Page  426 ï~~ _ILME 2012NON-COCHLEAR SOUND LJUBLJANA _9.-14. SEPTEMBER Digital adaptions of the scores for Cage Variations I, H and I Lindsay Vickery, Cat Hope, and Stuart James Western Australian Academy of Performing Arts, Edith Cowan University ABSTRACT Western Australian new music ensemble Decibel have devised a software-based too/ for creating realisations of the score for John Cage's Variations I and I. In these works Cage had used multiple transparent plastic sheets with various forms of graphical notation, that were capable of independent positioning in respect to one another, to create specications for the multiple unique instantiation of these works. The digital versions allow for rea/-time generation of the specifications of each work, quasi-infinite exploration of diverse realisations of the works and transcription of the data created using Cage's methodologies into proportionally notated scrolling graphical scores. 1. INTRODUCTION John Cage's eight Variations (1958-67) occupy a unique position n the composer's output. By the late 1950s, Cage had made significant progress in exploring the use of indeterminate sound sources (such as radio and LP recordings1), a range of chance procedures for generating notation and indeterminacy of notation3. His attention now turned towards the indetenninacy and "flexibility" of formal structure itself "a way to further the diversity and flexibility of his compositions by removing the fixity of the score itself" [28]. The eight Variations were the principal vehicle for the exploration of this idea constituting nearly a quarter of his compositional output during this period. Following the completion of Variations VIII, the most open of the works in every respect, Cage returned, for the most part, to more traditional compositional outcomes marked by his exploration of the "recomposition" of pre-existing 4 works. aearly example is Credo in US (1942) [34]. 2 These included the use the I Ching as a source of aleatoricism in Music of Changes (1951) [29 pp. 78-88], "found systems" such as "folded paper templates" in Music for Carilion No. I (1952) [29 p. 92] and the "paper imperfection technique" in Music for Piano (1952-6) [29 p. 94]. Cage's use of Astronomical maps as "found systems" dates from Music for Carllion No. 4 (1961) [29 p. 211] and was incorporated in Variations V (1965). SCage's explration of indeterminate notation began in Music for Piano (1953) and culminated in 1958 with the magnum opus Concer for Piano and Orchestra, [29 p. 109], [33 p. 132], [2]. 4 Examples ae recomposition of pitches of Satie's Socrates (1918) in C'hea Imitation (1969) [4], "subtraction" of matedil from anthems and congregationa music Apartent House 1776 (1976) and 'tubbing" of Satie Chorales in Song Book (song 85) [27]. Over the ten years from 1958 to 1967, Cage revisited to the Variations series as a means of expanding his investigation not only of nonlinear interaction with the score but also of instrumentation, sonic materials, the performance space and the environment The works chart an evolution from the "personal" sound- world of the performer and the score, to a vision potentially embracing the totality of sound on a global scale. Table 1 gives a summary of the evolution of Cage's approach to the score, sound sources and the performance space in the Variations series. Score specification sound sources performance space 1 (1958) instruments quasi determinate sound II producing unspecified (1961) prous means III indeterminate actions (1963) score actions sound IV topographcal poung (1963) map means means V astronomical (1965) charts electronic sound system soundsystems 19 component integrated diagram VII real-time (1966) sounds remarks [13] "silence VIII (ambient sounds) Table 1: A summary of Variations I to VIII. Although Decibel created digital versions of Variations I-VI this paper focuses upon the digital realization of Variations I1 I and III, works that employ multiple transparent plastic sheets inscribed with either points lines or circles, for the purpose of creating a unique score for a performer to read The instructions read "as though there were a drawing of the controls available and - on transparency - transcription from astronomical atlas which (if it were superimposed) would give suggestions for use of controls" [12]. Variations IV-VIgenerate specifications for the placement of sounds in the space, for electronic controller variables and for the assembly of electronic components in the space respectively.

Page  427 ï~~ 1KM [2 012 NON-COCHLEAR SOUND LJUBLJANA 9.-14. SEPTEMBER There is relatively strong documentation of the evolving non-digital performance practice of the Variations as performed by David Tudor (Variations 11-1961 [30], [31], [22]), John Cage (Variations 1/I-1963 [28]), John Cage, Merce Cunningham et al (Variations V-1965[26], [19]), David Miller (Variations I and 11-2003 [24]),.zoviet (*france:, Wand, and Tanaka (Variations V1 -2008 [1]). Traditionally, the realisation of Variations I and 11 in particular has necessitated time-consuming manual measurement and collation of multiple coordinates. In 2006 digital versions of Variations 11 were created independently by Nicholas Knouf and Pierpaolo Leo (Variations 11-2006 [20], [23]). Both of these adaptations were "installation"-based, in that they generated both the score and a sonification of the score for viewers to manipulate in an art gallery, rather than scored materials for live performance. The impetus behind Decibel's realisation of these works has been principally performative: to create practical tools for the realisation of these works that retain both the indeterminacy and the precision of the Cage's specification. 2. VARIATIONS I AND H In Variations I and I, Cage's materials generate what might best be described as a blueprint for the creation of a determinate score. (Miller describes them as "toolkits" [23 p. 21]. Although Cage states that the score resulting from the application of "rules" of this work may be "simply observed" by the performer, there are significant challenges involved in actualising Variations I or // in this way (as will be discussed below). At first glance these works appear to be a deconstruction of traditional score, with only the five stave lines and the noteheads remaining and left to float freely in two dimensions. The lines and points are in fact used by the performed to generate a unique score, in which the distance of each point from each line determines one of five musical parameters: frequency, duration, amplitude, timbre and point of occurrence. James Pritchett identifies the "BV" notation from Cage's Concertf/r Piano (1958), illustrated in Figure 1 as the origin of this approach [29]. The connections between the "paper imperfection technique" works such as Music Jor Piano (1952-6), in xwhich points representing events w ere spacially' located on the page at knots in the surface of the paper and to and the 'folded paper templates" of Ausic for Ccari/lion No. 1 (1952), in which points were notated at intersections between creases in folded paper, are aLso significant. In Varia/ion s I the notation is, more mobile, as the lines and points are printed on transparent sheets, howveer the "fixes the number and structure of events" is still fixed [289 p. 136]. Earle Brown's concep t of proportional notation [18], developed some years earlier, is taken it to its logical endpoint: here everything is measured. The ability to "read" the score in any orientation also draws on Brown's December 1952 (1954) which may be read in any direction (Left to Right, Top to Bottom, Right to Left, Bottom to Top). Tr EEAE (4 0 og $o I$,S LAsE(r4if3lps O -Leo D ), v' A AW. uoT(SJN6SonU. J8FE 5 m ES A' A TE o E Figure 1: The BV notation from Cage's Concert for Piano (1958) [6]. The precisely defined multi-parametrical nature of Variations I also suggests the influence of the integral serial methods of the European Avant Garde, which had dominated Cage's "chart" compositions [29 p. 78-90]. But most importantly, in these works Cage demarcates a new end point for the act of composition, leaving not only the interpretation, but also the final realisation of the works to the performer. The materials for Variations I comprise six square transparencies: the first printed with points and the other five printed with lines. Square 1 consists of 27 points of four sizes corresponding to the nurnber of sounds they represent as illustrated in Table 2. Square 1 27 Points No. of Sounds 13 Very Small 1 7 Small but Larger 2 3 Greater size 3 4 Largest 4+ Table 2: The contents of Variations I square 1 Each of the five additional squares is printed with five lines corresponding to the five parameters shown in Table 3. The performer may freely choose which parameter to apply to each line. Squares 2-6 5 Lines 1 ~ fr-equency 2 overtone structure 3 amplitude 4 duration 5 occurrence Table 3: Variations 1 Squares 2-6 showing the parameters to be assigned to each line. 427

Page  428 ï~~ A reading of the work is created by measuring the distance from each point to each of the five lines to generate a composite of parameters that define each event with the following attributes: number of sounds (I - 4+), frequency, duration. amplitude, timbre and point of occurrence. These attributes are relative with the continuum upon which the parameter is measured defined by the performer. For example: the point of occurrence of each event is relative to the total duration of the work (which is not defined by Cage). Figure 2 illustrates the measurement process required to define one event [16]. Indeterminate Frequency/Overtone/ open Amplitude Range Instrumentation open Total Duration/Event occurrence open Table 4: Determinate and indeterminate qualities of Variations L Variations II uses a similar system of dots and points, with some small but significant differences. There are six transparencies each with a single line and five transparencies each with a single point. The sixth line determines the structure of the musical event, whether it is a single sound, an aggregate or a constellation of sounds, the function that had been determined by the size of the points in Variations I. The orientation of the lines and points is therefore completely open, meaning that there are an infinite set of potential configurations of the score. A performance consists of any combination of configurations and therefore in theory Variations II may describe any possible musical work [24 p. 42]. In this sense it "represents the most flexible composition tool that Cage ever invented" [29 p..136]. d n Fitialec.. JN Cag,;tns r a1kmpoier a \ ii y. Pefra cy of Variaions I n II has",traiioal IXI inove neo\tre ehods:Isimply observmg [5] the rsultng scre, nnotaing n inttinoth scre[5[2] r rascibngthdtale mesreet ofanintntatonitoa prfrnnc coe"[4p.2] Fiue3annotated score o Variations]. Figure 2: For each event, five parameters (A-E) are defined by the measurement of the perpendicular distance from each point to each line. This procedure results in a mixture of determinate, permutable and indeterminate variables in Variations I. The number and position of the points and lines is fixed and there is a finite number of possible combinations and orientations of the transparencies, however the range of the continuum upon which each parameter is plotted is indeterminate. Table 4 illustrates the determinate, permutable and indeterminate factors involved in the generation of an instantiation of the work. Determinate No. Points/Sounds 27 Lines/Parameters 5 Min. no. of parameters 135 (27x5) Permutations Orientation of Points Square 8 Function of Lines 5! (120) Orientation of Lined Squares 8 No. of Lined Squares 5 Max. No. of Permutations 38400

Page  429 ï~~ derived from measuring perpendicular distances is evaluated and then used to generate a scrolling, proportionally notated screen-score. The score moves from right to left with the point of occurrence of each event, rendered as a horizontal rectangle, indicated by its point of contact with a vertical line or "play-head" on the left of the screen. In this way the score moves "towards" the performer from the right in the same direction as a traditional paper score. a\ Figure 4: Reading the score for Variations I in two dimensional arcs. The principal issue associated with "simply observing" or annotating the score, as can be observed in Figure 3, is that the notation on Cage's transparencies is twodimensional as opposed to traditional one-dimensional linear musical notation. To preserve the order of note occurrence, the transparencies must be read "twodimensionally" in arcs emanating from the line that determines "point of occurrence" as shown in Figure 4. The distances to the other four lines and calculation of their parametrical value must occur simultaneously. Figure 5: David Tudor's transcription of Variations II [301 Although David Tudor's realisation of Variations I relied on "careful definition of measurement scales and a precise performance score" [30 p. 2], James Pritchett shows that Tudor's version of Variations II reduced Cage's prescribed measurements to binary values: simple and complex. Figure 5 shows Tudor's transcription of two events from the work. Tudor's score overcomes the issue of reading multiple axes (the 50 events he used were aligned in rows), however its transformation of the multi-parametrical notation into single- or double-bordered squares with intersecting lines and circled or plain points is nearly as enigmatic looking as the original. 3. THE SCORE-READER FOR VARIATIONS I AND II The imperative of generating performance materials that are easily and intuitively read, led Decibel to a decision to transcribe the data created in Variations I and II, into proportionally notated graphical scores. In Decibel's realisations of Variations I and II the parametrical data Figure 6: Decibel's scrolling, proportionally notated screen-score for Variations I. The arrow indicates the direction of the scrolling score. Duration is represented proportionally by the length of the rectangle. The vertical position of the rectangle indicates its frequency, thickness indicates volume and shade indicates timbre. The number of sounds in each event is specified by a number attached to each rectangle. A portion of such a realisation is shown in Figure 6. The notation draws on conventions established in works by Cage and his colleagues Earle Brown and Christian Wolfe, as illustrated in Figure 7. lrtic a. b. Figure 7: Graphical Notation Conventions drawn from a.) Cage Aria (1958) [8J - Timbre-Shade equivalence; b.)Wolff Duo for Pianists 1(1957) [35J - numbers representing the number of sounds in an event: c.) Brown Folio and 4 systems (1954) [5J Proportional Notation: length-duration and thickness-amplitude equivalence [2J, [17J, [311, [321 429

Page  430 ï~~ ILME 2012NON-COCHLEAR SOUND ___ LJUBLJANA _9.-14. SEPTEMBER This transcription enables a faster reading for performers using familiar symbols. In addition the graphics appear ahead of the 'playhead' givingthem time to consider their approach to the graphi cs. The score can be read by a single performer or multiple versions of the score can be generated for a group of performers networked to a master computer. A control panel (shown in Figure 8)allows for determinationof total duration of the piece as well as the relative duration of the events. The range of the continuums of frequency, amplitude and timbre indicated by the score is interpreted by the performer(s) on their own instrument The duration of the work effects the density of events on the score: for example a duration of 360 seconds will distribute the 27 events over six minutes. iriz=0; for (z = 0;z coords.leength; z++ g[0]z; storage.seteell(g 0, coords[z][6]); outle(0, "Finished'); And here we see the score player mechanism referencing a stored Jitter matrix of note values determining the note polyphony withina designated time frame: { irtthishroup=0; irtgouped= 1; inti = index-I val = times.getcell dloat(i)[0]; if (i> timesetDimQ[09{ i= (times. getDimQ[0])-1 for(int j (i+1l); <times.getDimQ[0]); j++) va2= times. getellI dFloatj)[0]; value = va12-vall; if (value < timesc ale) g ouped++; else if (value > timescale) break; outlet(2ti outlet(1, groued) grouped= 0; outlet(0, vall); 4. VARIATIO III In Variations 11, Cage moved to a significantly different score paradigm. Here the composer's focus was on actions rather than sounds. Tie score is created by distributing 40 circlesorinted on individual tasarenci es) onto a surfa ce and then removin g all but the largest gro up o f circles that are in direct contact with one another According to Pritchett, Cagets aim was to enable ftee and direct action in the performance - one Variatica2s 1I "included mtanging ele ctrical cords, putting on his g.asses, smoking a cigarette, writing a letter; and drinking a glass ofwater" [29 p.l149] Figure 8: The master controlpanel for Decibel's realisation of theCage Vo n The evaluation of the data to generate the scores of Vaw/athoer wr sIan12 and a component of the score player were itte in Java and ebedded within the MaMsP patch. The Jam code for Vratons andi and the score player mechanism efitten by Stuart James, and the Java code fr V ariations III was rittn by Aaron Wyatt. There were several advantages for re-implementing these processes in Java. One of these Was the ability to access the same memory space that Max!? SP is pointing to, namely Jitter matrices, b utilizing the Java Jitter API. This marrying o f both Java an d Jitter processing proved to be an efficient wy of accumulating, toring, and sorting tables of values required fr building no te events in Vraiowns d 1IT For example here we see values stored into a Jitter matrix that are generated recursively in an earlier section of code: 430

Page  431 ï~~ 1KM [2 012 NON-COCHLEAR SOUND ___ LJUBLJANA 9.-14. SEPTEMBER For this purpose there were advantages for implemention in a procedural language like Java by making use of recursive function calls. This proved to be significantly faster to process this way than using a scheduled message environment like Max. The calculations were made in the following way: for (int j = iÂ~ 1; j circles.length; j++) { double distanceSquared= pow(circles[i].getX() circles[j].getXO, 2) + pow(circles[i].getYO - circles[j].getYQ, 2); double distance = sqrt(distancesquared); if (distance <= (inlets[3] * 2)) if (circles[].getGroup = 0) { circles[j].setGroupcircles[i]getGroup); else if (circles[j].getGroupQ circles[i].getGroupQ) { for (int k 0; k <circles.length; k++) { if (circles[k].getGroupQ circles[i].getGroupQ &&k! i) { circles[k].setGroup(circles[j].getGroupQ); circles[i].setGroup(circles[j].geteroupO); Recursion was used repeatedly throughout all implementations of the Variations. It also proved advantageous to declare all coordinate values in the Java code, rather than in the usual data structures used in. MaxMSP such as the coil object. Figure 9 shows four instantiations of Variations III created by the Decibel scoreplayer, illustrating the sequential fading of all but the largest overlapping group. In this realisation no adaptation of the two-dimensional layout of the score is made. It would be possible for example to "unwind" the circles along an arbitrarily determined axis, while retaining the points of intersection with other circle, in order to create a linear horizontal score. However, whereas the materials of Variations I and II give rise to a linear series of events and are therefore most appropriately rendered as a linear score, Variations III specifically evokes the indeterminacy of the two-dimensional score itself Cage instructs the performer to "start at any circle" and "move on to any circle" only requiring the performer to "observe the number of circles which overlap it" [10]. This realisation then, simply provides the means to (very quickly) re-generate the score, until they are content with the resulting graphic, while retaining the indeterminate latitude that Cage affords the performer in the original score. 5. CONCLUSION Rendering these works digitally annuls two diametrically opposed arguments often raised against nonlinear indeterminate works such as the Variations I, II and HI. On one hand, since the audience always hears the works in a linear fashion sequentially in time there is always the question that the indeterminacy is somehow "fake" that the performers arranged it before hand. In addition such works sometimes provoke in the audience the notion that the performers are themselves "making it up" because "the there is no way to detennine whether they are accurately reading the score. The precision provided by the score-players for Variations I and II, arguably lends legitimacy to the performance, because the score that is created is both "accurate" to a reasonable degree and easily read by the performers in a verifiable manner. On the other hand, such works are sometimes criticised on the grounds that potential existence of other versions implies that the particular one that is being performed might not be the best exemplar of the work. The ability to almost instantaneously generate multiple versions of the work, as demonstrated in Variations III provides the opportunity to choose interesting and promising instantiations of the work. We have attempted to be as authentic as possible to the specifications Cage prescribed in these three works, using technology to provide a platfonn that is precise and accurate in its realization while still leaving open the human element of interaction with the score. As Miller expresses in regard to "authenticity" in the perforrnance of these works: Cage's formal statements (..) should be taken as points of departure and of periodic return in the course of developing realizations. They are the documents that express, however enigmatically at times, the works' potentials and particularities [25 p. 64]. Figure 9. Four instantiations of Variations III created by the Decibel score-player, showing the superfluous circles in various stages of fading. 431

Page  432 ï~~ ILME 2012NON-COCHLEAR SOUND __ LJUBLJANA _9.-14. SEPTEMBER REFERENCES [1]:zoviet(*france:, Wand, M., & Tanaka, A. (2008). Variations VII by John Cage [2] Behrman, D. (1976). What Indeterminate Notation Determines. In B. Boretz & F. T. Cone (Eds.), Perspectives on Notation and Performance (pp. 74-89). New York: Norton. [3] Bernstein, D. W. (2001). In Order to Thicken the Plot. In D. W. Bernstein & C. Hatch (Eds ), Writings through. John Cage's Music, Poetry and Art. Chicago: The University of Chicago Press. [4] Bernstein, D. W. (2001). Techniques of appropriation in music of John Cage. Contemporary Music Review, 20(4), 71-90. [5] Brown, E. (1954). Folio and Four Systems, New York: AMP! Schirmer [6] Cage, J. (1958). Concert for Piano. New York: Henmar Press. [7] Cage, J. (1960). Variations I. New York: Henmar Press. [8] Cage, J. (1960). Aria. New York: Henmar Press. [9] Cage, J. (1961). Variations II. New York: Henmar Press. [10] Cage, J. (1963). Variations III. New York: Henmar Press. [11] Cage, J. (1963). Variations IV. New York: Henmar Press. [12] Cage, J. (1965). Variations V. New York: Henmar Press. [13] Cage, J. (1966). VariationsVI. New York: Henmar Press. [14] Cage, J. (1972 [1966]). VariationsVll. New York: Henmar Press. [15] Cage, J. (1978 [1967]). Variations VII. New York: Henmar Press. [16] DeLio, T. (1981). John Cages Variations II: The Morphology of a Global Structure Perspectives of New Music, 19(1/2), 351-371 [17] DeLio, T. (1981. Sound, gesture and symbol The relation between notation and structure in American experimental music. Interface, 10(3-4). [18] Gresser, C. (2007). Earle Brown's 'Creative Ambiguity' and Ideas of Co-creatorship in Selected Works. Contemporary Music Review, 26(3), 377 - 394 [19] Hoover, E. (2010). Variations V: "Escaping Stagnation" Through Movement of Signification. Current Musicology, 90(Fall), 61-79. [20] Knou, N. (2006). Variations 1Ob: A Digital Realization of Cage's Variations II Paper presented at the MM'06 Santa Barbara. [21] Kopatchinskaja, P. (u.d.). CAGE, John (1912 - 1992): Variations I(1958) from http:// T.patkop.ch/cagetxt.htm [22] Kuivila, R. (2004). Open Sources: Words, Circuits and the Notation-Realization Relation in the Music of David Tudor Leonardo Music, 14, 17-23. [23] Leo, P. (2006). VARIATIONS II: sound installation by Pierpaolo Leo from http1www.pierpaololeoit/interactiod/variationsh rtm [24] Miller, D. (2003). The Shapes of Indeterminacy: Joh Cage's Variatiorr I and Variations II. FZMw, 6, 18-45. [25] Miller, D. (2009). Indeterminacy and performance practice in Cage's Variations, Aerican Music, Spring, 60-86. [26] Miller, L. (2001). Cage, Cunningham, and Collaborators: The Odyssey of Variations V. The NMusica Quarteriy, 85(3), 545-567. [ 27] Nicholls, D. (2002). The Cambridge Companion to John Cage. Carnbridge: Cambridge Universit Press. p. 137) [28] Pritcheft, J. (1988). Chapter 6: "The Ten Thousand Things" (1953-1956), [excerpt from his PhD Thesis "The development of chance techniques in the music of John Cage, 1951-1956"], from http://xw.rosewhitemusic.com/cage/texts/DissCh6.html [29] Pritchett, J. (1996). The Music of John Cage. Cambridge: Cambridge University Press. [30] Pritchett, J. (2001). David Tudor as Composer/Performer in Cage's Variations II. Paper presented at the The Art of David Tudor, Getty Research Institute. [31] Pritchett, J. (2001). Audio and Video: Variations 11(1961) from http://ww.getty. edu/research/tools/guides bibliographies /davidtudor/av/variations.html [32] Shultis, C. (1995). Silencing the Sounded Self: John Cage and the Intentionality of Nonintention. The Musical Quarterly, 79(2), 312-350. [33] Thomas, P. (2007). Determining the Indeterminate. Contemporary Music Review, 26(2), 129-140. [34] Tone, Y. (2003). John Cage and Recording. Leonardo Music, 13, 11-15. [35] Young, L., & Mac Low, J. (1963). An Anthology of Chance Operations. New York: Jackson Mac Low. 432