1.1 Why this piece now? roughout my studies, I have been fascinated by the academic ĕeld of musical aes- thetics. e question of compositional intent has motivated me to explore a variety of contemporary philosophical thought. Is my artistic goal simply to entertain, or to communicate an ideal, to express myself, some combination thereof, or something else entirely? I have certainly not fully answered any these questions, althoughmy en- counters with various thinkers—and of course, inĘuential contemporary composers such as Helmut Lachenmann, Luciano Berio and Brian Ferneyhough—have led me to explore a variety of new compositional techniques and their affects. Many of my past works can now best be viewed as contributing to experimenta- tions with a particular theme or technique. For example, Variations and ...then burn 2 me, both electroacoustic works for tape, are explorations of the sonic potential of a single sound source. Bent wallpaper is a string quartet that followed my initial encounters with the extended instrumental techniques present in Helmut Lachen- mann’s works, and is also my ĕrst work that is heavily inĘuenced by a non-musical source (a set of computer-generated ‘nonsense’ text). Happy pink music, for soprano saxophone and live electronics, is a virtuosic solo work combined with an electroa- coustic component that utilises the saxophonist’s performance output to generate a real-time accompaniment. Sans ĕn sans represents a culmination and synthesis of these past works, and also provides me with a number of new directions for future pursuit. 3 Chapter 2 InĘuences, Materials & Resources e composition of sans ĕn sans was inspired by a variety of musical and extra- musical sources: the prose of Samuel Beckett; philosophical concepts from Gilles Deleuze and Félix Guattari; the ĕeld of computer-assisted composition; spectralism; and, the theoretical writings of James Tenney and Brian Ferneyhough. e following chapter will provide some background and context for each of these inĘuences. 2.1 Form & Conception e initial inspiration that led to the composition of sans ĕn sans began through an encounter with a short work by Samuel Beckett, titled Lessness. Fascinated by its af- fect, I began to explore its underlying structure and resultant philosopho-aesthetic questions. is led me to examine a variety of contemporary aesthetic philosophies and conceptualise a means to reĘect these inĘuences inmy own compositional work. Each of these extra-musical sources, their relationships to each other, and their im- pact on sans ĕn sans will be explored in this section. 2.1.1 Samuel Beckett “Almost nothing happens” (Graver and Federman 1979). Quoted in Graver’s and Federman’s Samuel Beckett, this excerpt from a review of the play Endgame aptly summarises much of Beckett’s later work. During this period, Beckett’s prose em- braces a dramaticminimalism—with ever shorter, more distilled writing—oen only 4 amounting to a few pages of text. His drama and ĕction dispense with conventional plot and the unities of time and place to become abstract narratives on the basis of experientiality. 2.1.1.1 Lessness Beckett’s experimental prose piece Lessness—ĕrst published in French as Sans in 1969, and followed by Beckett’s own English translation in 1970—depicts a nameless pro- tagonist within a barren world: “Grey face two pale blue little body.... Scattered ruins same grey as the sand ash grey true refuge.” (Beckett 1970) e work consists of sixty sentences, structured into six groups (A-F) of ten sen- tences each (A1...A10, B1...B10, etc.) ese six groups are differentiated by a par- ticular thematic element that recurs in all ten sentences: decor, body, ruins, refuge forgotten, time past, and time future (Solomon 1980). ese sentences were then ordered by means of a chance process: Beckett wrote each of the sixty sentences on a piece of paper, placed them in a box, and randomly selected them. eprocedurewas then repeated, resulting in 120 sentences (each of the original 60 restated once) which were subsequently ordered into paragraphs through a similar chance procedure. e numbers 3, 5 and 7 were written on four pieces of paper each, and the numbers 4 and 6 on six pieces of paper each, which were then also chosen randomly. is organised the ĕnal 120 sentences into 24 paragraphs, each consisting of a minimum of three, and a maximum of seven sentences (see Table 2.1) (Hulle 1980). 2.1.1.2 (end)Lessness Lessness embodies a ‘Beckettian’ philosophy, a discourse with themes such as purga- tory, despair and loneliness within an over-arching philosophy of the absurd. is absurdity is revealed at its most basic level as an engagement with nothing, and the repetition of nothing. is is not some nihilistic notion of emptiness, or lack-of- something, but rather a discourse with the dissolution of meaning. As Adorno re- marks, “Beckett’s [works] are absurd not because of the absence of any meaning, for then they would be simply irrelevant, but because they put meaning on trial; they unfold its history.” (Adorno 1997, 153–4) is results in an art-form that cannot easily be explained through the constraints and conventions of a traditional narra- 5 Table 2.1: Ordering of Sentences in Lessness Paragraph Part I Part II I A3, B9, C9, A2 C4, B6, A2 II A9, D3, E9, B8, E2 B8, B10, F2, F7 III F10, C6, D8 E6, B2, F8, B4 IV E6, D7, C1, F8, A5 D1, B3, A9, A5, E2, E9 V B4, C4, B1 A1, F4, D6, C9, F6, B5, D7 VI F3, E4, C7, B7, F2, B6 C3, C10, E5, F3, F5, E8 VII A4, C2, E3, C10, F5, E5 A7, E1, D5, E3, D3 VIII A1, C8, A6, B2, D5, A8 A10, D9, F9, B1, A8, E4, C6 IX C5, F9, B5, D10, B3, D6, F1 A3, E7, D2 X A10, E8, D9, E10 A4, B7, F1, C5, D10, B9 XI F6, B10, F7, A7 C2, A6, D8, F10, D4 XII D4, E7, D1, E1, C3, D2 C7, C1, C8, E10 tive structure. More speciĕcally in the case of Lessness, there is an implicit reĘection of the arbitrary structure that human beings have placed on time: twelve months in a year, twenty-four hours in a day, sixty minutes in an hour, etc. e impersonal and atemporal prose presents a confrontation with unending time and the futility of attempting to ĕx that which is always moving. As a means of encouraging this challenge, Beckett offers the reader a series of sentences that have no immediately predictable relation or linear progression. It is a work of extreme concision, with a very small vocabulary employed alongside a high frequency of nominal constructions (Solomon 1980). Confronted with sameness and stasis, the readermust grasp for meaning by searching the seemingly chaotic text for any discernible pattern. Consequently, fragments are cognitively re-arranged in an attempt to create a suitable narrative structure, forcing the reader to truly interact with the work and ultimately become aware of their own interpretive strategies. Further reĘection on the affect of Lessness quickly engenders a need to situate any analysis within a larger philosophical framework. Beckett has been widely discussed by a variety of contemporary Western thinkers: Adorno, Bataille, Blanchot, Deleuze and Badiou have all written large-scale works devoted to Beckett, while many other authors have connected Beckett to various post-structuralist thinkers including Der- rida and Foucault, as well as those already mentioned. An examination of the inĘu- 6 ence of Lessness and its connection to sans ĕn sans will be explored within this scope, speciĕcally through the investigation of several ideas put forth by Gilles Deleuze and Félix Guattari. 2.1.2 Gilles Deleuze and Félix Guattari GillesDeleuze belongs to the predominantly French school of post-structuralist thought. Post-structuralism emerged in the late twentieth-century as a response to phenomenol- ogy and structuralism. Phenomenology developed early in the twentieth-century, with thinkers such as Edmund Husserl and Martin Heidegger building a means to objectively study the structures of consciousness. Structuralism is generally associ- ated with the linguist Ferdinand de Saussure, and was an attempt to study linguis- tics—and later, culture and society—as a system where meaning is not inherent, but is instead derived from relationships with other components of its system. e post- structuralist movement responded to the perceived impossibility of both previous groups founding their knowledge on an objective, absolute ‘Truth’. Various thinkers took different approaches to this challenge: Michel Foucault disputed the view that certain social constraints can be considered ‘natural’ (e.g, sex- uality), showing them to instead be historical; and, Jacques Derrida exposed how language constrains ideas with the privileging of particular terms over their comple- ments (e.g., masculine over feminine). Deleuze also confronted generally accepted ways of thinking, preferring to view philosophy in terms of of its possibility, rather than as a means to categorize and deĕne. Deleuze’s “great problem and contribu- tion” (Colebrook 2002, 2) were the ideas of difference and becoming. ese are both encounters with identity and ontology. 2.1.2.1 Immanent Difference For Deleuze and other continentalƬ thinkers, ontology is the study of being, or per- haps more to the point, it is the question: “what is it for something to be?” (May 2005, 13) Attempts to describe ‘being’ (or ‘Being’) most oen lead to notions of tran- scendence, or ‘out-of-world’ existence (i.e., ‘Truth’, ‘God’, ‘Beauty’, etc.). Difference then becomes grounded upon identity (i.e., one object is different from another based ƬGenerally mainland European philosophers outside the tradition of analytical philosophy. 7 uponwhat it is, or what it represents). Deleuze reverses this relationship with a ‘plane of immanence’, built upon a univocity of being. Instead of allowing for the existence of external matter, “the substance of being is one and indivisible.” (May 2005, 34) Iden- tity results from the expression or actualisation of this Spinozian substance: identity becomes difference, or, difference is identity. In slightly more practical terms, this en- courages new ways of thinking that are not attempts to represent pre-existing truths, but are instead immanent creations of difference that transform experience itself. Deleuze encourages a capacity to think differently. To achieve this transformation, there needs to be a creation of “new concepts (through philosophy) and new percepts and affects (through art).” (Colebrook 2002, 25)rough the concept of immanent difference, Deleuze advocates an artistic prod- uct which will “shock, shatter and provoke experience.” (Colebrook 2002, 1) is creation is not an act of variation on an already extant object (i.e., a communica- tion of ‘Truth’ or ‘Beauty’), but is instead a pulling-apart of our existing opinions and ideas. ere are no stable ‘beings’, only Ęows of ‘becoming’. In Aousand Plateaus, Deleuze and his co-author, French psychoanalyst Félix Guattari, conceptualise the vehicle of this becoming as an abstract machine. 2.1.2.2 Abstract Machine Deleuze and Guattari use the idea of an abstract machine—an object with no sub- jectivity or intent—to describe “a production that is immanent... production for the sake of production itself ” (Colebrook 2002, 55). An abstract machine “is the vital mechanism of a world always emerging anew”, it “creates a new reality, constructs new ways of being” (Zepke 2005, 2). e abstract machine has no being itself, it only becomes, but as Zepke notes: “we should remind ourselves that we are [still] speak- ing of practical matters, of machines and their constructions.” (Zepke 2005, 2) An abstract machine is a dynamic process of deterritorialisation, or becoming something other. In Aousand Plateaus, Deleuze and Guattari present a model of a deterritorial- ising abstract machine with two distinct stages, called a double articulation (Deleuze and Guattari 1987, 40). Within it, a ‘ĕrst articulation’ collects similar units into potentialities: a ‘plane of consistency’; while a ‘second articulation’ establishes struc- 8 tures from actualisations of these possibilities: a ‘becoming’. Or, as James Bell writes: “[a] process involv[ing] both differentiation... and differenciation... consistent, ho- mogeneous layers are transformed (or actualised, as Deleuze oen says) into a new, identiĕable entity.” (Bell 2006, 213) rough this process, possibilities become con- crete. 2.1.2.3 Art and Philosophy It is not difficult to view Lessness as a double-articulation abstract machine. e ini- tial sentences and their themes constitute a consistent collection with a multiplicity of potential combinations via random ordering—a ĕrst articulation. e second ar- ticulation is the actualised ordering of the sentences by a speciĕc outcome of the chance process. Freeing his original text from its ĕxed order and viewpoint, Beckett produces a new affect which encourages the reader to think differently about their own concepts of time and engagement with Beckett’s text (see Section 2.1.1.2). e result is Art as abstract machine. 2.2 eoretical Foundations What formdoes a (musical) abstractmachine take? How can it be constructed? What does it do? e speciĕc articulations (i.e., difference and becoming) of the sans ĕn sans abstract machine will be explored in the next chapters. First, there needs to be a discussion of the theoretical underpinnings of its assemblage. 2.2.1 Algorithmic (Computer-Assisted) Composition Much of the subsequent discussion of sans ĕn sans presents the use of procedures and calculations that may be viewed as forms of algorithmic composition. While the ĕeld of algorithmic composition is usually associated with the use of mathematics, com- puters, and other electronic aids, it is at its base simply composition with formal sets of rules. Algorithmic procedures in music predate the computer era—Fuxian species counterpoint with its strict constraints is a prime example—with many composers employing mathematical systems to explore various compositional strategies (e.g., 9 the ubiquitous Fibonacci seriesƭ). It would be seen as suspect, however, to suggest that Western art-music com- posers of the ‘classical’ era employed algorithmic composition techniques, despite the clear procedural rules surrounding common-practice tonal harmony and formal organisation. As Luke Dubois notes in his dissertation, “where an extreme break be- tween a musical form and our prevailing musical perception has occurred... we are much more likely to construe that music as mathematically induced” (DuBois 2003, 2–3). e implicit artistic value-judgement of ‘mathematical’ music aside, it is clear that the term is most oen applied to music from the mid-1950s onward. Focusing on works composed in the last half-century, two distinct—but not nec- essarily mutually exclusive—applications of algorithmic music can be identiĕed: 1) the use of algorithms to generate music via human-machine interaction (i.e. auto- matic music composition); and, 2) the use of algorithms to generate musical ma- terials to be further manipulated, incorporated and reĕned by the composer (i.e. computer-assisted composition). Martin Supper further divides this latter descrip- tion into “score synthesis (the computer-aided working out of a composition...)”, and “sound synthesis (the computer-aided working out of a synthetic sound...)” (Supper 2001, 48). e use of algorithmic composition in sans ĕn sans is best categorised as score synthesisƮ. Important considerations for the selection or creation of a generative algorithm include: 1) which algorithms produce abstract structures or systems with qualities sufficiently interesting or useful enough to be applied to the compositional process?; and, 2)whichmeans can be used to successfullymap these abstract notions tomusical parameters? For sans ĕn sans, the answer to the ĕrst question lies within the extra- musical disciplines of chaos theory, fractal geometry and automata theory. ƭExamples of this sequence as applied to musical form—oen through the use of the golden mean, or '—include Bartok’s Music for Strings, Percussion and Celesta and ‘ReĘets dans l’eau’, from Debussy’s Images. Ʈe speciĕc computer-assistance tool utilised for sans ĕn sans is Ircam’s OpenMusic soware, a graphical environment based upon the Common Lisp programming language (Agon et al. 2008; Bresson et al. 2005). is extensible environment allows users to visually interact with musical and non-musical data structures via various included and user-deĕned functions. OpenMusic provides composers a platform to practically represent, manipulate, and experiment with otherwise restrictively complex and time-consuming calculations and logical structures. 10 2.2.1.1 Fractals Fractals and chaos provide a useful environment formathematicallymodelling struc- tures of natural phenomena⁴. Music has long been associated with—and oen jus- tiĕed by—relationships to the natural world (i.e., Pythagoras and his analysis of vi- brating strings, the golden ratio, etc.). It is generally accepted that some form of consistent structural unity—be it Fuxian counterpoint, common-practice tonality, dodecaphony, total serialism, etc.—provides the basis for an aesthetically-pleasing musical work. Fractals supply ameans to explore new and complex dynamic-systems for such use. edeĕning characteristic—and source of interest—of a fractal is expressed through the concept of self-similarity, whereby the recursive repetition of a process results in the shape of the whole as composed of same- or similarly-shaped parts. A fractal has structure on multiple ‘sizes’, if considered visually. e Mandelbrot set is a popular example, named aer the mathematician who ĕrst deĕned the term fractal in 1975 (see Figure 2.1). Each numbered area is self-similar to the others, at different size scales⁵. e production process for fractal structures introduces the idea of a feedback machine (Peitgen et al. 1992, 17): an abstract machine that processes an input into an output that is subsequently fed back into the system during the next discrete itera- tion (see Figure 2.2). It is important to note that while attention is most oen focused on the ĕnal product of the machine, the intermediate stages are deserving of equal interest. ese steps are more easily conceptualised via the application of a particu- lar type of automata⁶: a parallel string-substitution production system proposed by Dutch botanist Aristid Lindenmayer. 2.2.1.2 Lindenmayer Systems Lindenmayer developedhis theoretical framework—knownasL-systems—as ameans to study natural growth processes, beginning with simple multi-cellular organisms ⁴A an excellent starting point to survey the ĕeld of chaos theory and fractal geometry is Peitgen et al. (1992). ⁵It should be noted that the Mandelbrot set is not purely self-similar, as various scale versions differ slightly ⁶Automata are theoretical state-machines that recognise formal languages, and are most oen en- countered in computer-science roles such as compiler design. 11 Figure 2.1: AMandelbrot Set processing unitIN feedback line OUT Figure 2.2: A Feedback Machine before formalising a description of plant growth (Lindenmayer 1968; Prusinkiewicz and Lindenmayer 1990). is framework consists of a feedback machine that trans- forms a given input according to a set of production (string-rewriting) rules. ese production rules are applied concurrently to all symbols within the input string. e connection to fractal production is immediately apparent, and the recursive nature of L-systemsmake the process very suited to a computer implementation. L-systems are already beginning to ĕnd use amongst composers (DuBois 2003; Manousakis 2006; Supper 2001), and when combined with fractals they provide an excellent means to explore ‘natural’ developmental processes. 12 L-systems are formally deĕned by an alphabet, or set of symbols containing ele- ments that can be replaced (variables, represented by V ); an initial system state, or axiom (represented by !); and, a set of production rules deĕning the way variables are to be rewritten with new sets of symbols. e actual symbols used are irrelevant to the functioning of the system, but will take on a signiĕcance during subsequent interpretation (see Section 2.2.1.3). A sample L-system can be represented: Alphabet: V : AB Production rules: A! AB B ! A Axiom ! : B which produces for each step n: n = 0: B n = 1: A n = 2: AB n = 3: ABA n = 4: ABAAB n = 5: ABAABABA etc... is particular example, taken fromPrusinkiewicz andLindenmayer (1990), is known as a context-free L-system as its productions are in the form predecessor! successor. It is also considered to be deterministic, as each symbol appears only once at the le of a production rule (i.e., there is no ambiguity about how to replace the successor). Various other categories of L-systems are possible; a comprehensive summary may be found in Manousakis (2006, 21–31). e resulting sequences of strings from an L-system evaluation provide a wealth of self-similar data, but without context. A simple and commonly-acceptedmeans of representing these L-systemoutput stringswas selected byPrusinkiewicz (Prusinkiewicz 1986), which produces a visual interpretation through the use of turtle graphics. 13 Table 2.2: Available Turtle Graphics Commands Command Description F move forward by a ĕxed step length l and draw a line f move forward as above for F but do not draw the line + turn le (counterclockwise)by a ĕxed angle   turn right (clockwise) by a ĕxed angle  2.2.1.3 Turtle Graphics Developed by Seymour Papert at MIT for inclusion with the LOGO programming language, turtle graphics is now a common term for a method of drawing vector graphics. e ‘turtle’ is deĕned as a two-dimensional—although multiple dimen- sions are possible—automaton whose state consists of a current position (x; y), and a current heading (). is is written as a triple (x; y; ). e turtle is able to move forward and turn by sequentially interpreting a series of instructions, drawn from Table 2.2. By substituting these new symbols into an L-system deĕnition, it becomes very easy to visually construct fractals. As an example, consider a Koch curve. Named aer the Swedish mathematician who introduced it in 1904, it is oen regarded as a ‘classical’ fractal. It can be con- structed by beginning with a straight line, which is then divided into three equal parts. Next, the middle portion of this division is replaced by an equilateral trian- gle with no base. is step is then repeated multiple times for each of the resulting line segments (see Figure 2.3). e process can be represented with the following L-system: Alphabet: V : F + Production rules: F ! F + F F + F +! +  !  Axiom ! : F Parameter  = 60 degrees which produces for each step n: 14 Step 4 Step 0 Step 1 Step 2 Step 3 Figure 2.3: First Stages of a Koch Curve n = 0: F n = 1: F + F F + F n = 2: F + F F + F + F + F F + F F + F F + F+ F + F F + F etc... By interpreting these strings with the commands from Table 2.2, the visual output is nearly identical to Figure 2.3, although issues of scale are ignored (i.e., to accurately reproduce the shown graphic, the ĕxed lengthF would need to reduce proportionally aer each iteration). It also useful to note that the resultant strings quickly become very large, and the use of a computer is essential for the efficient exploration of this and other fractals. 2.2.1.4 Musical Interpretation e ĕnal stage in this process is a musical interpretation of these generated sym- bols. To be successful, this step requires an effective spatial mapping strategy. Ini- tial attempts were simple connections between the graphical output and musical pa- 15 rameters such as pitch and duration (Prusinkiewicz 1986), while subsequent sys- tems increase in complexity to address timbre, polyphony and ultimately, real-time generative routines (Chapel 2003; DuBois 2003; Manousakis 2006). Dubois sug- gests discarding the visual stage completely, advocating the mapping of an expanded symbol-vocabulary directly to discrete musical events (DuBois 2003, 28–32). is approach is an extension of the systemwherebymultiple—if not all—musical param- eters are controlled by a single L-system. For sans ĕn sans, I limit my use of L-systems to an exploration of harmonic spectra, and as such, require a means by which the two-dimensional turtle graphics output can be mapped to musical pitch classes. is mapping strategy is best explained within the context of a compositional approach known as spectralism. 2.2.2 Spectralism Julian Anderson’s article, A Provisional History of Spectralism, begins by noting the disparate background of the various ‘spectral’ composers, their lack of conscious par- ticipation as a coherent group, and the tendency to somewhat simplisticly reduce their common connections to the obvious use and manipulation of sound spectra: “ere is no real school of spectral composers; rather, certain fundamental problems associated with the state of contemporary music, since at least 1965, have repeat- edly provoked composers... into searching out some common solutions.” (Anderson 2000, 7) Attempts have been made to outline these ‘common solutions’ as a vari- ety of concepts and techniques central to the spectral movement (Fineberg 2000; Moscovich 1997; Wannamaker 2008)—those most directly applicable to sans ĕn sans are: 1) the basic notion of deriving pitch aggregates from spectral models; 2) the investigation of continuous state transformations; and, 3) the exploration of sonic experience beyond semantic meaning. e latter two items fall within the previous theoretical discussion of theDeleuzian concept of art as abstract machine (see Section 2.1.2), equating to ideas of becoming and difference, respectively. e remainder of this section will investigate the ĕnal item: sound spectra as a harmonic resource and a domain rich for potential use in L-system interpretation. 16 2.2.2.1 Spectral Harmonic Structures For the European-centric spectral regime—most commonly associated with com- posers such as Grisey, Murail, and Harvey; and attached to the ongoing research at the Institut de Recherche et Coordination Acoustique/Musique (Ircam)—harmonic and timbral structures are built upon musical frequencies. Pitches result from con- versions of sets of frequencies that have been derived via spectral analysis of a partic- ular sound sample and possible manipulation through various synthesis techniques (e.g., frequencymodulation, additive synthesis, subtractive synthesis, etc.), techniques adopted from use in electroacoustic music. Parallel to these developments in Europe, American composer and theorist James Tenney was also intensely occupied with utilising harmonic spectra as a structural resource⁷. Of prime importance to Tenney’s compositional procedures is the explo- ration of the harmonic (or overtone) series, deĕned as a set of simple periodic waves (partials) that are whole number multiples of some fundamental frequency. His ef- forts resulted in ameans to generate ‘pitch crystals’ in a lattice-likemulti-dimensional harmonic space. 2.2.2.2 Harmonic Space Tenney’s concept of harmonic space—which is extrapolated from Cage’s writings on harmony—is designed to express perceptions of pitch relationships beyond a single- dimensional continuum running from low to high. Tenney uses the phenomenon of octave equivalence to illustrate a frequency relationship that cannot be easily explained by simply applying ‘higher’ or ‘lower’ descriptions (Tenney 1983, 21). Within this multi-dimensional space of pitch perception, pitches are “represented by points... and each is labelled according to its frequency ratio with respect to some reference pitch” (Tenney 1983, 22). Materially and conceptually related to the overtone series, these whole-number frequency ratios represent musical intervals (i.e., a pitch one octave above a reference has the frequency ratio 2/1, a pitch a perfect ĕh above a reference has the frequency ration 3/2, etc.). In order to transform a ratio into a co-ordinate or ‘point’ within harmonic space, Tenney makes use of a fundamental mathematical theorem: any integer can be represented by a unique product of prime numbers. is ⁷For more on Tenney’s ‘spectralist’ works, see Wannamaker (2008). 17 product is called its prime factorization. Each musical interval can thus be represented within harmonic space by the prime number factor exponents of its frequency ratio. For example, the interval of a ĕh, with its ratio of 3/2, would be encoded as a pitch-point of (1; 1), a co-ordinate obtained by multiplying 21 and 31. Harmonic space can be expanded into multi- ple dimensions corresponding to the number of prime number factors (i.e., 2, 3, 5, 7, 11, 13, etc.) required to specify particular frequency ratios. Each additional di- mension allows for the representation of a larger collection of ratios. For example, using only the ‘Pythagorean’ intervals of unisons, perfect ĕhs, perfect fourths and octaves (ratios 1/1, 3/2, 4/3 and 2/1, respectively), a two-dimensional harmonic space is sufficient to deĕne its members (see Table 2.3). Adding the remaining Riemann just-intervals of thirds and sixths requires a new dimension, corresponding to the next prime number in the series, which is ĕve. is new construct can be referred to as 5-limit harmonic space, referencing the highest utilised prime factor. Similarly, the earlier Pythagorean intervals exist within a 3-limit harmonic space. More com- plex integer ratios can be added, and further dimensions explored, resulting in an ex- tended just-intonation area of 7-, 11- and 13-limit harmonic space (Hasegawa 2006), and beyond, to 23- and even 31-limit harmonic space (Sabat 2008a,b). Tenney does note that the concept of a tolerance range does constrain the extension into unlimited dimensions of harmonic space. As such, “at some level of scale-complexity, intervals whose frequency ratios involve a higher-order prime factor will be indistinguishable from similar intervals characterized by simpler frequency ratios, and the prime fac- tors in these simpler ratios will deĕne the dimensionality of harmonic space in the most general sense” (Tenney 1983, 23). Tenney and Sabat outline a last reĕnement to harmonic space: pitch-height con- strained harmonic space (Sabat 2008b, 61), or pitch-class projection space (Tenney 1983, 25). is space ‘collapses’ the 2-dimension by using an octave-equivalence principle. at is, as 2-limit harmonic space is only capable of representing octaves or unisons, the 2-dimension is not required to uniquely identify intervals less than one octave. It is therefore sufficient to write any octave-related ratio in its simplest form. For example, a just major third (ratio 5/4) is encoded with the pitch-point of (2; 0; 1)⁸ in 5-limit harmonic space, while a just major tenth (ratio 5/2) would ⁸is co-ordinate is obtained by multiplying 22, 30 and 51 18 Table 2.3: Pythagorean Intervals in 2-limit Harmonic Space Interval Name Co-ordinates Limit Ratio unison (0,0) 2- 1/1 ĕh (-1,1) 2- 3/2 fourth (2,-1) 2- 4/3 octave (1,0) 2- 2/1 be encoded with the pitch-point of (1; 0; 1)⁹. However, in pitch-class projection space, the 2-dimension can be ignored and both of these intervals—in addition to any other octave-related distance—can simply be referred to by the pitch-point (0; 1). is principle effectively allows a representation of the primary ratios of triadic/tonal music (5-limit harmonic space) within a two-dimensional co-ordinate system. As noted earlier, the concept of harmonic space was developed to explore ex- tended pitch relationships. Tenney’s speciĕc use of this theory stems from his desire to achieve harmonic coherence via the “use of relatively compact, connected sets of points... [where] every element is adjacent to at least one other element in the set.” (Tenney 2008, 47) e connection between any two points in harmonic space is conceptually quantiĕed as harmonic distance. Tenney deĕnes this measurement to be “proportional to the sum of the distances traversed on a shortest path connecting [the two points]”, and is calculated using a logarithmic function: log(a) + log(b) = log(ab), where fa and fb are the fundamental frequencies of the two tones, a = fa/gcd(fa; fb), b = fb/gcd(fa; fb), and a  b (Tenney 1983, 24). Consequently, his ‘crystal growth’ algorithm chooses sets of points “in some n-dimensional har- monic space, under the condition that each new point must have the smallest possi- ble sum of harmonic distances to all points already in the set.” (Tenney 2008, 47)is algorithm has subsequently been reĕned and expanded byMarc Sabat(Sabat 2008b). While Tenney’s algorithm and its output are certainly of interest, it is the larger framework of harmonic space that holds themost appeal formy usewith sans ĕn sans. Mapping graphical L-system output to this theoretical model appears to provide a wealth of compositional potential. e speciĕc application of this connection to sans ⁹is co-ordinate is obtained by multiplying 21, 30 and 51 19 ĕn sans will be discussed in the next chapter. e next and ĕnal section will explore a few relevant ideas ofmusical time. 2.2.3 Musical Time e relationship between time and music is a fascinating one. Being a temporally perceived art-form, discussions oen privilegemusic and its ability to represent time. is type of thinking quickly leads to “the realisation that certain fundamental meth- ods for understanding musical phenomena can be formulated—if at all—only in philosophico-aesthetic terms” (Klein 2004, 133), and that “without doubt, the ques- tion of time is one of these [phenomena]” (Klein 2004, 134). Klein’s essay provides an excellent introduction to various philosophical thoughts on musical time. For sans ĕn sans, a large-scale dialogue with musical time can best be viewed in terms of Jonathan Kramer’s deĕnitions ofmultiply-directed linear time, and, to a lesser degree, moment time/form (Kramer 1988); while more localised rhythmic explo- rations have been inspired by composer Brian Ferneyhough (Ferneyhough 1995a,b). Each of these categories will be explored in turn. 2.2.3.1 Non-linear Musical Form Traditional musical time can be seen to be linear: there are beginnings, endings and middles, and the progress of works reĘecting this type of time demonstrate a “temporal continuum created by a succession [of] events in which earlier events im- ply later ones and later ones are consequences of earlier ones.” (Kramer 1988, 20) e fragmentation, re-ordering and de-construction of linear time results in what Kramer calls multiply-directed linear time: a multi-dimensional work where “some processes... move towards one ormore goals yet the goals are placed elsewhere than at the ends of the processes.” (Kramer 1988, 46) Finally, moment time/form represents a complete discontinuity in the musical process and a destruction of the beginning- middle-end logic of the dramatic curve. Initially formulated by Stockhausen in the early 1960s, the abstract aesthetic con- cept of moment time is clearly exhibited in Beckett’s Lessness. e prose inhabits a world of timelessness, describing only Ęeeting moments; while the chance construc- tion techniques employed by Beckett bring further fragmentation and disorder to 20 the work. Nevertheless, this resulting arbitrary ordering cannot fully disguise the relations which exist between the sentences (discussed earlier in Section 2.1.1.1, see Table 2.1). It is within these relationships that moment time and multiply-directed linear time meet. Many of the construction techniques and linkages between the generative structure of Chapter 3 and the resulting piece described in Chapter 4 are attempts to explore the consequences of these two theories of musical time. How- ever, in order for these formal relationships to exist there was a need to apply some level of a directed connection to localised rhythms. 2.2.3.2 Duration and Rhythm Ferneyhough’s work is notable for his complex confrontation with contemporary compositional problems related to the musical demarcation of time. His scores are precisely notated examples of extreme virtuosity. A proliĕc writer as well, Ferney- hough notes: “the issue of rhythmic structuring in contemporary music has long remained vexed” (Ferneyhough 1995a, 51). Further, “there is arguably little point in retaining regular iterative rhythmic structures in a stylistic context devoid of tonal (or tonal-type) harmonic patterns.” (Ferneyhough 1995a, 51) Or, as Gérard Grisey notes in his article onmusical time: “Without a reference pulse we are no longer talk- ing of rhythm but of durations... perceived quantitatively by [their] relationship to preceding and successive durations.” (Grisey 1987, 240) Ferneyhough’s solution is to create rhythmic andmetric structures based on ratio relationships. A straight-forward example, taken from Ferneyhough (1995b, 54), is to build two simple numerical sequences: A : (3; 4; 5); and, B : (4; 5; 6; 7). Com- bining them to form simple ratios results in a new sequence: C : (3 : 4; 4 : 5; 5 : 6; 3 : 7; 4 : 4; 5 : 5, etc.). e unequal lengths of both sequences provides a further potential point of interest. Figure 2.4 demonstrates a possiblemusical representation. For sans ĕn sans, a connection with the ratios expressed in harmonic space suggest a parallel extension of pitch-relationships into the rhythmic realm. Together, these relationships provide a level of goal-direction to the musical material, and support a future reorganisation of these linear lines into the realm of multiply-directed linear time. is procedure can be further combined with a process Ferneyhough refers to 21  85 83 5:4 6:5 7:6 8483 84  Figure 2.4: Rhythmic Ratio Sequence 2 1 3 5 4 5 2 3 1 4 4 2 3 5 1 1 2 3 5 4 1 2 3 4 5 Figure 2.5: Example of a Random Funnel series as a random funnel: a cyclic, linear random procedure whereby “a ĕxed, unordered number series is randomly permuted until it reaches a contextually pre-determined, ĕnal destination” with the caveat that “if a number arrives at its destination before the last stage it simply repeats, or remains in place.” (Feller 2004, 179) Again, a simple example can be used to illustrate the procedure. Given a sequence: A : (1; 2; 3; 4; 5), a possible random funnel process output can be found in Figure 2.5 (emphasised numbers indicate those which have reached their ĕnal destination). More elaborate versions of these procedures will govern much of the surface-level metric activity of sans ĕn sans (see Section 3.2). A ĕnal theoretical concept of Ferneyhough’s that will be evidenced in sans ĕn sans is interruptive polyphony, or interference form (Feller 2002; Ferneyhough 1995b). Clearly related to multiply-directed linear time, it involves the convergence of two or more independent rhythmic processes (usually notated on separate staves) into a sin- gle stream. Employed explicitly in Ferneyhough’s solo instrument works—although also evident in ‘soloistic’ works such as Terrain—the “monophonic capability of the instrument comes into continual conĘict with the highly polyphonic nature of the superincumbent materials” (Ferneyhough 1995b, 48). In practical terms, materials or events from one process are continually being interrupted by those from the oth- ers, resulting in subverted durations and ‘broken’ gestures. Figure 2.6 demonstrates a two-part interruptive polyphony for solo violin active during the ĕrst fewmeasures 22 Figure 2.6: Measures 1–4 of Ferneyhough’s Terrain of Terrain (Ferneyhough 1993). Its use in sans ĕn sans can be observed at the formal level (see Section 4.1.1). 2.3 Summary is chapter has covered a diverse array ofmaterial. By extrapolating severalDeleuzian philosophico-aesthetic ideals from Beckett’s Lessness, and exploring various algorith- mic functions (i.e., pitch and rhythmic derivations from harmonic space) as produc- tion means, the theoretical pieces for sans ĕn sans have been arranged. 23 Chapter 3 Pre-compositional Work Various pre-compositional decisions were made prior to writing sans ĕn sans. As is usual for my work, this stage exhaustively details many musical parameters, in- cluding rhythmic and harmonic resources as well as large-scale form. For sans ĕn sans, this work constituted a concrete implementation of the various theories and philosophico-aesthetic concerns outlined in Chapter 2, building a collection of pitch, form and durational materials. ese components then guided the composition of a generative structure. 3.1 Pitch Material eharmonic resources of sans ĕn sans are akin to theDeleuzian plane-of-consistency: a homogeneous collection of materials resulting from a ĕltration-systemwhich actu- alises pitch-ĕelds from a common source, analogous to the process of sedimentation described in Deleuze and Guattari (1987, 41). Overlooking the extra-musical inĘu- ence, this approach is similar to one employed by Ferneyhough. He has described his use of serialism for pitch selection “as being something like a sieve, a set of ĕlter systems, which I forcibly impose on the basic mass of initially unformed or unartic- ulated [elements].” (Boros and Toop 1995, 227) For sans ĕn sans, a pitch sequence was generated via the mapping of an L-system output to 5-limit harmonic space (i.e., interval ratios which require the prime expo- nents of 2, 3 and 5). is output was then delimited into chords through a process of circular range-‘wrapping’. In order to accomplish this production, a custom Open- 24 Music library was authored. 3.1.1 omlsystem: An OpenMusic library As discussed in Section 2.2.1, the various calculations and products of an L-system quickly become cumbersome to employ without the assistance of a computer. e OpenMusic system (Agon et al. 2008; Bresson et al. 2005) provides an excellent working environment for this task, and it has the additional feature of providing tools to translate abstract output to musical entities. However, as OpenMusic does not provide higher-level functions to work directly with L-system concepts, it was necessary to create a custom user-library. Called omlsystem, this library provides an implementation of the mathematical theories discussed in Section 2.2.1.2: 1) a tur- tle graphics interpretive module; 2) a processing engine that will evaluate a given L-system; and, 3) a mapping system to translate the turtle graphics output to pitch values via harmonic space co-ordinates. See Appendix A for a full source code listing of the library. 3.1.1.1 Turtle Graphics Interpretation e basic data-object of the omlsystem library is the turtle (see Section 2.2.1.3 for a deĕnition). It keeps track of its own position, and responds to functions that correlate to the instructions given in Table 2.2Ƭ. e turtle’s subsequent state aer evaluating a functionF ,+, or is calculated with simple trigonometric functions (see Table 3.1). Here, l represents the value the turtle moves forward by (the default is 1.0), and  is the angle by which the turtle turns le or right (the default is 90). A polar co- ordinate system is used (i.e., 0 is facing right, or the 3 o’clock position), and the initial starting point of the turtle is the state (0; 0; 0). e turtle graphics module was designed to be of general-purpose use, and is not strictly tied to the evaluation of L-systems. However, one particular requirement be- came apparent during the mapping phase: for any meaningful location in harmonic space, the (x; y) co-ordinates must remain integers. is resulted in a speciĕc mode of evaluation for the turtle, where the real number co-ordinates are rounded to inte- ger values by a function that essentially ‘locks’ the turtle’s rotation angle to multiples Ƭe omlsystem library did not implement f, as it was not utilised for sans ĕn sans. 25 Table 3.1: Turtle Graphic State Evaluation Command State (x; y; ) Evaluation F (x+ l cos; y + l sin; ) + (x; y; + )  (x; y;  ) of 45. Aswell, this functionmodiĕes the length l that the turtlemoves forwardwhen its heading is not parallel to either the x- or y-axis such that its ĕnal location can be represented by integer values. e remaining elements of the turtle graphics module include implementations of two comparison functions: one that performs a standard ‘equals’ evaluation, and a second that determines if two turtle objects occupy the same (x; y) position (re- gardless of heading). As well, helper functions exist to read the (x; y) position of a turtle object or list of turtle objects. 3.1.1.2 L-system Processing Engine Rather than implementing a speciĕc L-system as a single procedure (as is most com- mon), omlsystemprovides a graphicalmeans to evaluate a variety of possible L-systems. A single end-user function takes as input an axiom and a paired-list of production rules, each made up of references to the turtle command functions described in Ta- ble 3.1. ere are two outputs from this function: a turtle object corresponding to the ĕnal position of the evaluation, and a list of turtle objects that equate to the positions the turtle has passed through during evaluation (i.e., each position of the turtle aer processing an F function). e result is an environment that is easily correlatable to the form of L-system deĕnitions encountered in Section 2.2.1.2. Formally, the L-system processing engine performs two procedures: 1) given a listL of functions, and a list P of paired-production rules (i.e., string replacements), apply the substitutions in P to L; and, 2) given a list L of functions (i.e., F ,+ or), and a turtle-objectX , apply the functions in L toX . ese functions can be consid- ered a substitution phase and an evaluation phase, respectively. e engine functions by recursively performing these phases in sequence fornnumber of stages, beginning 26 with a substitutionƭ. As an example, lets return to the Koch curve from Figure 2.3. e corresponding omlsystem representation can be seen in Figure 3.1. e L-system evaluation engine takes three inputs: 1) an integer detailing the recursion depth; 2) the axiom (repre- sented as a list of turtle objects); and, 3) a paired-list of production rules composed of a turtle object signifying the string to be replaced and a list of turtle objects repre- senting the actual substitution string. e output is a list of turtle objects, which are then ready to be translated into a list of speciĕc pitches. 3.1.1.3 Harmonic Space Mapping is translation process makes up the ĕnal component of the omlsystem library, and maps a turtle’s position onto harmonic space. Since the turtlemodule operates within a relatively simple two-dimensional space, it may seem that the omlsystem library is constrained to a 3-limit harmonic space (i.e., a harmonic space that requires only two prime factors to specify its location). However, by employing pitch-class pro- jection space and its removal of the 2-dimension (see Section 2.2.2.2), the inter- vallic possibilities of the system are expanded into 5-limit harmonic space—albeit normalised to include only intervals less than one octave—while still allowing for a two-dimensional representation. Table 3.2 provides all available intervals and their corresponding location in 5-limit harmonic space. Both the ordering and naming of these intervals are taken from Sabat (2008b, 58–61). Bymapping these values to two- dimensional space (see Figure 3.2), another interesting quality is made apparent: the resulting structure is not square, but rather lattice-like, the ‘crystal’ end-product of Tenney’s growth algorithm. A lookup-table provides the translation between a turtle’s co-ordinates and an interval value in cents (i.e., a unit of pitch measurement where an octave is divided into 1200 equal segments). is level of granularity allows for a representation of the micro-tonal intervals involved in multi-dimensional harmonic space. However, while the system is capable of producing a higher degree of accuracy, a quarter-tone resolution was chosen for sans ĕn sans due to practical performance considerations. To demonstrate this translation process, the omlsystem version of a Koch curve ƭBy starting with a substitution, the axiom is not included in the evaluation phase, and is therefore not part of the engine’s output. 27 Figure 3.1: An omlsystem Koch Curve 28 Table 3.2: Available Intervals in 5-limit Harmonic Space Interval Name Co-ordinates Limit Ratio Cents unison (0,0) 2- 1/1 0 pythagorean ĕh (1,0) 3- 3/2 702 pythagorean fourth (-1,0) 3- 4/3 498 major wholetone (2,0) 3- 9/8 204 ptolemaic major third (0,1) 5- 5/4 386 ptolemaic major seventh (1,1) 5- 15/8 1088 ptolemaic major sixth (-1,1) 5- 5/3 884 ptolemaic tritone (2,1) 5- 45/32 590 ptolemaic minor third (1,-1) 5- 6/5 316 ptolemaic minor sixth (0,-1) 5- 8/5 814 ptolemaic minor seventh (2,-1) 5- 9/5 1018 major diatonic semitone (-1,-1) 5- 16/15 112 pythagorean minor seventh (-2,0) 3- 16/9 996 pythagorean major sixth (3,0) 3- 27/16 906 minor wholetone (-2,1) 5- 10/9 182 ptolemaic diminished ĕh (-2,-1) 5- 64/45 610 pythagorean minor third (-3,0) 5- 32/27 294 ptolemaic augmented ĕh (0,2) 5- 25/16 773 ptolemaic diminished fourth (0,-2) 5- 32/25 427 minor chromatic semitone (-1,2) 5- 25/24 71 ptolemaic augmented second (1,2) 5- 75/64 275 large diminished octave (1,-2) 5- 48/25 1129 ptolemaic diminished seventh (-1,-2) 5- 128/75 925 ptolemaic wide fourth (3,-1) 5- 27/20 520 major limma (3,1) 5- 135/128 92 ptolemaic narrow ĕh (-3,1) 5- 40/27 680 (-3,-1) 5- 256/135 1108 pythagorean major third (4,0) 3- 81/64 408 comma-diminished octave (-4,0) 3- 128/81 792 Rameau’s tritone (-2,2) 5- 25/18 569 ptolemaic augmented sixth (2,2) 5- 225/128 976 Rameau’s false ĕh (2,-2) 5- 36/25 631 ptolemaic diminished third (-2,-2) 5- 256/225 223 29 25/18 25/24 25/16 75/64 225/128 40/27 10/9 5/3 5/4 15/8 45/32 135/128 128/81 32/27 16/9 4/3 1/1 3/2 9/8 27/16 81/64 256/135 64/45 16/15 8/5 6/5 9/5 27/20 256/225 128/75 32/25 48/25 36/25 Figure 3.2: ‘Crystal’ Structure of 5-limit Harmonic Space  Figure 3.3: Musical Mapping of a ĕrst-stage Koch Curve in Figure 3.1 will produce a ĕrst-stage output of ((1; 0); (1; 1); (1; 0); (2; 0)) in har- monic space co-ordinateswith a starting point of (0; 0), corresponding to the instruc- tionsF +F F +F . Only four co-ordinates are output as the non-movement in- structions (i.e.,+;) are not recorded. e translated intervals are (702; 1088; 702; 204), or by name, (pythagorean ĕh, ptolemaic major seventh, pythagorean ĕh, major who- letone). e musical mapping, with middle-C as the base tone and rounding to the nearest quarter-tone, is shown in Figure 3.3. One ĕnal component of the omlsystem library is a customisable constraint func- tion to keep the output co-ordinates within 5-limit harmonic space. Once a co- ordinate extends beyond the lattice, for example (5; 0), the out-of-bounds value is ‘wrapped’ as though the lattice were placed on the surface of a sphere (i.e., in a man- ner similar to a two-dimensional representation of a map of Earth). is allows for complex and cumulative explorations of 5-limit harmonic space. 3.1.2 endlessness Aer experimenting with a variety of classical fractals and their musical mappings, I selected a randomised quadraticKoch curve to serve as the basis for the pitch-generation model of sans ĕn sans. A more advanced version of the Koch curve discussed earlier (see Figure 2.3), it provides a suitably varied and non-trivial exploration of 5-limit 30 harmonic space without excessive computational complexity. e curve can be rep- resented with the following L-system: Alphabet: V : F + Production rules: F 50%! F + F  F  FF + F + F  F F 50%! F  F + F + FF  F  F + F +! +  !  Axiom ! : F Parameter  = 90 degrees While still context-free, this L-system is non-deterministic, as it has an element of ran- dom choice. e decision of which string substitution for F to apply at each point in the process is determined by a stochastic process, with a 50% probability that the ĕrst choice will be selected and a 50% probability that the second choice will be se- lected. As a result, the output from this system will be different each time it is run. e omlsystem patch for this system is shown in Figure 3.4. Owing to its larger string substitution length, the size of the output of this system grows very quickly. Aer the ĕrst stage only eight intervals are generated, however, by the completion of the fourth stage there are over four-thousand. e ‘endless’ nature of this sequence is clearly evident. In order to aggregate these intervals into usable pitch-ĕelds, an algorithm was created that ‘wraps’ chords built on these intervals at an upper- and lower-limit based upon the traditional guitar range (i.e., low open string E2 to 12th-fret top string E5, without the scordatura discussed in Section 3.3). Once a pitch exceeds the upper limit, it is transposed down the necessary octaves to ‘ĕt’ into the lower register of the guitar. It is also at this point that a new chord begins. Aer applying this procedure—andbeginningwithE2 raised by a quarter-tone—the intervals of the fourth-stage are accumulated into 577 chords. It is from this collec- tion that I withdrew the harmonic material for sans ĕn sans. Once the various rhyth- mic and formal decisions of the next two sections were implemented, the harmonic language of sans ĕn sans constituted the ĕrst 152 chords of this selection. See Ap- pendix B for the complete chord sequence. 31 Figure 3.4: An omlsystem Randomised Quadratic Koch Curve 32 (1; 1; 3; 2; 4; 3; 9; 8; 5; 4; 15; 8; 5; 3) Figure 3.5: Basic Durational Sequence in sans ĕn sans 3.2 Duration Beyond common pitch relationships, the generativematerials of sans ĕn sans also em- ploy homogeneous treatments of duration. Metrical consistency of the originating structure is maintained by way of a cyclic repetition of a durational sequence derived from the ratio-relationships of harmonic space. Following the order provided byTen- ney’s algorithm (see Table 3.2), a basic sequence is assembled (see Figure 3.5). en, a base rhythmic value of an eighth-note is applied to this sequence, creating a fourteen- bar unit: (1/8; 1/8; 3/8; 2/8; 4/8; 3/8; 9/8; 4/4; 5/8; 2/4; 7+8/8; 5/8; 3/8). e end result is a structure for potential musical ‘sentences’, each made up of exactly 71 eighth-note pulses. In addition to the rhythmic-Ęow of each line, the main surface-level activity of sans ĕn sans is also governed by a variant of this durational sequence. By splitting the ratios of Table 3.2, two sequences are deĕned. A random funnel algorithm (see Section 2.2.3.2) is then applied until the original ordering is obtained. e resulting sequences, shown in Table 3.3, are combined with the rhythmic ‘sentence’ structure to create a grid of various rhythmic polyphonies. As an exam- ple, Figure 3.6(a) displays the rhythmic pulses of the ĕrst four measures of iteration I. Each measure is subdivided via an application of the (sometimes simpliĕed) ran- dom funnel sequence. Comparable rhythmic-skeletons were created for each of the remaining groups. ese were then further processed by accumulating beats either within or across measures based upon a further numerical sequence. For example, Figure 3.6(b) shows an accumulation process where the subdivisions of Figure 3.6(a) are grouped into longer rhythmic pulses starting from the third position of the origi- nal ordering of the basic durational sequence (i.e., 3, 2, 4, 3, etc.). Figure 3.6(c) shows the same procedure applied within individual measures only. ese various means of partitioning the initial subdivided structure using simi- lar numerical sequences creates a sense of ‘textural time’, to use Ferneyhough’s ter- minology. “Just as pitch-partitioning operations allow pitch-space to be traversed in many subtly nuanced ways, so different ‘textural-times’ can be evoked by distributing 33 Table 3.3: Random Funnel Sequence in sans ĕn sans Iteration Random Funnel Sequence I 8 16 5 3 4 6 9 27 1 15 3 16 5 45 8 3 3 5 5 5 2 32 5 16 8 1 4 9 II 1 15 8 9 5 6 1 27 9 3 45 16 4 16 3 8 3 8 4 5 1 32 5 2 1 1 1 9 III 1 8 8 9 5 15 1 27 9 3 4 16 9 6 1 1 3 8 4 16 3 32 1 5 9 3 8 5 IV 1 3 16 9 5 15 5 9 3 8 4 16 9 27 1 1 3 8 4 16 3 32 5 5 9 15 1 8 V 1 9 1 9 5 3 5 45 6 8 1 16 4 27 1 2 1 8 4 1 3 32 5 5 1 15 9 8 VI 1 3 4 9 5 3 5 45 6 8 1 16 1 27 1 2 3 8 4 1 3 32 5 5 2 15 1 16 VII 1 3 4 9 5 15 5 45 6 8 9 16 16 27 1 2 3 8 4 8 3 32 5 5 5 15 9 16 available impulses according to hierarchically-preferential schemata” (Ferneyhough 1995a, 58). In sans ĕn sans, I have attempted to build an internal consistency by ex- pressing the ratios of harmonic space within a rhythmic context. 3.3 Form To this point, it may appear that sans ĕn sans is the product of a particularly strict, sterile computational system. How does creativity factor into the compositional pro- cess, beyond the selection of particular algorithms or mapping strategies? Admit- tedly, there has been little evidence yet for such concerns; nevertheless, musicality and intuition do play a vital role. At this stage, the various skeletal structures of pitch and duration will be intuitively assembled into an originating structure consisting of seven musical groups. is overall generative form of sans ĕn sans mimics Beckett’s Lessness (see Sec- tion 2.1.1.1), with a fewminor alterations. e seven groups of musical lines are each composed of focused, short phrases from one to ĕve measures in length—analagous 34  81 81 3 5 3 5:4 82 82 83 83  (a) Initial Subdivision  81 82 8281 3 5 5:4 83 83  (b) Accumulation Across Measures  533 3 81 81 83 83 3 5:4 82 82  (c) Accumulation Within a Measure Figure 3.6: Rhythmic Processes in sans ĕn sans to the paragraphs and sentences of Beckett’s prose—all related by a particular the- matic element. Like elaborate studies, these phrases explore their particular musical ‘topic’ (See Table 3.4), various technical means of producing its expressions on the guitar, and distinct manifestations of an overall pre-occupation with resonance. Ad- ditionally, an exploration of levels of ‘tension’ within three other themes occur: attack density, texture, and contrast (see Table 3.5). Musical parameters such as phrasing, dy- namics, articulation and gesture—as well as the duration of speciĕc pitch-ĕelds—are all intuitively composed to best express each line’s particular thematic characteristics. All of the generative material composed for sans ĕn sans was written for the solo guitar only. As will be seen in Chapter 4, the ensemble’s main function is to help 35 Table 3.4: Large-scale Formal emes in sans ĕn sans Group eme I harmonics and tremolo II percussive resonance III repeated notes IV arpeggios V counterpoint and silence VI open strings VII glissando Table 3.5: Tensions of Musical Parameters in sans ĕn sans Group Attack Density Resonance Texture Contrast I med high low high II med low med med III high high low low IV high med low med V med med high high VI high high med med VII high high high med delimit the actualisation of the originating structure, and as such, it has no role in this ĕrst stage. is approach reinforces the guitar’s position as the work’s conceptual focus. Since the source pitch sequence producedmicrotonal sonorities, it was necessary to employ a scordatura tuning to allow for the production of all the quarter- and three- quarter-tone pitches present. Four alternately-tuned strings are arranged around two strings with normal tuning: the low E string is raised by a quarter-tone, the second A string is also tuned up by a quarter-tone, the D and G strings remain at their normal pitches, the B string is tuned down to an A, and the upper E string is tuned down a quarter-tone to D (see Figure 3.7). is system provides access to all the necessary quarter- and three-quarter-tone 36  651 432  Figure 3.7: Scordatura Tuning of the Guitar pitches of the harmonic sequence (with octave equivalency in effect), while stillmain- taining the traditional limit of adjacent semi-tones on each string. Nevertheless, the instrument’s usual resonance has been distinctly altered. is change, along with the cyclic rhythmic patterns discussed in Section 3.2, evoke a strong sense of non-Western musics (e.g., Hindustanic and Carnatic music). And, the use of gui- tar techniques originating from Toque, or the guitar playing form of Spanish Fla- menco—which are discussed in the next section—further connect sans ĕn sans to a broad musical aesthetic. 3.3.1 Musical Material Group I of the generative structure begins with an exploration of two separate means of plucked resonance: natural harmonics, and tremolo. ese two levels of polyphony focus on the ĕrst three strings plus the low sixth string, and the remaining fourth and ĕh string, respectively (see Figure 3.8). e contrast is very high between the singly articulated harmonics and the repeated-attacks of the tremolo. Once each harmonic is plucked, the player’s le-hand returns to the sounding tremolo. ese micro- interruptions are expected, but the performer is challenged to make these transitions as smooth as possible, as well as to avoid dampening any sounding string. Despite the near-constant tremolo, the overall character of this group is one of stasis. Group II explores the use of percussive attacks on the guitar’s sounding board (golpe), as well as striking the strings with the right-hand palm while the le-hand ĕngers the indicated chord (tamburo). e use of golpe includes both single-attacks with the ring ĕnger on the lower-body of the guitar, and ‘rolls’ between the thumb on the upper-body and the ring ĕnger. ese resonances extend or alternatively ar- ticulate normally-played material, and are techniques drawn from Flamenco music. 37 Figure 3.8: Sketch of Group I, mm. 1–4 Groups III and IV also utilise Flamenco techniques, and are related through the var- ied use of right-hand articulation patterns. Techniques include extending from rel- atively simple repeated index ĕnger strikes to more complex rasgueado strumming, as well as employing ‘pulling’ (tirando) and ‘resting’ (apoyando) strokes. eĕrst four groups share amore homogeneous approach to their thematic areas, with generally low textural variation. e last three collections, however, are more dramatic and virtuosic with a wider variety of accompanying material beyond their particular themes. Group V alternates between scalar-runs in one voice and chordal progressions in the second, while Groups VI and VII approach ‘fantasia’-like units with denser textural layers and sudden alterations between contrasting materials. By the end of Group VII, the guitar has engaged with many diverse playing techniques and dramatic forces. 3.4 Summary is chapter has been concerned with the construction of pre-compositional or gen- erativematerial—the ĕrst articulation of a double-articulation abstractmachine—for 38 sans ĕn sans. e end result of applying the theories and ideals of Chapter 2, this orig- inating structure contains the work’s harmonic, melodic and rhythmic resources; all built from explorations of the ratio-relationships of harmonic space coupled with an over-arching theme of resonance. 39 Chapter 4 Analysis: sans ĕn sans As discussed in Section 2.1.1.2, Beckett’s Lessness challenges the reader to confront their own interpretation of a non-linear prose. Sans ĕn sans also confronts the lis- tener with a splintering of the generative structure outlined in Chapter 3. Moreover, I was presented with a compositional challenge: how was I to fashion a successful musical work from these fragmented raw materials? In essence, my personal musi- cal ideas and tastes were overlaid onto a reordering of the originating elements during a process of actualisation, or becoming-music (in Deleuzian terms). Of particular note in this process are the connections between the solo guitar- only generative structure, and the full ensemble actualisation. It is analogous to the compositional procedures of Luciano Berio and his series of Sequenzas and Chemins. ese works present a virtuosic composition for a solo instrument (the Sequenza), and a related composition where the original solo material is transformed into a concerto-like work for soloist and instrumental group (the Chemins). It is an ad- ditive process that develops the musical potential of existing materials. In the case of sans ĕn sans, this expansion is particularly focused on the possibility for timbral development. 4.1 Becoming-music e resultant form of sans ĕn sans again follows Beckett’s construction method for Lessness. e order of the originating musical ‘sentences’ of Section 3.3—71 in to- tal—was determined via a simple randomisation process where each fragment was 40 24 7 33 14 59 30 7 8 41 64 52 42 66 1 32 21 58 28 60 29 25 3 2 68 62 15 55 18 22 48 67 36 47 6 23 46 36 27 64 58 22 51 25 15 10 4 55 61 13 57 19 27 57 3 45 23 50 38 28 63 61 11 47 40 30 68 59 49 2 70 54 29 34 14 53 46 70 6 26 12 63 69 39 35 10 37 20 41 34 53 16 49 39 4 67 50 17 5 24 56 16 69 65 43 60 62 48 9 21 8 12 43 17 45 5 19 31 44 31 32 35 54 33 56 26 9 52 18 1 37 44 38 13 11 42 65 66 51 71 40 20 71 Figure 4.1: ‘Sentence’ Ordering in sans ĕn sans allowed to appear twice in a variable location. However, unlike Beckett’s plan, the end-work is not divided into two parts, and each sentence is free to appear in any position. See Figure 4.1 for the complete listing. is speciĕc ordering is only one ofmultiple possibilities or other lines-of-becoming. Like Lessness, it is not a progression to an end, but instead is an active transforma- tion and production of itself. It is a Deleuzian deterritorialisation of the relationships of the generative structure that encourage new perception. Patterns do emerge, and I emphasise these through an application of Ferneyhough’s concept of interruptive polyphony (see Section 2.2.3.2). 4.1.1 Interruptive Polyphony e reordered musical fragments of sans ĕn sans are combined in two distinct ways: stratiĕcation and interlockƬ. Stratiĕcation is characterised by materials which “con- tinuously recombine and are subject to interruptions”(Feller 1999), while interlock- ing—or ‘slippage’, to use Ross Feller’s terminology—involves sequential orderings which rarely recombine. While no pre-determined plan existed (i.e., combinations occurred in an intuitivemanner), stratiĕcation proceduresweremost oen applied to the multi-textural fragments of Groups V–VII of the originating structure, whereas Ƭese terms are taken from a discussion of Stravinsky’s methods in Cone (1962, 19) 41 Table 4.1: Location of Group I Fragments Fragment Location 1 mm. 19–23 3,2 mm. 36–40 4 mm. 63–66 3 mm. 74–77 2 mm. 94–95 4 mm. 118–121 1 mm. 161–165 V V 82 82 83 83 82 82 42 42 82 82 Gtr. œµ o> ‰ ‰ SSœ o> 3 œœµ æ 6 3p 5 4 sœ ˙m o > 5 .œ sœœµ æ œœmµ æ 2 œ sœ˜ o>3 ‰ œµ o> 3 œœµ æ ssœœ˜ æ 5 1 ˙ ‰ .œm o> œœ˜ æ œœm˜ æ 2 sœ ‰œ œœm˜ æ (a) Group I Fragment 1 V V 85 85 44 44 85 85 83 83 Gtr. ȯ> sœ Œ .œµ>o ‰ ˙ ˙ mµ æ π œ Œ ‰ sœ˜>o œ.˙ Œ wwmµ æ œ Œ . ‰ ˙µ>o ..œœmµ æ œœµµ æ .œ˜>o .œ ..œœµµ æ (b) Group I Fragment 4 Figure 4.2: Sample Group I Fragments interlocking was generally used on the mono-textural materials of Groups I–IV. e result is a formal series of phrases with contrasting levels of tension. emost pronounced effect of the selected ordering of these phrases is a periodic occurrence of the fragmented harmonics/tremolo-themed Group I (see Table 4.1, 4.2(a) and 4.2(b)). Interlocked with surrounding fragments, these recurring and 42 Table 4.2: Large-Scale Form of sans ĕn sans Section Location I mm. 1–35 II mm. 36–62 III mm. 63–73 IV mm. 74–93 V mm. 94–117 VI mm. 118–160 VII mm. 161–181 timbrally-distinct sentences form thematically recognisable areas of relatively low tension. is music becomes a refrain—functioning as sectional beginnings—that delimits and binds together the non-linear Ęow of musical sentences. While main- taining a common texture, these repetitions are varied via length, pitch use and or- chestration. As a result, the actualised large-scale form of sans ĕn sans consists of seven sections (reĘecting the seven Group I fragments). is form is outlined in Ta- ble 4.2. Each section opens with a Group I phrase, with the exception of Section I, which instead begins with an introductory guitar solo. e overall sectional delin- eation is further articulated by the accompanying octet. 4.1.2 e Ensemble e ensemble of sans ĕn sans utilises the same instrumentation as Edgar Varèse’s Oc- tandre. is selection was deliberately made to reĘect both my past exposure and high regard for the 1923 work, as well as its potential as a rich timbral vehicle. Offer- ing a large palette of instrumental sounds and combinations as well as the ability to produce wide dynamic contrasts, its timbral resources are elevated to the same level of importance as the more traditional musical parameters of pitch, rhythm and dy- namicsƭ. In sans ĕn sans, the instrumental ensemble and its potential combinations and sonorities both reinforce and help create the overall musical form. e composition of the ensemble portion of sans ĕn sans was performed in a ƭis raising of the signiĕcance of instrumental timbre is also a characteristic shared by many spec- tralist composers. 43 far less structured and controlled manner than the solo guitar part. Nevertheless, algorithmic routines were still utilised to generate pitch and rhythmic materials. 4.1.2.1 Rhythm e rhythms of the ensemble instruments were selected from a pool of potential choices created by a variant of the process discussed in Section 3.2. e random fun- nel permutation for each particular group (from Table 3.3) was used to create a list of durations and a list of rhythmic pulses. Each duration was subdivided by its corre- sponding number of pulses, and the end result was mapped onto the basic repeating durational cycle (see Figure 3.5). Finally, two variants of this result were created by injecting periodic rests and ties into the sequence, and by inverting the rhythms of that result such that every note became a rest and every rest became a note. A visual representation of the patch is shown in Figure 4.3. As with the process of assign- ing pitch-ĕelds to the musical fragments, rhythmic selection from these variants was done intuitively. 4.1.2.2 Pitch e pitch material for the ensemble was drawn from the same harmonic-ĕelds ac- tivated by the guitar (see Appendix B). While the guitar constantly unfolds these pitches into melody, the ensemble explores the available pitches in a more harmonic or chordal sense. Pitches existing in the ĕeld but not articulated by the guitar are oen used, or particular pitches sounded by the guitar are chosen and emphasised. As with the rhythmic selection of the previous section, these choices are made instinctually in an effort to reveal patterns within the randomised form. 4.1.3 Timbre and Form sans ĕn sans begins with 18 measures of guitar solo, clearly presenting the guitar as the centre-piece of the work. is soloistic role remains in place throughout the piece (with the exception of four measures at the start of section IV). However, the en- semble does not respond with simple accompaniment. Instead, it functions on an almost-equal level, activating fundamental, shared or even missing pitches from the operative harmonic-ĕeld. 44 Figure 4.3: OpenMusic Rhythm Patch 45 &? V ? 45 45 45 45 44 44 44 44 85 85 85 85 83 83 83 83 Tpt. Tbn. Gtr. Cb. Ÿ~~~~~ Ÿ~~~~~ 32 ˙ sœµ ˙ sœ˜ . s¿æ ‰ œµ sœm Œ ® .SSœn sœµ ‰ 3 œ œ œ œ œ œ œ œ . .. . S Oœ˜˜ æ ® Œ Œ r R 4 3 qwÈ con sord. e = 57 valve clicks senza sord. p e = 57 ß pont. sœm sœµ ® .sœ œ˜ ® sœ sœ˜ ‰ . ss¿æ ¿æ œµ œµ œ œ˜ œ œ œ œ r Rw p valve clicks + air 6 5 ‰ sœ œ˜ ‰ ® Sœµ 5 œµ œµ œµ œ˜ Ø r RqÈe 6 5 . sœ˜ œm 7 œµ œ œµ 7 œ˜ œ˜ œ œµ r R 6 5 q. gliss. gliss gliss gliss gliss. gliss. gliss. gliss.gli s Figure 4.4: sans ĕn sans, mm. 32–35 46 Two examples of this resonance expansion can be found in Figure 4.4 and Fig- ure 4.5. e former demonstrates a quasi-chordal diffusion of the pitch-ĕeld artic- ulated by the guitar; while the latter is a more active, contrapuntal stretching of the harmonic space. e ensemble is never employed as a single, homogeneous unit, with preference instead given to partitioning it into various combinations. It is composed of duets plus single instruments in section I; duets, trios and quartets plus single instruments in section II; solos and duets in section III; paired duets in section IV; varied ensem- bles in sections V & VI; and, remains mainly absent in the ĕnal section. A full listing of the ensemble combinations can be found in Table 4.3. Notably, at various points throughout the latter portion of the work each woodwind instrument, as well as the double bass, is given a solo line marked espressivo. Table 4.3: Ensemble Combinations Section Location Ensemble I mm. 1–18 guitar solo mm. 19–23 guitar + (ob., cl.) + dbl. mm. 24–27 guitar + (Ę., bsn.) + tbn. mm. 28–31 guitar solo mm. 32–35 guitar + (tpt., tbn.) + dbl. II mm. 36–42 guitar + (Ę., bsn., hn.) + (hn. + tpt.) + dbl. mm. 43–46 guitar + (ob., cl.) + dbl. mm. 47–49 guitar + (hn., tpt., tbn.) mm. 50–53 guitar + (hn., tbn.) + dbl. mm. 54–58 guitar + (Ę., ob., cl., bsn.) + dbl. mm. 59–62 guitar + (Ę., ob., cl., bsn.) + dbl. III mm. 63–66 guitar + ob. mm. 67–69 guitar + (cl., bsn.) mm. 70–73 guitar solo IV mm. 74–77 (bsn., hn., tpt., tbn., dbl) mm. 78–81 guitar + (cl., bsn.) + (hn., tpt.) Continued on the next page 47 Table 4.3 – continued from the previous page Section Location Ensemble mm. 82–85 guitar + (Ę., bsn.) + hn. mm. 86–87 guitar + (Ę., cl.) + (tbn., dbl) mm. 88–93 guitar + cl. V mm. 94–99 guitar solo mm. 100–106 guitar + (Ę., cl., hn., tbn., dbl.) + (bsn., tpt.) + (ob., tbn.) mm. 107–109 guitar + (hn., tpt., dbl.) mm. 110–114 guitar + (picc., dbl.) mm. 115–117 guitar + (ob., cl.) VI mm. 118–121 guitar solo mm. 122–127 guitar + (Ę., ob., hn., dbl.) mm. 128–129 guitar + (cl., bsn., tbn., dbl.) mm. 130–134 guitar + (picc., tbn., dbl.) + (ob., cl., bsn.) mm. 135–137 guitar + (ob., cl., bsn.) + tbn. mm. 138–140 guitar + dbl. mm. 140–144 guitar + picc. mm. 145–147 guitar + (Ę., hn., tpt.) + (hn., tpt., tbn.) + dbl. mm. 148–151 guitar + (hn., tpt., tbn.) + (bsn., hn.) + dbl. mm. 152–155 guitar + (bsn., hn., tbn., dbl.) mm. 156–160 guitar + (Ę., ob., tpt.) VII mm. 161–166 guitar solo mm. 167–170 guitar + bsn. + (Ę., cl., hn., tbn., dbl.) mm. 171–175 guitar solo mm. 176–178 guitar solo mm. 179–181 guitar solo 48 &? & & V 83 83 83 83 83 44 44 44 44 44 Fl. Bsn. Hn. Tpt. Gtr. Ÿ~~~~~~~ 83 œ . .œmæ œ- Œ ssœ+ ssœœœœœœµm ˜ µ ssssœœœœœœµ m µ µ m 9 SS R f bouche-cuivre f Flz. piccoloœm˘ œ˘ .œ˘ Ù SSSS œÆ œ> œm> œ> œ˘ œ˘ œ˘ œm Æ ‰ SSS œ œ˘ œ˘ œ> œ> œ> œm˘ œ˘ œ˘ œÆ Ù œm .œn .œ Œ sœµ œµ œ˜ œ œµ œ œ œµ œ œ sss s œ 9 ƒ RH tasto f f F F Fz con sord. f 5 6 5 œ> œ ‰ œm . œm > œ œ. œm> .œ ® œm . .œ> Sœ Œ 6 3 œ œm . œ> œ˜ œ. ® œ > œm ® . œµ> œ˜ . Sœµ . Œ 6 3 œµ + .sœ œ+ œ Œ7 œ Œ sœœ œµ ˜m ‰ œµ o Ó bouche-cuivre F P f P ord. F ß XIII to ute liss. Figure 4.5: sans ĕn sans, mm. 83–85 49 V82 82 44 44 83 83 ∑ sœœœœœœµ ˜ ˜ sœœœœœœ˜m̃µ T p π ∑ wæ 2"U i i RH pont. π ∑ œµ œ œm œ œ œ œ œ œ œ œp a i m... π 3 2 r R 4 1 4 1 q. ord. ‰ ssœ ≈ ssœ ≈ ssœ ≈ 3 3 S œœœ˜µ S œœœ œo œ˜ oT 4 1P *Gtr. Figure 4.6: sans ĕn sans, mm. 8–11 4.1.3.1 Musical Material e creative challenge of sans ĕn sanswas to shape the rawmaterials of Chapter 3 into a viable, uniĕed musical work. Although pitch and rhythm were to some degree pre- determined via algorithmic procedures, the next step was not simply to ‘plug in’ these values for a ĕnal result. Both aesthetic and playability concerns affected the choice of speciĕc elements from the pre-compositional structure, and these issues also dic- tated that these selections were sometimes necessarily modiĕed. As well, all of the remaining undetermined musical parameters (i.e., orchestration, timbre, dynamics, phrasing, etc.) were created through traditional compositional practices. Sans ĕn sans opens with a number of very quiet, repeated-note guitar ĕgures. ese gestures are quickly juxtaposed with increasingly dramatic chordal, percus- sive and scalar outbursts lasting until m. 18. (See Figure 4.6). e resulting con- trasts between relative stasis and interruptive attacks foreshadow much of the en- suing dramatic form of the piece. At m. 19, an ensemble duet comprised of the oboe and clarinet enters for the ĕrst time. ey accompany the ĕrst fragment of the harmonics/tremolo-themed Group I as played by the guitar and double-bass (see Figure 4.7). Together, these events mark the beginning proper of Section I. e sub- sequent music continues to develop the alternation between moments of calm and more active discharges. An extended period of tremolo-like ĕgures in the guitar, with timbral accompaniment provided by muted trumpet and trombone, bring this section to a close. Section II begins with another Group I fragment, this time accompanied by Ęute, bassoon and horn. From m. 41, a chordal attack in the guitar is expanded to in- clude brass ĕgures against a woodwind tremolo (see Figure 4.8). As this section pro- 50 && & ? V V ? 82 82 82 82 82 82 82 83 83 83 83 83 83 83 82 82 82 82 82 82 82 84 84 84 84 84 84 84 82 82 82 82 82 82 82 Flute Oboe Clarinet Bassoon Solo Guitar Bass ∑ ‰ ® œ œµ .œn 7 ® œµ œ œm œn œ œµ œm œn œµ 6 7 ∑ œµ o> ‰ ‰ SSœ o> 3 œœµ æ Sœµ o .SSœ ® ∏ e = 53 ∏ 6 3p ord. 5 4 p i a m i π ∑ sœ œ œ œ œ œµ3 Sœ ˙m æ 5 ∑ sœ ˙m o > 5 .œ œœµ æ œœmµ æ ∑ 2 ∑ sœµ œµ 3 œæ sœµ æ 3 ∑ œ sœ˜ o>3 ‰ œµ o> 3 œœµ æ ssœœ˜ æ 5 ∑ 1 ∑ .sœm SSœ œ œæ œn æ ∑ ˙ ‰ .œm o> œœ˜ æ œœm˜ æ ∑ p 2 ‰ œ˜ œm œm sœæ ‰ ‰ œ˜ œ sœ ‰œ œœm˜ æ ® œ>æ œmæ œµæ œæ œ˜æ ≈ 3 ∏ π ∏ pont. π Figure 4.7: sans ĕn sans, mm. 19–23 51 & ? & & V V & 86 86 86 86 86 86 86 44 44 44 44 44 44 44 87 87 87 87 87 87 87 82 82 82 82 82 82 82 Fl. Bsn. Hn. Tpt. Gtr. Cb. 40 Œ Œ œµ œn ‰ ® .SSœ œ œµ œ ® œ œ sœ ‰ Œ Œ ∑ ‰ œµ o> .œ.˙ sœœœµ˜ ‰ sœ œ œm œn ‰ sœœœµ˜ 3 ∑ π F F ∏ 6 T T P PF wµ wn w wµ Œ ‰ . œ œm œ œ> .œ> œn æ 5 6 Œ ‰ . œm œn œµ œn> .œæ œæ5 6 ∑ sœœœœœœµm ˜ µ                                       ssssœœœœœœµ m µ µ m 9 ‰ ∑ ? con sord. con sord. f f f f Flz. Flz. e = 59 R f ƒ ˙µ ˙n Œ ‰ ˙ ˙µ Œ ‰ æ̇ Œ ‰ ˙æ Œ ‰ ∑ sœœœœœœµ ˜ µ b œœœœœœ ...... œœœœœœ sœœœœœœ ≈ sœœœœœœµ ˜ ˜ m œœœœœœ œœœœœœ ...... œœœœœœ œœœœœœ ≈ 5 5 5 ‰ ≈ Sœµ ˝ ® ‰ Œ ® œ˜ œ> ‰ 7 7 pizz. ç f T T f ∑ ∑ ∑ ∑ ∑ sœœœµµm ® .œµ œœœ 5 sssœœœmµ˜ H≈ . ‰ P P e = 53 p gliss Figure 4.8: sans ĕn sans, mm. 40–43 52 gresses, the static elements dominant in Section I appear less frequently. is section concludes in mm. 60–62 with a dynamic climax involving woodwind multiphonics, scratch tones in the double-bass, and open-string chords with Bartok-style pizzicato strikes in the guitar. A static exploration of alternate ĕngerings marks the start of the third section. It functions as an echo or refrain of the vigorousmaterial fromSection II. At only eleven measures, it is the shortest of the seven sections. e beginning of the next region, Section IV, is unique within the piece as the only point in which the guitar is not the main melodic and harmonic focus. Instead, it is silent, replaced by the double-bass in its upper register and an accompanying bassoon/brass chorale-like progression (see Figure 4.9). e guitar returns in m. 78, and begins a series of broken, staccato ĕgures contrasted with legato scalar runs. Following another climax in mm. 83–84, a clarinet duet with the guitar from mm. 88–90 transitions to a quiet sectional end in m. 93. Echoing the distinction between themore homogenousmaterials of the ĕrst four groups of the generative structure and the ‘fantasia’-like last three groups (see Sec- tion 3.3.1), Sections V & VI move away from the distinct juxtapositions of earlier sections, and instead function as larger-scale refrains and developments of previous sections, respectively. SectionVopenswith a short fragment and initial thematicma- terial in the guitar, before being interrupted by an ensemble quintet (Ęute, clarinet, horn and double-bass) in m. 100 (see Figure 4.10). Aer this intrusion, fragmented and accented ĕguresmotivically related to the staccato lines of Section IV are realised before an espressivo-solo in the oboe closes this passage. Section VI is the longest of the piece, lasting 43 measures. Aer beginning with a straight-forward presentation of a Group I fragment, the musical discourse of the remainder of the section can be best viewed in a developmental context as previous materials are transformed alongside the introduction of new thematic material. For example, in mm. 131–133, repeated staccato ĕgures in the oboe, clarinet and bas- soon combined with the more legato melodic material of the Ęute and double-bass accompany new material in the guitar (see Figure 4.11). e ĕnal section of the piece forms a coda-like ending, with the solo guitar in- terrupted only once by the ensemble in m. 170. Functionally, this refrain is meant to balance the varied instrumental combinations and developmental materials of the 53 &? & & ? V & 83 83 83 83 83 83 83 44 44 44 44 44 44 44 85 85 85 85 85 85 85 82 82 82 82 82 82 82 85 85 85 85 85 85 85 Cl. Bsn. Hn. Tpt. Tbn. Gtr. Cb. 74 ∑ Œ Sœm - Œ sœ˜ - sœ˜ - .ssœ ® ‰ Œ sœµ - ∑ ‰ œ-Œ . e = 53 π ∏ ∏ ∏ p ∑ ˙ .œm - Sœ- œ Œ Œ ‰ sœm - ∑ ˙ .œµ - sœµ - ∑ .˙ Œ Ó ˙˜ - ∑ ˙m - Sœm - œ Œ ‰ Œ ≈ sœ˜ - œ 3 ˙ sœµ - ∑ Œ . œ- ˙ Sœ ∑ œm - ≈ ssœm - sœ ssœ ≈ ‰ œ ∑ œ Sœ ‰ ‰ œ Æ ‰ œµ Æ Œ ‰ 6 ‰ œµ Æ ‰ œÆ Œ ‰ 6 ssœ ≈ ‰ ≈ œ> œ> œ> œmfl ‰ sssœ> œ ≈ œm> 7 5 3 ≈ œ. œ. Ù œ. œ. œm . ® œm . œ. œ. œm . sssœ. ® ≈ Œ ∑ œµ> œµ œ œ œn œ œµ œm> œµ œm œ˜ œ˜ sœœœµ sœœœœµmµ 5 ∑ ? e = 64 T p F p P p P π P P F Figure 4.9: sans ĕn sans, mm. 74–78 54 && ? & ? V ? 42 42 42 42 42 42 42 82 82 82 82 82 82 82 85 85 85 85 85 85 85 Fl. Cl. Bsn. Hn. Tbn. Gtr. Cb. Ÿ~~~~~~~ 98 œœ œœœœœœµ ˜ µµ sœœœœœœm ˜ µmµ ‰ sœœœœœœm ˜ µmµ 5 3 T P . .œ˜ œµ œm œ SSœ o ‰ . 3 5p œ˜æ œmæ œµæ œæ̃ œmæ œµæ 3 3 œæ œµ æ œm æ œ˜ æ œæ œµ æ 3 3 ‰ .œm œ Œ Sœµ 3 ‰ Sœµ œµ Flz. F Flz. F F P ß p Œ ‰ ® sssœm sœ> œ> œ> 6 5 œ .œ> ‰ ‰ Œ sœm ‰ Œ .œµ o œ .œµ S Oœ œµ m ˜ ‰ S O œœ˜ n µ ‰ p Íp p smorzato p gliss. gliss Figure 4.10: sans ĕn sans, mm. 98–101 55 && & ? ? V ? 89 89 89 89 89 89 89 83 83 83 83 83 83 83 89 89 89 89 89 89 89 Fl. Ob. Cl. Bsn. Tbn. Gtr. Cb. 131 ∑ Œ ‰ ŒU ≈ . . SSSS œm Æ œ. œ. ≈ Ù SSSS œn Æ ≈ . œ. œm . œm . œµ . ≈ . Œ ‰ ŒU ≈ . . SSSS œµ Æ œ. œ. ≈ Ù SSSS œm Æ ≈ . œ. œ. œ˜ . œm . ≈ . Œ ‰ ŒU ≈ . . SSSS œÆ œm . œµ . ≈ Ù SSSS œm Æ ≈ . œ. œ˜ . œ˜ . œ. ≈ . œ œµ .œ Sœ ‰ Œ U Œ Œ sOœœµµ ‰ ‰ sœm sœn U ‰ sœ sœm ‰ sœ sœ˜ ‰ Sœ SSœ ≈ ‰ ‰ Œ Œ ‰ . SSœ ≤ 5 vib. p π π π P espressivo ≈ . œ- œm œÆ œµ œ˜ ∑ ∑ ∑ ∑ ‰ ‰ œµ - œ˜ œ 3 œ œ œµ piccolo P p œ œ. œn œm - ≈œ œm - SSœ ≈‰ ‰ Œ Œ Œ Œ ‰ ® œµ - œm ® œm - œm œm œµ ® œÆ ® ‰ ‰ 3 3 3 Œ Œ ‰ ® œm - œ œm œn ® œm Æ ® œµ - œm œ œÆ 3 3 3 Œ Œ ‰ ® œ' ® œ- œ œµ œµ ® œm - œ ® ‰ sœ' 3 3 3 ∑ œ œ œm œ œm œm œ sœm ssœµ . ≈ ssœœœµnm . ≈ ssœœœ˜nµ . ≈ 3 3œm S œœmµ œµ œ sœ œm ssœ ≈ ‰ ‰ Œ Œ 5 F p p p π F P p π p p p Í Íp Figure 4.11: sans ĕn sans, mm. 132–133 56 previous sections. e work ends very quietly, with the open-string guitar chords invoking the full harmonic-space of sans ĕn sans. 4.1.4 Tempo As a last means of providing structural emphasis and musical unity, the sectional units of Table 4.3 are reinforced via a series of variable tempos (see Table 4.4). ese reĘect the constantly changing stratiĕcation of the instrumental combinations. Each distinct tempo is based upon a sometimes simpliĕed ratio-relationship of harmonic- space applied to a base tempo of 71 eighth-note beats per minute (e.g., 71  3/2 = 53). However, unlike the similar relationships evident in both the pitch and rhythmic constructions of sans ĕn sans, these tempo Ęuctuations are not applied in a system- atic manner. Notable, however, is the assigning of a constant tempo (53 eighth-note BPM) to the recurring Group I fragments that signal the start of each new section. Table 4.4: Tempo Map of sans ĕn sans Section Location Tempo (eighth-note BPM) Ratio I mm. 1–23 53 3/2 mm. 24–27 71 1/1 mm. 28–35 53 3/2 II mm. 36–53 53 3/2 mm. 54–58 64 9/5 mm. 59–62 71 1/1 III mm. 63–73 53 3/2 IV mm. 74–77 53 3/2 mm. 78–85 64 9/5 mm. 86–90 53 3/2 mm. 91–93 64 9/5 V mm. 94–106 53 3/2 mm. 107–109 79 9/8 mm. 110–114 64 9/5 mm. 115–117 71 1/1 Continued on the next page 57 Table 4.4 – continued from the previous page Section Location Tempo (eighth-note BPM) Ratio VI mm. 118–160 53 3/2 VII mm. 161–181 53 3/2 4.2 Summary is chapter has outlined the actualisation of one of the many potentialities inher- ent in the generative structure of Chapter 3. A process of ‘becoming’, raw musical materials were shaped to express their inherent connections and possibilities. ese relationships were also emphasised by particular ensemble orchestrations and a cor- responding map of tempo alterations. e end result is sans ĕn sans. 58 Chapter 5 Conclusion Sans ĕn sans is my attempt to create a musical work that expresses itself. Philoso- phy, according to Deleuze, creates concepts that are creative rather than representa- tional. ese concepts encourage people to push thought to its limits, pull it apart and see what our thinking can do. My response to this challenge is a musical work that does not attempt to communicate a speciĕc meaning, or represent a particular image or feeling, but instead conveys what it does. e result of an engagement with Samuel Beckett’s Lessness, sans ĕn sans is constructed from a series of algorithmically- derived pitches and rhythms which are assembled, fragmented and transformed via a machinic process of ‘becoming’. is process is purely creative, combining custom- ary compositional techniques with parameters generated through an exploration of fractal geometry and mathematical automata. e end result is a piece that—like Beckett’s—challenges the listener to become aware of how it works, what it does, and through these questions, what it is. Future possibilities for development of the compositional techniques presented in this dissertation include the expansion of the pitch-generation algorithms ofChap- ter 3 into higher dimensions of harmonic space and the investigation of more com- plex fractal patterns, as well as the exploration of a more subtle means of structural fragmentation beyond simple randomisation (i.e., constraints-based). Additionally, a cognitive evaluation of how listeners react to non-linear musical discourse would undoubtedly prove fascinating. 59 Bibliography Adorno, eodor W. 1997. Aesthetic eory. Minneapolis: University of Minnesota Press. Trans. Robert Hullot-Kentor. ! pages 5 Agon, Carlos, Jean Bresson, and Gèrard Assayag. 2008. Openmusic: Design and implementation aspects of a visual programming language. In 1st European Lisp Symposium ELS’08. Bordeaux, France. ! pages 10, 25 Anderson, Julian. 2000. A provisional history of spectral music. 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Cambridge University Press. ! pages 7, 8 Moscovich, Viviana. 1997. French spectral music: an introduction. Tempo 200:21–27. ! pages 16 Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. 1992. Chaos and Fractals: New Frontier of Science. New York: Springer-Verlag. ! pages 11 Prusinkiewicz, Przemyslaw. 1986. Score generation with L-systems. In Proceedings of the 1986 International Computer Music Conference, 455–457. ! pages 13, 16 Prusinkiewicz, Przemyslaw, and Aristid Lindenmayer. 1990. e Algorithmic Beauty of Plants. New York: Springer-Verlag. ! pages 12, 13 Sabat, Marc. 2008a. An algorithm for real-time harmonic microtuning. In 5th Sound and Music Computing Conference. http://music.calarts.edu/~msabat/ms/pdfs/MM.pdf, accessed on 26 February 2009. ! pages 18 —. 2008b. ree crystal growth algorithms in 23-limit constrained harmonic space. Contemporary Music Review 27(1):57–78. ! pages 18, 19, 27 Solomon, Philip H. 1980. Purgatory unpurged: time, space and language in ‘lessness’. Journal of Beckett Studies http://www.english.fsu.edu/jobs/num06/Num6Solomon.htm, accessed 26 February 2009. ! pages 5, 6 62 Supper, Martin. 2001. A few remarks on algorithmic composition. Computer Music Journal 25(1):48–53. ! pages 10, 12 Tenney, James. 1983. John Cage and the theory of harmony. http://www.plainsound.org/pdfs/JC&ToH.pdf, accessed on 26 February 2009. ! pages 17, 18, 19 —. 2008. On ‘crystal growth’ in harmonic space (1993–1998). Contemporary Music Review 27(1):47–56. ! pages 19 Wannamaker, Robert A. 2008. e spectral music of James Tenney. Contemporary Music Review 27(1):91–130. ! pages 16, 17 Zepke, Stephen. 2005. Art as Abstract Machine: Ontology and Aesthetics in Deleuze and Guattari. New York and London: Routledge. ! pages 8 63 Appendix A omlsystem Source Code A.1 turtle.lisp 1 ;;;;============================================================================ 2 ;;;; 3 ;;;; OML-System 4 ;;;; author: J. Scott Amort 5 ;;;; 6 ;;;; An OpenMusic library developed to facilitate experiments 7 ;;;; with Lindenmayer systems, including the interpretation 8 ;;;; of strings (lists) as turtle graphics commands. 9 ;;;;============================================================================ 10 11 (in-package :lsystem) 12 13 ;;;-------------------------------------------------- 14 ;;; constants 15 ;;;-------------------------------------------------- 16 17 (defparameter *rotate-by-integer* t) ; will use integer instead of real value for rotations 18 (defparameter *initial-heading* 0.0) ; initial heading value for turtle 19 (defparameter *standard-rotation* 90.0) ; default rotation value 20 (defparameter *standard-length* 1.0) ; default length to move turtle forward 21 (defparameter *turtle-icon* 801) 22 23 ;;;-------------------------------------------------- 24 ;;; A turtle graphic object 25 ;;;-------------------------------------------------- 26 27 (om::defclass! turtle () 28 ((x 29 :initarg :x 30 :initform 0.0 31 :type float 32 :accessor x 33 :allocation :instance 34 :documentation ”x-coordinate”) 35 (y 36 :initarg :y 64 37 :initform 0.0 38 :type float 39 :accessor y 40 :allocation :instance 41 :documentation ”y-coordinate”) 42 (heading 43 :initarg :heading 44 :initform 0.0 45 :type float 46 :accessor heading 47 :allocation :instance 48 :documentation ”heading (in degrees)”)) 49 (:icon *turtle-icon*) 50 (:documentation ”a turtle graphic object”)) 51 52 (defmethod initialize-instance :after ((self turtle) &key) 53 (with-accessors ((heading heading)) self 54 (setf heading (mod heading 360)))) 55 56 ;;;-------------------------------------------------- 57 ;;; Operators 58 ;;;-------------------------------------------------- 59 60 ;; default constraint function peforms no constraint (can be customized by other libraries/patches) 61 (defparameter *constraint-function* #’(lambda (co-ordinates) (cons (cdr (car co-ordinates)) (cdr (cdr co-ordinates))))) 62 63 (om::defmethod! f ((turtle turtle)) 64 :indoc ’(”a turtle instance”) 65 :icon *turtle-icon* 66 :doc ”move turtle object forward” 67 (with-accessors ((x x) (y y) (heading heading)) turtle 68 (let ((newx (+ x (* *standard-length* (cosine heading)))) 69 (newy (+ y (* *standard-length* (sine heading))))) 70 (let ((constrained (funcall *constraint-function* (cons (cons x newx) (cons y newy))))) 71 (setf x (car constrained)) 72 (setf y (cdr constrained))))) 73 turtle) 74 75 (om::defmethod! plus ((turtle turtle)) 76 :indoc ’(”a turtle instance”) 77 :icon *turtle-icon* 78 :doc ”rotates a turtle instance counter-clockwise” 79 (with-accessors ((heading heading)) turtle 80 (let ((new-heading (mod (+ heading *standard-rotation*) 360))) 81 (setf heading (if *rotate-by-integer* 82 (round new-heading) 83 new-heading)))) 84 turtle) 85 86 (om::defmethod! minus ((turtle turtle)) 87 :indoc ’(”a turtle instance”) 88 :icon *turtle-icon* 89 :doc ”rotates a turtle instance clockwise” 90 (with-accessors ((heading heading)) turtle 91 (let ((new-heading (if (< (- heading (mod *standard-rotation* 360)) 0) 92 (+ 360 (- heading (mod *standard-rotation* 360))) 93 (- heading (mod *standard-rotation* 360))))) 94 (setf heading (if *rotate-by-integer* 95 (round new-heading) 96 new-heading)))) 97 turtle) 98 99 ;;;-------------------------------------------------- 65 100 ;;; Comparisons 101 ;;;-------------------------------------------------- 102 103 (om::defmethod! is-same? ((turtle1 turtle) (turtle2 turtle)) 104 :indoc ’(”a turtle instance” ”a turtle instance”) 105 :icon *turtle-icon* 106 :doc ”determines if two turtle instances are the same” 107 (with-accessors ((x1 x) (y1 y) (heading1 heading)) turtle1 108 (with-accessors ((x2 x) (y2 y) (heading2 heading)) turtle2 109 (and (= x1 x2) (= y1 y2) (= heading1 heading2))))) 110 111 (om::defmethod! is-same-pos? ((turtle1 turtle) (turtle2 turtle)) 112 :indoc ’(”a turtle instance” ”a turtle instance”) 113 :icon *turtle-icon* 114 :doc ”determines if two turtle instances are at the same position (ignores heading)” 115 (with-accessors ((x1 x) (y1 y)) turtle1 116 (with-accessors ((x2 x) (y2 y)) turtle2 117 (and (= x1 x2) (= y1 y2))))) 118 119 ;;;-------------------------------------------------- 120 ;;; Helper methods 121 ;;;-------------------------------------------------- 122 123 (om::defmethod! copy-turtle ((turtle turtle)) 124 :indoc ’(”a turtle instance”) 125 :icon *turtle-icon* 126 :doc ”makes a copy of a turtle instance” 127 (with-accessors ((x x) (y y) (heading heading)) turtle 128 (make-instance ’turtle :x x :y y :heading heading))) 129 130 (om::defmethod! turtle->coord ((turtle turtle)) 131 :indoc ’(”a turtle instance”) 132 :icon *turtle-icon* 133 :doc ”converts a turtle instance to an x,y coordinate cons” 134 (with-accessors ((x x) (y y)) turtle 135 (cons x y))) 136 137 (om::defmethod! turtle->coord ((tlist list)) 138 :indoc ’(”a list of turtle instances”) 139 :icon *turtle-icon* 140 :doc ”converts a list of turtle instances to a list of x,y coordinate cons” 141 (loop 142 for turtle in tlist 143 collect (turtle->coord turtle))) A.2 lsystem.lisp 1 ;;;;============================================================================ 2 ;;;; 3 ;;;; OML-System 4 ;;;; author: J. Scott Amort 5 ;;;; 6 ;;;; An OpenMusic library developed to facilitate experiments 7 ;;;; with Lindenmayer systems, including the interpretation 8 ;;;; of strings (lists) as turtle graphics commands. 9 ;;;;============================================================================ 10 11 (in-package :lsystem) 12 13 ;;;-------------------------------------------------- 66 14 ;;; Comparisons 15 ;;;-------------------------------------------------- 16 17 (defun is-f? (func) 18 ”determines if a function performs the same operation as f” 19 (is-same? (funcall func (make-instance ’turtle)) (f (make-instance ’turtle)))) 20 21 (defun is-plus? (func) 22 ”determines if a function performs the same operation as plus” 23 (is-same? (funcall func (make-instance ’turtle)) (plus (make-instance ’turtle)))) 24 25 (defun is-minus? (func) 26 ”determines if a function performs the same operation as minus” 27 (is-same? (funcall func (make-instance ’turtle)) (minus (make-instance ’turtle)))) 28 29 ;;;-------------------------------------------------- 30 ;;; Helper methods 31 ;;;-------------------------------------------------- 32 33 (om::defmethod! remove-rotations ((slist list)) 34 :indoc ’(”a list of interpreted stages”) 35 :icon *turtle-icon* 36 :doc ”removes rotation-only turtles from a list of interpreted stages” 37 (loop 38 for stage in slist 39 counting stage into size 40 collect (let ((egats (reverse stage))) 41 (loop 42 for i from 1 to (length egats) 43 for slist = (nthcdr (- i 1) egats) 44 collect (cond 45 ((= (length slist) 1) (first slist)) 46 (t (if (is-same-pos? (first slist) (second slist)) nil (first slist)))) into tlist 47 do (format t ”turtles remaining for stage ~a: ~a~%” size (length slist)) 48 finally (return (remove nil (reverse tlist))))))) 49 50 (defun introspect-func (func) 51 ”return function name of input func” 52 (cond 53 ((is-f? func) #’f) 54 ((is-plus? func) #’plus) 55 ((is-minus? func) #’minus))) 56 57 ;;;-------------------------------------------------- 58 ;;; Interpretation 59 ;;;-------------------------------------------------- 60 61 (om::defmethod! perf-subst ((stage list) (production-rules list)) 62 :indoc ’(”list of symbols” ”association list of production rules”) 63 :icon *turtle-icon* 64 :doc ”performs (string) substitutions on stage according to production rules” 65 (om::flat (loop 66 for symbol in stage 67 collect 68 (let ((subst (cdr (assoc (introspect-func symbol) production-rules)))) 69 (cond 70 ((eql subst nil) symbol) 71 (t subst)))))) 72 73 (om::defmethod! eval-stage ((stage list) (turtle turtle)) 74 :indoc ’(”list of symbols” ”a turtle instance”) 75 :icon *turtle-icon* 76 :doc ”evaluates the symbols within stage starting from turtle” 67 77 (loop 78 for symbol in stage 79 collect (if (= (length elist) 0) 80 ; always copy first turtle 81 (funcall symbol (copy-turtle turtle)) 82 (cond 83 ; only copy subsequent turtles if moving turtle forward 84 ((not (is-f? symbol)) (funcall symbol (copy-turtle (car (last elist))))) 85 (t (funcall symbol (car (last elist)))))) into elist 86 finally (return (delete-duplicates elist)))) 87 88 (om::defmethod! interpret-lsystem ((num-stages integer) (axiom list) (production-rules list) &rest alternates) 89 :indoc ’(”number of stages to interpret” ”list of symbols” ”association list of production rules”) 90 :icon *turtle-icon* 91 :doc ”interpret a given l-system” 92 (let ((prules (if (= (length alternates) 0) 93 production-rules 94 (append (list production-rules) alternates)))) 95 (loop 96 for i from 1 to num-stages 97 collect (if (= i 1) 98 (perf-subst axiom (if (= (length alternates) 0) 99 prules 100 (nth (random (length prules)) prules))) 101 (perf-subst (car (last stages)) (if (= (length alternates) 0) 102 prules 103 (nth (random (length prules)) prules)))) into stages 104 collect (if (= (length slist) 0) 105 (eval-stage (car (last stages)) (make-instance ’turtle :heading *initial-heading*)) 106 (eval-stage (car (last stages)) (car (last (car (last slist)))))) into slist 107 do (format t ”processing stage ~a:~% ~a~%” i (car (last stages))) 108 finally (return slist)))) A.3 pitchspace.lisp 1 ;;;;============================================================================ 2 ;;;; 3 ;;;; OMPitch-space 4 ;;;; author: J. Scott Amort 5 ;;;; 6 ;;;; An OpenMusic library developed to facilitate experiments 7 ;;;; with James Tenney’s concept of harmonic space, where each 8 ;;;; pitch is represented by coordinates which are exponents 9 ;;;; of the prime factors of their frequency ratio. 10 ;;;;============================================================================ 11 12 (in-package :pitch-space) 13 14 ;;;-------------------------------------------------- 15 ;;; 5-limit harmonic space 16 ;;;-------------------------------------------------- 17 18 ; coordinates | prime limit | ratio | cents | interval name 19 ; (0,0,0) | 2- | 1/1 | 0 | unison 20 ; (-1,1,0) | 3- | 3/2 | 702 | fifth 21 ; (2,-1,0) | 3- | 4/3 | 498 | fourth 22 ; (-3,2,0) | 3- | 9/8 | 204 | major wholetone (dominant wholetone) 23 ; (-2,0,1) | 5- | 5/4 | 386 | ptolemaic major third 24 ; (-3,1,1) | 5- | 15/8 | 1088 | ptolemaic major seventh 25 ; (0,-1,1) | 5- | 5/3 | 884 | ptolemaic major sixth 68 26 ; (-5,2,1) | 5- | 45/32 | 590 | ptolemaic tritone 27 ; (1,1,-1) | 5- | 6/5 | 316 | ptolemaic minor third 28 ; (3,0,-1) | 5- | 8/5 | 814 | ptolemaic minor sixth 29 ; (0,2,-1) | 5- | 9/5 | 1018 | ptolemaic minor seventh 30 ; (4,-1,-1) | 5- | 16/15 | 112 | major diatonic semitone 31 ; (4,-2,0) | 3- | 16/9 | 996 | pythagorean minor seventh 32 ; (-4,3,0) | 3- | 27/16 | 906 | pythagorean major sixth 33 ; (1,-2,1) | 5- | 10/9 | 182 | minor wholetone (subdominant wholetone) 34 ; (6,-2,-1) | 5- | 64/45 | 610 | ptolemaic diminished fifth 35 ; (5,-3,0) | 5- | 32/27 | 294 | pythagorean minor third 36 ; (-4,0,2) | 5- | 25/16 | 773 | ptolemaic augmented fifth 37 ; (5,0,-2) | 5- | 32/25 | 427 | ptolemaic diminished fourth 38 ; (-3,-1,2) | 5- | 25/24 | 71 | minor chromatic semitone 39 ; (-6,1,2) | 5- | 75/64 | 275 | ptolemaic augmented second 40 ; (4,1,-2) | 5- | 48/25 | 1129 | large diminished octave 41 ; (7,-1,-2) | 5- | 128/75 | 925 | ptolemaic diminished seventh 42 ; (-2,3,-1) | 5- | 27/20 | 520 | ptolemaic wide fourth 43 ; (-7,3,1) | 5- | 135/128 | 92 | major limma 44 ; (3,-3,1) | 5- |40/27 | 680 | ptolemaic narrow fifth 45 ; (8,-3,-1) | 5- | 256/135 | 1108 | 46 ; (-6,4,0) | 3- | 81/64 | 408 | pythagorean major third 47 ; (7,-4,0) | 3- | 128/81 | 792 | comma-diminished octave 48 ; (-1,-2,2) | 5- | 25/18 | 569 | Rameau’s tritone 49 ; (-7,2,2) | 5- | 225/128 | 976 | ptolemaic augmented sixth 50 ; (2,2,-2) | 5- | 36/25 | 631 | Rameau’s false fifth 51 ; (8,-2,-2) | 5- | 256/225 | 223 | ptolemaic diminished third 52 53 ;;;-------------------------------------------------- 54 ;;; Constants 55 ;;;-------------------------------------------------- 56 57 (defparameter *5limit-prime-form* (make-array 33 58 :initial-contents 59 ’(0 702 498 204 386 1088 884 590 316 814 1018 112 996 906 182 610 294 773 427 71 275 1129 925 520 92 680 1108 408 792 569 976 631 223))) 60 61 (defparameter *5limit-lookup-table* (make-array ’(5 9) 62 :initial-contents 63 ’((nil nil 569 71 773 275 976 nil nil) 64 (nil 680 182 884 386 1088 590 92 nil) 65 (792 294 996 498 0 702 204 906 408) 66 (nil 1108 610 112 814 316 1018 520 nil) 67 (nil nil 223 925 427 1129 631 nil nil)))) 68 69 ;;;-------------------------------------------------- 70 ;;; Utilities 71 ;;;-------------------------------------------------- 72 73 (om::defmethod! coords->cents ((clist list)) 74 :indoc ’(”a list of x,y cons co-ordinates”) 75 :icon 178 76 :doc ”converts a list of x,y co-ordinates to interval values (in cents)” 77 (let ((lookup *5limit-lookup-table*)) 78 (loop 79 for coord in clist 80 ; array indexes are offset (x by 2, y by 4) to account for negative coordinate values 81 collect (aref lookup (+ (round (cdr coord)) 2) (+ (round (car coord)) 4))))) 82 83 ;;;-------------------------------------------------- 84 ;;; Customizations for use with omlsystem library 85 ;;;-------------------------------------------------- 86 87 (defun constrain (co-ordinates) 69 88 ”constrains the maximum of a set of orig/new co-ordinates” 89 ;; this function keeps co-ordinates within 5-limit pitch space 90 ;; by ’wrapping’ at the edges of the crystal 91 ;; constrains f for use with the pitch-space library 92 (let ((origx (car (car co-ordinates))) 93 (newx (cdr (car co-ordinates))) 94 (origy (car (cdr co-ordinates))) 95 (newy (cdr (cdr co-ordinates)))) 96 (cond 97 ; evaluate special cases (as crystal is not square) 98 ; ((and (= (abs newx) 3) (< (abs newy) 1)) (cons newx newy)) 99 ; ((and (= (abs newx) 4) (= newy 0)) (cons newx newy)) 100 ; ((and (= (abs newx) 3) (= (abs newy) 2)) (cond 101 ; ((= (abs origx) 3) (cons origx (* origy -1.0))) 102 ; (t (cons (* origx -1.0) (* origy -1.0))))) 103 (t (cond 104 ((and (= origx newx) (= origy newy)) (cons newx newy)) 105 (t (cons (if (> (abs newx) 2.0) 106 (* origx -1.0) 107 newx) 108 (if (> (abs newy) 2.0) 109 (* origy -1.0) 110 newy)))))))) 111 112 (defparameter lsystem::*constraint-function* #’pitch-space::constrain) 70 Appendix B Pitch-Fields in sans ĕn sans 71 72 73 74 Appendix C Musical Score of sans ĕn sans 75 sans n sans (endlessness) j. scott amort 76 Scoring solo guitar, slightly amplied (for balance only) 1 ute, doubling piccolo 1 oboe 1 clarinet in A 1 bassoon 1 trumpet in C 1 horn in F 1 trombone 1 double bass Scordatura: Guitar Duration: approx. 15 minutes *NOTE: Lower two strings are to be tuned one-quarter tone sharp, and the top string one-quarter tone at. 77 Notes The score is notated in C The guitar and double-bass sound one octave lower than notated The piccolo, one octave higher Guitar Techniques and Notations 82 82 ‰ ssœ ssœ 3 golpe percussion-staff for guitar denotes golpe (striking the body), with thumb above strings (top staff), or with ring nger below strings (bottom staff) V 82 82 sœœœœœœµ ˜ ˜ sœœœœœœ˜m̃µ T p T indicates tambora (sounding the indicated strings by striking with the palm) œœœœœœµ ˜ ˜ ssssœœœœœœ˜m̃µ R P f R indicates rasgueado (nger strumming) Slashed, double-stemmed chords indicate repeated articulations at the approximate value of the upper stem, lasting for the value of the lower stem V 85 85 œm œn œm œm œm œn œm œm 3 2 qÈer R 4 1 4 1 ≈ repeat pattern for indicated length Ensemble 4 4 Œ S÷ ÷ ÷ multi multi multi f f f SS ÷ S÷ S÷ ‰ choose multiphone to sound in given range œb . .œ œ Sœ alt. ngerings choose alternate ngerings for given pitch to emphasise timbre difference 78 V85 85 82 82 81 81 82 82 85 85 Solo Guitar ∑ œm œn œm œm œm œn œm œm π3 2 qÈer R p a i m... e = 53 ∑ œn œ œ œm œn œ œ œm π3 2 qÈer R ‰ ssœ ⋲ ssœ 3 ⋲ SS œœœm S œœœ T P golpe ∑ ⋲ œœœœœœµ ˜ ˜ œœœœœœ 3 T π p ⋲ ssœ ⋲ ‰ 3 œo œ˜ o ‰ 4 1 ∑ œœœœœœµ ˜ ˜           ssssœœœœœœ˜m̃µ R P f ‰ .œ .œ Sœ> sœœœœœœµ ˜ µ mmm ‰ Œ ‰ T P p π V 82 82 44 44 83 83 82 82 42 42 Gtr. 8 ∑ sœœœœœœµ ˜ ˜ sœœœœœœ˜m̃µ T p π ∑ wæ i i RH pont. π 2"U ∑ œµ œ œm œ œ œ œ œ œ œ œ π3 2 r Rq.ord. ‰ ssœ ⋲ ssœ ⋲ ssœ ⋲ 3 3 ⋲ SS œœœm S œœœ œo œ˜ oT 4 1P .ssœ ® ⋲ . ssœ 5 ∑ p π U1" ∑ œm œm œ œm œ œm .œ > Ù 9 S œœm SF p ∑ œœœm                 œœœµ             5 ˙ F p gli ss & & V ? 82 82 82 82 82 83 83 83 83 83 44 44 44 44 44 82 82 82 82 82 83 83 83 83 83 Ob. Cl. Gtr. Cb. 15 ∑ ∑ ∑ ⋲ œµ œ˜ œµ œµ> ∑ p ∑ ∑ ∑ ‰ œœmm Sœ œ ∑ F ∑ ∑ ∑ œœmm œµ œµ œ˜ ® œ˜ œ˜ œm œm œ œ˜ œµ 9 œ ∑ ∑ ∑ ∑ V wµ æ ∑ i i RH pont. π U U U 3" 3" 3" ‰ ® œ œµ .œn 7 ® œµ œ œm œn œ œµ œm œn œµ 6 7‰ ‰ ssœo> 3 œµ o> œœµ æ S Oœµµ ..SSOœ ® ∏ ∏ 6 3 π pord. 5 4 p i a m i XIX VII sœ œ œ œ œ œµ3 Sœ ˙m æ 5 .œ Sœ ˙m o> 5 sœœµ æ œœmµ æ ∑ 2 XII Flz. g ss . sans !n sans j. scott amort Score in C (endlessness) ª ª ª ª * ** * tambora ** rasgueado 79 && & ? ? V V ? 82 82 82 82 82 82 82 82 84 84 84 84 84 84 84 84 82 82 82 82 82 82 82 82 84 84 84 84 84 84 84 84 82 82 82 82 82 82 82 82 Fl. Ob. Cl. Bsn. Tbn. Gtr. Cb. 21 ∑ sœµ œµ 3 œæ sœµ æ 3 ∑ ∑ sœ Œo 3 œ S œ˜ o> 3 œœµ æ ssœœ˜ æ 5 ∑ 1 VII ∑ .sœm SSœ œ œæ œn æ ∑ ∑ ˙ ‰ .œm o> œœ˜ æ œœm˜ æ ∑ p 2 ‰ œ˜ œm œm sœæ ‰ ‰ œ˜ œ ∑ sœ ‰œ œœm˜ æ ® œ>æ œmæ œµæ œæ œ˜æ ⋲ 3 π ∏ ∏ pont. π ˙˜ ˙m ∑ ∑ ˙˜ ˙ ∑ ∑ œµ œ œ œ œ˜ œm œµ œ˜ œµ œ˜ œ œµ œ œ œ œ 5 ∑ P P r Rq. F p6 5 e = 71 e = 71 œ˜ œm ‰ ∑ ∑ œ˜ œ ‰ ⋲ . ssœm> sœ 5 ∑ œ˜ > œ œ œ œ˜ > œ œ œ œ > œ œ œ œ > œ œ œ ∑ π π con sord. P p ∑ ∑ ∑ ∑ .œ œm ∑ œ œm œ œ˜ œ œ œ œ ∑ 4 3 0 2 4 1 0 2 sans !n sans 80 ?V 42 42 44 44 84 84 Tbn. Gtr. 27 œ œµ> ⋲ ŒU ssssœm ⋲U œµ œ œ œ˜ ∏ ß-p ∏ p ∑ œ œµ œ œµ œ œ œ œ r Rw 2 1 e = 53 ∑ sœ œ> œ˜ œµ œm œµ œ œ œm œ ⋲ SS O œ˜ µ . . O œ œ˜ œn> œn œm œ œµ œ œ œ˜ 5 F P4 5 4 5 4 ‰u ‰ ‰u ‰ sœµ sœm U ‰ sœµ sœ˜ U ‰ vib. vib. p π & ? V ? 42 42 42 42 45 45 45 45 44 44 44 44 Tpt. Tbn. Gtr. Cb. Ÿ~~~~~~ Ÿ~~~~~~~~ 31 ∑ ∑ ⋲ œœœœœµ ˜ µ       sœœœœœœm ˜ µmµ ‰ sœœœœœœm ˜ µmµ 5 3 ∑ F p π T U3" ˙ sœµ ˙ sœ˜ . s¿æ ⋲ ‰ œµ     sœm Œ ® .SSœn œµ ‰ 3 œ œ œ œ œ œ œ œ . .. . S Oœ˜˜ æ ® Œ Œ r R 4 3 qwÈ con sord. valve clicks π ∏ senza sord. p ß pont. sœm œµ ® .sœ sœ˜ ® sœ œ˜ ‰ . ss¿æ ¿æ ∑ œµ œµ œ œ˜ œ œ œ œ ∑ r Rw p valve clicks + air ∏ 6 5 gliss. gliss gliss gliss. gliss. gliss. sans !n sans ª ª 81 &? & & ? V V 85 85 85 85 85 85 85 83 83 83 83 83 83 83 44 44 44 44 44 44 44 85 85 85 85 85 85 85 42 42 42 42 42 42 42 Fl. Bsn. Hn. Tpt. Tbn. Gtr. 34 ∑ ∑ ∑ ‰ sœ   œ˜ ‰ ® Sœµ     5 ∑ œµ œµ œµ œ˜ ∏ Ø r RqÈe 6 5π ∑ ∑ ∑ ⋲ . sœ˜   sœm 7   œµ ⋲ œ   sœµ 7 ∑ œ˜ œ˜ œ œµ r R 6 5 q. .‚m œ œµ œœ> 6 Œ sœm+ ∑ ∑ ‰ œ >o Œ. Œ Sœœmµ æ π2 p π Íp 4 5 hollow tone XIX A A .‚ Œ ∑ w ∑ ∑ .˙ Œ˙˜>o ˙̇mµ æ ..œœmµ æ Sœœµæ P 1 ∑ œm œ œ ‰ Œ sœm> .œ œ˜ + ∑ ∑ Œ . œ>o˙ ‰ ˙̇mµ æ sœœ˜µ æ Íp π p 2 5 6 ∑ ∑ ˙ ∑ ∑ œ Œ Œ ‰ S œ˜>o ˙̇˜µ æ 1 gliss. gliss gliss.g iss sans !n sans 82 & ? & & V V ? 86 86 86 86 86 86 86 44 44 44 44 44 44 44 87 87 87 87 87 87 87 82 82 82 82 82 82 82 Fl. Bsn. Hn. Tpt. Gtr. Cb. 40 Œ Œ œµ œn ‰ ® .SSœ œ œµ œ ® œ œ sœ ‰ Œ Œ ∑ ‰ œµ o> .œ.˙ sœœœµ˜ ‰ sœ œ œm œn ‰ sœœœµ˜ 3 ∑ π F F ∏ 6 T T P PF3 5 4 wµ wn w wµ Œ ‰ . œ œm œ œ> .œ> œn æ 5 6 Œ ‰ . œm œn œµ œn> .œæ œæ5 6 ∑ sœœœœœœµm ˜ µ                                     ssssœœœœœœµ m µ µ m 9 ‰ ∑ con sord. con sord. f f f f Flz. Flz. R f ƒ ˙µ ˙n Œ ‰ ˙ ˙µ Œ ‰ æ̇ Œ ‰ æ̇ Œ ‰ ∑ sœœœœœœµ ˜ µ b œœœœœœ ...... œœœœœœ sœœœœœœ ⋲ sœœœœœœµ ˜ ˜ m œœœœœœ œœœœœœ ...... œœœœœœ œœœœœœ ⋲ 5 5 5 ‰ ⋲ Sœµ ˝ ® ‰ Œ ® œ˜ œ> ≥ ‰ 7 7 pizz. ç f T T f ∑ ∑ ∑ ∑ ∑ sœœœµµm ® .œµ œœœ 5 sssœœœmµ˜ H⋲ . ‰ P P e = 53 p e = 53 gliss & V 83 83 44 44 43 43 85 85 Ob. Gtr. 44 ‰ ‰ ‰ sssœ 5 sœœœ œ˜ œ œm œµ 3 π .œ .œµ œ œ œµ ‰ ⋲ ‚ ‚ .‚ œ œµ5 6 ˙µ> ȯ ˙˜ o 3 tongue ram ∏ 3 4 1 V XII .u̇ .˙µu sœµ Sœmu ‰ sœµ sœu ‰ sœ sœµu ‰ vib. vib. vib. p œ œµ ‰ Œ œ œb œ œn œ œb œ œn r RqÈe π3 2 decel. RH tasto U3" sans !n sans ª ª *** ***bend with 1st !nger *** 83 && ? V 44 44 44 44 85 85 85 85 Hn. Tpt. Tbn. Gtr. 48 Ó œm æ œm æ .œæ .œæ œæœæ 6 6 Œ œm æ œm æ .œæ .œæ œæœæ ssœæŒ ssœæ 6 6 6 ® . .Sœ- .Sœ Œ ‰. SSœµ - . Sœ Œ 7 7 œœœœœœµm ˜˜µm                ‰ sœœœœœœµm ˜˜µm œœœœœœµm ˜˜µm                               7 ∏ p ∏ p Flz. Flz p T π ∏ ∏ ∏ senza sord. senza sord. ssœm æ Œ ssœm æ œæœæ .œæ .œæ œæœæ ssœæ Œ ssœæ 6 6 6 6 œm æ œm æœæ .œæ .œæ œæœæ ssœæ Œ ssœæ 6 6 6 ∑ S œ œµ ˜ ‰ œœµ ˜ œ œ µ œ œœµ µ œ œœ ˜ œ œœœn µ œœœœ ˜ ⋲ Sœµ o3 5 F pont. œm æ .œm + œ+ œ+ sœm o œ+ œ+ œ+ 6 œm æ Œ ‰ ‰ œµ - ‰ ® .Sœ- 7 ®. œm œ®. œ˜ œ˜ ® sœœœm̃m ® .œµ œœœmµ S œœœ 5 π π P π pπ .ssœm o ®Œ. œm + œ+ œ+ 7 ∑ Sœ ‰ Sœµ - SSS œ .œm ‰ 7 S œœœmµm S œœœ Œ ssœ ˝ ⋲ p ∏ P f gliss. & & & ? V 87 87 87 87 87 87 83 83 83 83 83 83 42 42 42 42 42 42 85 85 85 85 85 85 Fl. Ob. Hn. Tbn. Gtr. 52 ∑ ∑ Ȯ ssœ ⋲ Œ Œ . -̇ ∑ œµ œµ ⋲ œµ œµ œµ œµ ⋲ œµ œ˜ ssœœµµ ⋲ ssœœœµmµ ⋲ ssœœœµnµ ⋲3 3 lontano ∏ pont pizz p ∑ ∑ ∑ .ssœ ® Œ ⋲ . œ> œ Œ 5 .ssœ ˝ ⋲ sœœœœµmµ K ‰ 5 p F P ⋲ sœ œ œ˜ œ œµ œn - ‰ 3 Œ œ˜ > œm SS œT œ- SSœ 6 6 ∑ ∑ ∑ œµ œ˜ œ œ˜ œ˜ œ ‰ ® œm > œ œn ® œm œ œ 10 p e = 64 ß-p p pont F e = 64 2 4 3 4 Œ sœ˜ Sœ S œU S œ ‰ 3 œm T .œn œ- œ Sœ U Œ 7 ∑ ∑ ∑ œ˜ œm œ œµ œn ® œ˜ œµ S œ>U ⋲ œµ œn S œµ>U3vib. vib. p P p P p5 3 5 2 sans !n sans ª ª 84 && & ? ? V ? 42 42 42 42 42 42 42 83 83 83 83 83 83 83 82 82 82 82 82 82 82 Fl. Ob. Cl. Bsn. Tbn. Gtr. Cb. 56 .œm - SSœ .Sœ ⋲ 7 .œ- SSœ .Sœ ⋲ 7 .œµ - ssœµ .sœ ⋲7 .sœm ⋲ Œ .sœµ ⋲ Œ œœœm>                 œœœµ>             5 ‰ ..sœœm ≥ œœ ..œœµ ≥ 5 π p π π p π π p π ß-p π ß-p π con sord. ß-p f ß-p ∑ ∑ ∑ ∑ ∑ œm ˝ ⋲ œµ œn œ œ˜ .. sœœ ⋲ Œ p ∑ ∑ ∑ ∑ ∑ œµ œ˜ œµ œµ ∑ r R 6 5 q. accel. ∑ ∑ ∑ ∑ ∑ œµ œµ œ œ˜ œ œ œ˜ œ œ œ œm œm œµ œm> œn œµ œ 9 ∑ e = 71 e = 71 3 sans !n sans 85 && ? V ? 85 85 85 85 85 44 44 44 44 44 89 89 89 89 89 Fl. Ob. Bsn. Gtr. Cb. 60 Œ Œ S÷ ‰ ÷ Œ .÷ œ œµ œ œ œ œ œ œ œµ œ œ œ œ œµ œ œ œ œ˜ œ œ œ œ œµ œ œ œm œ œ œ˜ œœœ œµ œœœ œµ œœœ ‰ ˙ multi multi multi f f f f scratch tone f SS ÷ ⋲ ‰ sœm ‰ Ó S÷ ‰ Œ Ó S÷ ‰ Œ ˙˜ ˝ ȯ ˙˜ o 3 ‰ œm         ⋲ Œ ‰ œm         ⋲ Œ 5 5 ƒ f p f p jete jete f tongue ram 1 XII 4 V ∑ ∑ ∑ œœœœœœµ ˜ µ m M ‰ œœœœœœµ ˜ µ m ‰ œµ ˝ ‰ .˙ Œ ‰ T p behind the tailpiece F p ƒ U3" sans !n sans 86 && ? V V 85 85 85 85 85 44 44 44 44 44 85 85 85 85 85 83 83 83 83 83 43 43 43 43 43 83 83 83 83 83 Ob. Cl. Bsn. Gtr. 63 ‰ œb . .œ œ Sœ ∑ ∑ >̇o ‰ Œ .œµ>o ‰ ˙̇mµ æ p alt. !ngerings e = 53 π 6 5 4 e = 53 B B 3 œ .œ Sœ œ .SSœ ® ‰ ⋲ .œm œ 3 6 ∑ ∑ ‰ sœm o> œ.˙ Œ wwmµ æ P P 4 IX œ S œ SSS œ ⋲ . Sœ ∑ ∑ .œ Œ ‰ ˙µ>o ..œœmµ æ œœµµ æ p p 6 Sœ .SSœ ® ‰ ∑ ∑ .œm>o .œ ..œœµµ æ ∑ œm œ . S œ œ 7 ⋲ .œ œ œ œ œ ⋲ . 6 ∑ sœµ œm       ‰ . sœµ œ       ‰ . sœ œµ       ‰ . alt. !ngerings alt. !ngerings π π R R R pf f p f p ∑ œ .œ .œ S œ S œ ‰. SSS œ œ 7 ∑ œµ œm œ œµ œ œ œµ œ œ œœœœœœµm ˜ µ m         œœœœœmµ         9 3 3 p p π F & ? V 85 85 85 42 42 42 83 83 83 84 84 84 Cl. Bsn. Gtr. 69 S œ œ . .œ Œ ‰ S œ œ œ S œ ‰. Œ 3 7 ‰ sœœœœµm ‰ sœœœœœ ˜m K‰ T p π ∑ ∑ ®. œo œo ® . œµ o œ˜ o ® sœœœœm ˜ µ > ® .œµ œœµµ œœ œœmm5 p P2 3 1 XII XVII XII 5 6 ∑ ∑ S œœœœmµ ‰ sœœœœœµ ˜m ‰ p π ∑ ∑ œ œm œo œo œ œµ œn > œµ o œ˜ o sœœœœn ˜ mµ > 5p ∑ ∑ ® .œµ œœµµ œœ œœµ œµ> œ˜ œµ œ> œ˜ œn S Sœm> ⋲5 6 ß ßp p ßp 5 4 6 0 2 sans !n sans ª ª 87 &? & & ? V & 83 83 83 83 83 83 83 44 44 44 44 44 44 44 85 85 85 85 85 85 85 82 82 82 82 82 82 82 85 85 85 85 85 85 85 Cl. Bsn. Hn. Tpt. Tbn. Gtr. Cb. 74 ∑ Œ Sœm - Œ sœ˜ - sœ˜ - .ssœ ® ‰ Œ sœµ - ∑ ‰ œ-Œ. π ∏ ∏ ∏ p senza sord. non vib. C C ∑ ˙ .œm - Sœ- œ Œ Œ ‰ sœm - ∑ ˙ .œµ - sœµ - ∑ .˙ Œ˙˜ - ∑ ˙m - Sœm - œ Œ ‰ Œ ⋲ sœ˜ - œ 3 ˙ sœµ - ∑ Œ . œ-˙ Sœ ∑ œm - ⋲ ssœm - sœ ssœ ⋲ ‰ œ ∑ œ Sœ ‰ ‰ œ Æ ‰ œµ Æ Œ ‰ 6 ‰ œµ Æ ‰ œÆ Œ ‰ 6 ssœ ⋲ ‰ ⋲ œ> œ> œ> œmfl ‰ sssœ> œ ⋲ œm> 7 5 3 ⋲ œ. œ. Ù œ. œ. œm . ® œm . œ. œ. œm . sssœ. ® ⋲ Œ ∑ œµ> œµ œ œ œn œ œµ œm> œµ œm œ˜ œ˜ sœœœµ sœœœœµmµ 5 ∑ ? e = 64 T p F p P p P π P P F e = 64 6 5 4 3 1 2 5 3 4 sans !n sans 88 &? & & V 82 82 82 82 82 83 83 83 83 83 42 42 42 42 42 82 82 82 82 82 Cl. Bsn. Hn. Tpt. Gtr. Ÿ~~~~~~~ 79 ‰ ⋲ SSœm Æ ‰ ⋲ SSœµ Æ œm> œ> ⋲ ‰ 3 ‰ œ> œ 3 sœm œ œµ > œm œ> œµ œ œm p Fz Fz P Œ œm Æ ® œ˜ Æ 5 Œ œµ Æ ® œÆ 5 ⋲ ® sssœ. œm . œ. ⋲ . ‰ . ssœn> 5 7 .œ Ù œ. œ. œm . œ. œ. ® œ œm sœ ⋲ . 5 7 œ˜> œµ œn œ œ œ˜ œ œn> ⋲ 3 P F P F P F P pizz. F5 6 5 0 0 0 Œ .œm Æ ‰ œm Æ Œ .œm Æ ‰ œÆ œ .œ .œ ® Œ ‰ ⋲ . sssœm . œn . œ. ® œ. œ. œ. œm . ® ⋲ œœœœœœµ B ˜ mm œœœœœœ œœœœœœ sœœœœœµ Bmµm ‰ ssœœœœ œµ Bmµm 5 F f F f F T T T P ∑ ‰ ⋲ sœ œ œm ∑ œ> œ> œ> Ù ⋲ ‰ sœµ œ œ˜ œµ œm œ œ œ œm œ œ œn œm œm œµ œ˜ œ œ> œ> 5 5 f p F f p 5 4 5 4 5 XV sans !n sans 89 &? & & V 83 83 83 83 83 44 44 44 44 44 Fl. Bsn. Hn. Tpt. Gtr. Ÿ~~~~~~~ 83 ∑ œ . .œmæ œ- Œ ⋲ ssœ+ ∑ ssœœœœœœµm ˜ µ                   ssssœœœœœœµ m µ µ m 9 SS R f bouche-cuivre f Flz. piccoloœm˘ œ̆ .œ̆ Ù SSSS œÆ œ> œm> œ> œ̆ œ̆ œ̆ œm Æ ‰ SSS œ ⋲ œ̆ œ̆ œ> œ> œ> œm˘ œ̆ œ̆ œÆ Ù œm œn .œ Œ sœµ œµ œ˜ œ œµ œ œ œµ œ œ sss s œ 9 ƒ RH tasto f f F F Fz con sord. f 5 6 5 ⋲ œ> œ ‰ œm . œm > œ ⋲ œ. œm> .œ ® œm . .œ > S œ Œ 6 3 œ œm . ⋲ œ> œ˜ œ. ® œ > œm ® ⋲ . œµ> œ˜ ⋲ . Sœµ . Œ 6 3 œµ + .sœ œ+ œ Œ7 œ Œ sœœ œµ ˜m ‰ œµ o Ó bouche-cuivre F P f P ord. F ß XIII to "ute liss sans !n sans 90 && ? V ? 87 87 87 87 87 83 83 83 83 83 Ob. Cl. Tbn. Gtr. Cb. Ÿ~~~~~~ 86 ‰ œµ œb sssœ> ® sœ œ> sœµ œµ> œ> sœ œ> œ> sœm œ> ‰ Œ ‰ sœæ ¿fl ®. œæ .œæ ¿fl .œm æ œæ ‰ Œ ® œµ > œµ> œ˜ œµ œm œµ œµ œµ œ œn œµ œ˜ ssœœœµµ ⋲ ssœœœµm ⋲ ssœ œœµµ µ ⋲3 3 S œµæ SSœæ ⋲ ‰ SS œ˜ ⋲ Œ ® œœ˜ ≤ œœµm> e = 53 Flz. tongue ram p p ßP p Pß Flz tongue ram p pizz.pont. pont ord. F p P p e = 53 5 6 4 5 6 4 5 45 6 3 4 6 ∑ ∑ œµ> œfl ® ‰ ‰ 3 ⋲ œœœœœœµµ ˜                     ‰ 6 sœœ ‰ ‰π T p ∑ ® œ œµ .œ œn œ œ 7 5 3 ∑ œµ œ œm œµ œ œµ œ˜ œµ œn œ œ˜ œµ œn œ œ˜ œ œµ œ˜ œ œn œ ∑ espressivo P pont. π5 4 5 & V 44 44 87 87 85 85 Cl. Gtr. 89 œ ‰ œm . .œµ œ .œ .œµ œ 3 sœœœœœœµm ˜ µ ‰ Œ S œœœœ œœµ m µ µ m ‰ Œ π ∏ T T œ sœ sœµ œ œm œ S œ ‰ sœœœœœœµ ˜ µ b ⋲ . ssœœœœœœµ ˜ µ bn sœœœœœ L ‰ sœœœœœœµ ˜ ˜ m ⋲ . ssœœœœœœµ ˜ ˜ m sœœœœœœ L 5 5TT π ∑ ® œµ œm œµ œ œm œ œµ ® œ œm œm œµ œ œ˜ œm œm œµ ssœœœµ mm ‰ 6 π pont e = 64 sans !n sans ª ª 91 VV 83 83 44 44 43 43 85 85 83 83 Gtr. 92 ∑ Oœœ˜mm ‰ O œœm ˜ m ‰ 4:3P ∑ wæ i i RH pont. π ‰ œm o > ˙ Œ. Ó S œ˜>o Œ Sœœmµ æ ˙̇æ Sœœ˜ æ π ord. e = 53 D sœ ‰ Œ Œ˙ œœæ ..œœmµ æ ‰ ∑ sœœœœœœµ m µm˜ ‰ ® œ˜ .œµ ˝ ® œ˜ .œµ ˝ ® sœœœœœµ m µ mm T F pizz. pizz. ∑ S œœœœmµm ® .œµ œœœm œœœ ..œœµ5 5 & & ? & ? V ? 42 42 42 42 42 42 42 82 82 82 82 82 82 82 85 85 85 85 85 85 85 Fl. Cl. Bsn. Hn. Tbn. Gtr. Cb. Ÿ~~~~~~~ 98 ∑ ∑ ∑ ∑ ∑ œœ œœœœœœµ ˜ µµ          sœœœœœœm ˜ µmµ ‰ sœœœœœœm ˜ µmµ 5 3 ∑ T P π ∑ ∑ ∑ ∑ ∑ ⋲ . .œ˜ œµ œm œ ⋲ SSœ o ‰ . 3 5 ∑ p π œ˜æ œmæ œµæ œæ̃ œmæ œµæ 3 3 œæ œµ æ œm æ œ˜ æ œæ œµ æ 3 3 ∑ ‰ .œm œ Œ Sœµ 3 ∑ ‰ Sœµ sœµ Flz. π F π Flz. π F π F P ß p "ute ∑ ∑ Œ ‰ ® sssœm sœ> œ> œ> 6 5 œ .œ> ‰ ‰ Œ   sœm ‰ Œ .œµ o œ .œµ S Oœ œµ m ˜ ‰ S O œœ˜ n µ ‰ ∑ p Íp ∏ p smorzato p 1 XII 3 VII gliss. gliss sans !n sans ª ª 92 &? & ? V 87 87 87 87 87 83 83 83 83 83 85 85 85 85 85 82 82 82 82 82 Ob. Bsn. Tpt. Tbn. Gtr. 102 ∑ sœ> . ssœ> ® Œ ⋲ ssœm œ> œ> œ> .œ> œ> Œ ‰ ⋲ ® ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ® ‰ ‰ ∑ ‰ sœ œµ ˜ ˝ > ‰ ® œ˜ .œµ > ® œ˜ .œµ > ® sœœœœµ m µ m ‰ F tongue ram π π smorzato p π3 3 ∑ ssœ> ⋲ ‰ ‰ ∑ ∑ SSœµ . ⋲ œµ œ œ ssœ' ⋲ 3 p œm Æ œµ Æ ⋲ œµ . ® œm . ® Œ ‰ ∑ ∑ Œ ‰ .Sœm sœn ⋲ œ œµ µ œœBm œœm ‰ S œœœœœB m µm Œ 3 π ∏ ∏ π ∏ 6 3 1 2 œÆ ® œµ Æ ® ‰ ∑ ∑ ⋲ ® Sœm sœ ® ∑ ∏ ∏ gliss. gliss. sans !n sans 93 && & ? V ? 44 44 44 44 44 44 85 85 85 85 85 85 44 44 44 44 44 44 89 89 89 89 89 89 Ob. Hn. Tpt. Tbn. Gtr. Cb. 106 œ. ® œ. ⋲ s¿ ‰ Ó ∑ ∑ ∑ wæ ∑ tongue ram π i i RH pont. π U U 3" 3" ∑ ‰ ®œ. œmfl ⋲ œµ ' ® ‰ œm . ® œµfl ⋲ œ' œ' ® œ˜ ' œm ' œæ 7 6 Œ ®œ. œµ fl ⋲ . œ˜ ' œm . ® SSSSœ̆ ⋲ . SS œµæ ® 7 ∑ ‰ œm œm œ œ˜> œ œm œ˜ œ˜> œn œm œ˜ œm . œµ o œ. œo œm . œµ o œ. œo œ. œo 6 ‰ . SSœ≤ œ œm œµ œ˜ e = 79 con sord. Flz. Flz. p Fz Fz con sord. p p p F ord. p P π e = 79 5 ∑ œæ œæ œm ' œm ' œ' ® ⋲ . ˙b æ> ∑ ∑ ˙µ ˙m o ˙m> 3 ˙m ˙µ ˙µ> sœµ F Fz P π ß π f F Fz Flz. ∑ sœæ ‰ Œ ˙m æ ‰ ∑ ∑ œœœœœœµ ˜ µ ˜ Œ œœœœœœµ ˜ µ ˜ Œ ‰ Œ Œ œ˜         Œ ‰ 5 p π p T jete π gl iss sans !n sans 94 &V ? 85 85 85 42 42 42 82 82 82 42 42 42 Fl. Gtr. Cb. Ÿ~~~~~~~~~~ Ÿ~~~~~~~~~ 110 ‰ œµ - œm œ ® ‰ œ - œµ œb ® œµ - œm œµ ' œn - œ ® ‰ œµ œµ œm œm> œµ œµ œ œ> œ œ œ œ> œ œ œ œn > œ. œµ œ œm 3 ‰ sœm œ œ .œæ œæ s pizz. punta arco gradually move to harmonic ∏ π e = 64 .œm - œ .œ ⋲ . œ˜ œ˜ œ œµ œ œ œ œ ® œm œ œ˜ æ .œæ œµ> œæ ∏ pizz. punta arco p P Fz pizz. pont. π ord. π r Rh ® œm> œ> œm> ⋲ ⋲ SSœm Æ 3 ‰ sœm œ œm œm œm .œ˜ Ù 9 S œæ œ˜ æ sœæ p π Fz tasto p œm Æ ⋲ . œ .œ œm> œ ® ‰ SSSœm Æ ® 3 .œ .œ˜ œµ œm œ ⋲ SSœµ o ‰ . 3 5 .ssœæ ® ‰ ‰ sœµ Fz π p ∏ on the bridge g ss. & & & V ? 83 83 83 83 83 85 85 85 85 85 Fl. Ob. Cl. Gtr. Cb. 114 ® œ> œm> œm> ⋲ ⋲ ‰ ‰ 3 ∑ ∑ .œµ o œ ˝ .œµ . S Oœ œµ m ˜ ‰ sœ Œ p P to piccolo ∑ œµ .œm œn œ œµ œm ∑ ® œµ œm œµ œ œm œ œµ ® œ œm œm œµ œ œm œm œm œµ sœœœµm ⋲ 6 ∑ espressivo p F pont p F e = 71 e = 71 ∑ Sœ , .œ .œm ‰ Œ .œm .œ ‰ œm œm œ œ˜> œ œm œ˜ œ˜> œn œm œ˜ œm . œµ o œ. œo œm . œµ o œ. œo œ. œo 6 ∑ π π p P P sans !n sans ª ª 95 && & V V ? 83 83 83 83 83 83 85 85 85 85 85 85 44 44 44 44 44 44 85 85 85 85 85 85 83 83 83 83 83 83 85 85 85 85 85 85 Fl. Ob. Hn. Gtr. Cb. 117 ∑ ∑ ∑ ∑ Oœœ˜mm ‰ O œœm ˜ m ‰ 4:3 ∑ P ∑ ∑ ∑ ȯ> sœ Œ .œµ>o ‰ ˙̇mµ æ ∑ e = 53 π e = 53 E E ∑ ∑ ∑ œ Œ ‰ sœm>o œ.˙ Œ wwmµ æ ∑ ∑ ∑ ∑ œ Œ. ‰ ˙µ>o ..œœmµ æ œœµµ æ ∑ ∑ ∑ ∑ .œm>o .œ ..œœµµ æ ∑ ® œ> œm œ .œm - œ sssœm ' œmæ œmæ œmæ Sœæ 7 5 ® œm> œm œ .œm - œ ® .œæ œmæ Sœæ 7 5 ® œæ+ œm æ+ œæ .œm æ+ œm æ+ œæ+ ssœ ⋲ . sœm+ 7 5 ∑ ® œm- œ ® œ˜ - œ˜ ® ® sœœœm̃m ® .œµ œœœmµ œœœ œœœmµm 5 .œ ≤ sœ˜ œm .œm ≤ sœ˜ œ œm sœµ ≥ Flz. P Í P P Flz. Flz. F pizz. pizz. arco arco F p p F F con sord. piccolo ord. g iss. g ss gliss. g ss. sans !n sans 96 && & V ? 42 42 42 42 42 82 82 82 82 82 83 83 83 83 83 42 42 42 42 42 Fl. Ob. Hn. Gtr. Cb. Ÿ~~~~~~~ 123 ∑ ∑ œ Œ Œ ⋲ œµ œ œ œ˜ œm æ œm ≥> .œn 5 p f ß-p ⋲ ssœ' œ . .œ' ⋲ ssœ' œ . .œ' ‰ ® œm æ+ œæ+ 6 sœ˜ œ œµ . œm> œ œµ> œ œm . . Sœ ® p p Í Í Flz. p π senza sord. œm> .œm - œ œm Æ œmæ œmæ œ æ œæ œæ 7 5 œm> .œ- œ œm ' œn æ .œæ œ˜ æ œæ 7 5 œæo œæ+ œæo . .œæ+ .œæ+ .œ æo œm æ+ ⋲ . 6 5 7 œ˜> œµ œn œ œ. œ˜ œ œ> ⋲ 3 Sœ˜ ≥> Sœ œ œ .œ˜æ 5ß-p pizz. arco Fz p P P P p p Flz. Flz. SS œæ ⋲ ‰ ‰ sœæ ⋲ ‰ ‰ ‰ . .sœ œœœœœ˜ µ µ           sœœœœœ˜ µ µ ⋲ œµ o œn o3 3 œµ sœ ‰π T π P Íp ∑ ∑ sœ ‰ Œ sœœœœœœµ ˜ µ mm ‰ sœœœœœœµ ˜ µ mm sœœœœœœµ ˜ ˜ mm ∑ & p g s s gliss sans !n sans 97 &? ? V & 85 85 85 85 85 85 44 44 44 44 44 44 Cl. Bsn. Tbn. Gtr. Cb. 128 œ œ œm œ œµ œm œ˜ œµ ⋲ . .œµ æ œm> ⋲ Œ ∑ œ˜ œµ œ œ œ œ˜ œ œ œ œµ œµ œ œµ œ œ œ˜ œ œ œ˜ œµ œ œ œ˜ œ œ œ œ œn œµ œ œ œ˜ œ œ˜ œ œ 9 9 9 9 ⋲ . .œæ œ Æ ⋲ Œ ? π cresc. f p Fç scratch tone gradually increase bow pressure p çF Flz p p f f ∑ ∑ ∑ ˙ ˙ œ œ œ 3 ∑ ∑ f ∑ ∑ Œ ‰ ® .SSœ œ˜ .œ œ œ ∑ wæ Œ ˙m œ .œµ∏ on the bridge p espressivo i i RH π tasto sans !n sans 98 && & ? ? V ? 89 89 89 89 89 89 89 83 83 83 83 83 83 83 89 89 89 89 89 89 89 Fl. Ob. Cl. Bsn. Tbn. Gtr. Cb. 131 ∑ Œ ‰ ŒU ⋲ . . SSSS œm Æ œ. œ. ⋲ Ù SSSSœn Æ ⋲ . œ. œm . œm . œµ . ⋲ . Œ ‰ ŒU ⋲ . . SSSS œµ Æ œ. œ. ⋲ Ù SSSSœm Æ ⋲ . œ. œ. œ˜ . œm . ⋲ . Œ ‰ ŒU ⋲ . . SSSS œÆ œm . œµ . ⋲ Ù SSSSœm Æ ⋲ . œ. œ˜ . œ˜ . œ. ⋲ . œ œµ .œ Sœ ‰ Œ U Œ Œ sOœœµµ ‰ ‰ sœm sœµ U ‰ sœ sœ˜ ‰ sœ sœ˜ ‰ Sœ SSœ ⋲ ‰ ‰ Œ Œ ‰ . SSœ ≤ 5 vib. p π π π P espressivoord. ⋲ . œ- œm œÆ œµ œ˜ ∑ ∑ ∑ ∑ ‰ ‰ œµ - œ˜ œ 3 œ œ œµ piccolo P p6 5 4 œ œ. œn œm - ⋲œ œm - SSœ ⋲‰ ‰ Œ Œ Œ Œ ‰ œµ - œm ® œm - œm œm œµ ® œÆ ⋲ Œ 3 3 3 Œ Œ ‰ œm - œ œm œn ® œm Æ ® œµ - œm œ œÆ 3 3 3 Œ Œ ‰ œ ® œ- œ œµ œµ ® œm - œ⋲ ‰ sœ' 3 3 3 ∑ œ œ œm œ œm œm œ sœm ssœµ . ⋲ ssœœœµnm . ⋲ ssœœœ˜nµ . ⋲ 3 3 Sœm ‰ Sœœmµ œµ œ sœ œm ssœ ⋲ ‰ Œ Œ F p p p π F P p π p p p Í Íp 2 4 2 4 2 to "ute sans !n sans 99 & & ? ? V ? 85 85 85 85 85 85 82 82 82 82 82 82 83 83 83 83 83 83 44 44 44 44 44 44 42 42 42 42 42 42 Ob. Cl. Bsn. Tbn. Gtr. Cb. Ÿ~~~~~~ Ÿ~~~~~~ Ÿ~~~~~~ Ÿ~~~~~~ Ÿ~~~~~~ Ÿ~~~~~~ 134 ⋲ ssœ' sœm ' Œ U ‰ Sœ ‰ ŒU ‰ ssœ ⋲ ‰ Œ U ‰ ∑ sœµ sœm ‰ sœµ sœ˜u Œ ∑ FzÍ vib. ∑ ∑ ∑ ∑ sœœœµµm ® .œµ œœœ 5 ∑ p ∑ ∑ ∑ ∑ sœœœ œ˜ œ œm œµ o 3 ∑ & Œ ⋲ œ' œ œµ œ œ' ®. œ' .œ Œ 3 5 Œ ⋲ œm Æ œ œ œ œÆ ⋲ . œÆ .œ Œ 3 5 Œ ⋲ œµ Æ œ œm œ œÆ ⋲ . œµ Æ .œ Œ 3 5 Œ ⋲ ® œµ œµ œµ œ œ œ œ Œ 5 S O œµ ˜ ‰ Oœµ ˜ O œ µ œœœµ œ œœ ˜ œ œœœn µ œœœœ ˜ ‰ 3 5 Ó Œ ‰ œ œ œ œ Sœ o π p con sord. ∏ ∏ ∏ espressivo ∑ ∑ ∑ ∑ œµ œ˜ œµ œµ œ˜> œ˜ œm œ Oµ3 œ œ œm≥? P ç-P g iss & V ? 83 83 83 82 82 82 83 83 83 Fl. Gtr. Cb. 139 ∑ ® œ œm œ˜ œm . œµ o œ. œo œm . œµ o œ. œo œ. œo 6 œ œµæ œm æ œ˜æ œnæ œµæ ® 6p punta arcovib. F ∑ œµ œµ œµ œ˜ œ œ œ œ ∑ r R 6 5 q. RH pont. p ⋲ ® SSSœµ - œ œm œm œ œµ µ œ œ˜ m œœm ‰ 3 ∑ π ord. p espressivo "ute œ œn œ œ œ> œn œb - ⋲ œ œn - S œœœœœB µ µ m Œ ∑ π π p sans !n sans ª ª 100 & & & ? & & V ? 89 89 89 89 89 89 89 89 89 82 82 82 82 82 82 82 82 82 85 85 85 85 85 85 85 85 85 83 83 83 83 83 83 83 83 83 Fl. Ob. Cl. Bsn. Hn. Tpt. Gtr. Cb. Ÿ~~~~~~~~~~~~~Ÿ~~~ Ÿ~~~~~~~~~~~~~Ÿ~~~ Ÿ~~~~~~~~~~~~~~ Ÿ~~~~~~~~~~~~ Ÿ~~~ 143 SS œ ⋲ Œ Œ Ó ∑ ∑ ∑ ∑ ∑ ∑ œ œ œm œ œm œm œ sœm ssœµ . ⋲ ssœœœµnm . ⋲ ssœœœ˜n . ⋲ 3 3 Sœm ‰ Sœœmµ œµ œ ∑ p π ∏ ∑ ∑ ∑ ∑ ∑ ∑ ‰ ssœ> ⋲ œœœœœœµm µ ˜                   sœœœœœœµm µ ˜ ⋲ œµ œµ 3 ∑ R f ƒ p f Œ Œ ⋲ SSœµ Æ Œ Œ ⋲ SSœÆ ‰ ⋲ SSSœ Æ œ œµ> œ œ˜ . ®. SSœ SSœ ⋲ 3 5 Œ Œ ⋲ SSœ˜ Æ ‰ ⋲ sssœ' œ œ> œ œ. ®. .ssœµ ssœ ⋲ 3 5 ‰ ⋲ SSSœµ Æ œ œm> œ œµ . ®. .ssœ ssœ ⋲ 3 5 ∑ œ œµ œ œ œn œ œµ œm œµ œm œ˜ œ˜ sœœœµ sœœœœµmµ 5 ‰ ⋲ ® œ≤ œµ œ œµ œ œµ œ œn œm œ˜ œµ 5 5 p con sord. p con sord. π π pizz arco π π p π π ord. ∑ ∑ ∑ ∑ ∑ ∑ ∑ œm œ œ œ œ œ œ œµ> 3 S œ Œ sans !n sans 101 && ? V ? 89 89 89 89 89 44 44 44 44 44 85 85 85 85 85 Hn. Tpt. Tbn. Gtr. Cb. 147 Œ Œ ‰ ⋲ . . ssssœm> œ. œ. ⋲ Ù ssssœµ> ⋲ . œ. œ. œµ . œµ . ⋲ . Œ Œ ‰ ⋲ . . SSSS œ> œµ . œµ . ⋲ Ù SSSS œ> ⋲ . œ. œ. œ. œµ . ⋲ . Œ Œ ‰ ⋲ . . SSSS œ> œm . œ. ⋲ Ù SSSS œm> ⋲ . œ. œµ . œµ . œµ . ⋲ . ® œœœœœ˜ µ µ             sœœœœœ˜ µ µ Œ ‰ sœœœœœ˜ µ µ ‰ sœœœœœ˜ µ µ ‰ 5 ∑ T con sord. π π π con sord. con sord. π p ∑ ∑ ∑ ⋲ œ˜ œµ œ œ˜ œ œµ .œ> œ œm œ œ˜ œ œm œm œ œm 10 9 ∑ p F 4 5 œµ - œm ® œm - œm œm œµ ® œn ' ⋲ Œ ⋲ ssœm 3 3 3 œm - œ œm œn ® œm ' ® œµ - œm œm œ Sœ 3 3 3 œ' ® œ- œ œµ œµ ® œm - œ ⋲ ‰ sœµ ssœ ⋲ 3 3 3 sœµ sœœœmn sœœµµ Œ sœœ˜µ Œ ‰ ® . SS œ≤ S œµ f Í Í Ípp p p p π 5 2 3 4 senza sord. senza sord. senza sord. sans !n sans 102 ?& & ? V ? 44 44 44 44 44 44 85 85 85 85 85 85 Bsn. Hn. Tpt. Tbn. Gtr. Cb. 150 ∑ .œ Œ .œ Œ .œµ Œ ® œœœœœ˜ µ µ             sœœœœœ˜ µ µ ‰ sœœœœœ˜ µ µ ‰ 5 S œ .œ> œ œ œ œµ .œ Sœ Íp Íp π T ‰ ˙ ˙ ‰ ˙ ˙ ∑ ∑ œµ œ œ œ œm œm œµ œ˜ œ˜> œ œ œ œ> œ œ œ œ> œ œ œ œ> œ œ œ œn> œm œ œ˜ œµ> œm œ œ 5 ∑ p F P P ∑ ∑ ∑ ∑ ˙µ o ˙m o ˙˜ o 3 ∑ ∑ ∑ ∑ ∑ ⋲ œœœœœœµ ˜ ˜                     sœœœœœœµ ˜ ˜ ‰ sœœœœœœµ ˜ ˜ 6 ∑ T π p sans !n sans 103 && ? & & ? V ? 42 42 42 42 42 42 42 42 82 82 82 82 82 82 82 82 42 42 42 42 42 42 42 42 83 83 83 83 83 83 83 83 Fl. Ob. Bsn. Hn. Tpt. Tbn. Gtr. Cb. 154 ∑ ∑ œµ œm œ˜ œn œ œ œm œ ∑ ⋲ . .œµ æ œ> ⋲ Œ œ˜> œµ œ œ œ œ˜>œ œ œ œµ> œ œ œµ>œ œ œ˜>œ œ œ˜> œ œ œ œ˜>œ œ œ œ œn>œ œ œ> œ˜ œœœ œ 9 9 9 9 ⋲ . .œæ œ Æ ⋲ Œ p çF Flz. p p f f p çF gradually increase bow pressure scratch tone p con sord. ∑ ∑ œ˜ œ œm œ ∑ ∑ Sœµ > œµ œ œ œ sœ ˝ ∑ p p ƒ œ. ⋲ œm . ⋲ œm . ⋲ Œ 6 œm . ⋲ œµ . ⋲ œ˜ . ⋲ Œ 6 ∑ ∑ œ˜ . ⋲ œ. ⋲ œ. ⋲ Œ6 ∑ œµ œ˜ œµ œµ œ˜> œ˜ œm œ Oµ3 ∑ π π π con sord. p F ssœm ' ⋲ Sœ ‰ ssœµ ' ⋲ sœm ‰ ∑ ∑ ssœµ ' ⋲ sœ˜ ‰ ∑ œµ œµ o œ œo œ œo œ œo œ œo 5 ∑ P P P p F p F p F sans !n sans 104 && & V V 82 82 82 82 82 83 83 83 83 83 82 82 82 82 82 83 83 83 83 83 82 82 82 82 82 42 42 42 42 42 82 82 82 82 82 Fl. Ob. Tpt. Gtr. 158 ⋲ . . SSSS œm . œµ - œµ ⋲ . ⋲ . . SSSS œµ . œµ - œ˜ ⋲ . ∑ ∑ ⋲ œµ> œ˜ œµ œµ p p F F p Ù SSSS œ˜> ⋲ . ‰ Ù SSSS œµ> ® ⋲ ‰ Ù ssssœµ> ® ⋲ ‰ ∑ sœœœmm œœmm œµ o œµ œ˜ S Sœ ß ß ß F to piccolo ∑ ∑ ∑ ∑ œµ œµ œµ œ˜ œ œ œ œ r R 6 5 q. p dampen U3" ∑ ∑ ∑ œµ o> ‰ ‰ SS œo> 3 œœµ æ 6 3p 5 4 F F XII ∑ ∑ ∑ sœ ˙m o > 5 .œ sœœµ æ œœmµ æ 2 ∑ ∑ ∑ œ sœ˜ o>3 ‰ œo> 3 œœµ æ ssœœ˜ æ 5 1 VII VII 3 ∑ ∑ ∑ ˙ ‰ .œm o> œœ˜ æ œœm˜ æ 2 ∑ ∑ ∑ sœ ‰œ œœm˜ æg ss ? V 85 85 44 44 42 42 83 83 Bsn. Gtr. 166 ‰ SSœm œ œ .œµ œ .œ œ>3 ‰ œµ œµ œ˜ œm> œµ œµ œ œ> œ œ œ œ> œ œ œ œn œ. ® ⋲ 3 espressivo p π œ œm œ˜ ˙ œ œ œm ⋲ œ˜ œµ œ œ˜ œ œµ .œ> œ œm œ œ˜ œ œm œm œ œm 10 9 p P œ œm ⋲ sœœœœœœµ B ˜ mm L ⋲ Œ p ∑ œœœœœœµm ˜ µ m         ⋲ œœœœœœmµ         ⋲ 3 3 π sans !n sans ª ª 105 && & ? V ? 82 82 82 82 82 82 83 83 83 83 83 83 42 42 42 42 42 42 44 44 44 44 44 44 Fl. Cl. Hn. Tbn. Gtr. Cb. Ÿ~~~~~~~ 170 œ˜æ œmæ œµæ œ˜æ œmæ œµæ 3 3 œæ œµ æ œm æ œ˜ æ œæ œµ æ 3 3 ‰ .œm œ Œ Sœµ 3 ∑ ‰ Sœµ œµ Flz π F π Flz π F π F P ß p piccolo con sord. con sord. ord. ∑ ∑ œ .œ> ‰ ‰   sœm ‰ ‰ œœœmmSœ ∑ p Íp P ∑ ∑ ∑ ∑ œœmm œµ œµ œ˜ ® œ˜ œ˜ œm œm œ œ˜ œµ œµ 9 œ ∑ ∑ ∑ ∑ ∑ sœœµ ‰ S œœœœm µm ‰ ∑ p ∑ ∑ ∑ ∑ sœœµ ‰ sœ˜ sœmu ‰ sœ Sœ U ‰ sœm sœ˜u ‰ ∑ vib. vib. vib. π gliss. gliss. g ss. V 82 83 82Gtr. 175 ∑U 3" œµ> œµ œ œ˜> œ œ œ˜> œ œ œµ œm œm œ˜ œµ> œn œµ œ 9 p sœœœœœœµ ˜ µ m L Œ f ⋲ œœœœœœµµ µ                     ‰ 6 P ‰ sœœœmm p ‰ sœœœœœœµ ˜ µ m π Œ sœœœœœœµ ˜ µ m 3 T ∏ sans !n sans ª ª 106

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