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Sound gesture and symbol The relation between notation and structure inAmerican experimental musicThomas DeLioaaDept. of Music, University of Maryland, College Park, Maryland, USA

To cite this ArticleDeLio, Thomas(1981) 'Sound, gesture and symbol The relation between notation and structure inAmerican experimental music', Journal of New Music Research, 10: 3, 199 219

To link to this Article: DOI: 10.1080/09298218108570338URL: http://dx.doi.org/10.1080/09298218108570338

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Interface, Vol. 10 (1981) pp. 199-219.

Sound, Gesture and SymbolThe Relation between Notation and Structure in AmericanExperimental Music

Thomas DeLio

ABSTRACTThis is a study of notation in recent m usic. Central to this exploration is the idea that, w ithrespect to much recent music, what composers notate are the activities associated with thecompositional process rather than the sonic remnants of that process. Two categories ofstructure and notation are defined and explored - behaviorism and pluralism. Works in theformer category which are studied are Christian Wolff;s F or 1, 2 or 3 P eopleand RobertAshley'sin mem oriam... Crazy Horse;works in the latter category, Pozzi Esco t'sNeyracLux and John Cage'sVariations II .

The radical nature of many of the new notational systems employed in themusic of the 60's and the 70's lends particular insight into the character of theirunique aural resu lts. With respect to much of this recent m usic, a study of th enotation employed can often supply valuable insight into many of the fun-damental premises upon which a composition's structure rests. As attitudestoward materials and morphology change, it has become imperative thatcomposers seek new methods by which their works may be no tated, therebyenabling the accurate and detailed modelling of many revolutionary conceptsof structure. Indeed, it has become apparent that "very often the notationsthemselves are the determining factors in the composition of a piece and hencethe piece's identity and structure". (Cardew, 1971, p. XV).The multifarious outpouring of new notational schemes in recent years is,

Manuscript received November 1980

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2 0 0 THOMAS DELIOof course, only a reflection of the amazing diversity of recent compositionalpractice. In fact, much of the impetus for recent explorations in the area ofnotation stems from the ongoing re-evaluation of our most basic notions ofstructure and the particular problems in charting, symbolically, the innova-tions which this re-evaluation engenders. Specifically, with respect to a greatdeal of new m usic one finds tha t activities which were once viewed as pre-com -positional and outside the realm of structure are now being integrated directlyinto a composition's framework. The very concept of musical notation hasbeen extended, then , to include not only the symbolic representation of formbut also the delineation of all the compositional methodology from which suchform issues.

More and m ore the composer finds himself facing the problem of no tatingthe activities of composition rather than any specific sonic results. It is thisconcern which links the notations of such diverse works as Iannis Xenakis'Linaia-Agon (1972), John Cage's Cartridge M usic (1960), and KarlheinzStockhausen'sSpiral (1968). In each of these works the activities of makingand shaping are externalized in some way and integrated into the very n otationof the composition.Two attitudes toward no tation will be discussed here, each of which revealsa very different vision of musical structure as reflected in the nature of theactivities symbolized in the scores. The first deals with an exploration of therelationships apparent between the structure of an artwork and the patterns ofhum an behavior. This attitude is exemplified in those seminal works of Chris-tian Wolff written throughout the 60's and many works of Ro bert Ashley. Thesecond attitude deals with various notions of pluralism as exemplified in manyworks of John Cage and the recent works of Pozzi Escot.

I . BEHAVIOROne of the most striking aspects of Christian Wolffs music and one of thecentral issues guiding the development of his innovative notation is the tacitrecognition that the morphology of form is nothing more, nor less, than aresonance of the structure of human behavior. Through this notion he directlyand incisively confronts the traditional view of struc ture as embodied meaningor meaning externalized through behavior. For -

"Human behavior is neither a series of blind reactions to external "stimuli" nor theprojection of acts which are m otivated by the pure ideas of a disembodied, worldless mind.It is neither exclusively subjective nor exclusively objective but a dialectical interchangebetween man and the world... It is a circular dialectic in which independent beings of the

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2 0 2 THOMAS DELIO

two or three people may perform, using any instruments, one or m ore of thescore pages in any o rder. The instructions for performance read, in abridge-ment, as follows:

"Play all that is notated on a page , in any convenient sequence, not repeating anything...Black no tes are variously short, up t o about o ne second. W ith stems as sixteenth notesthey are very short. White notes are of any length, sometimes determined by the require-ments of coordination...A diagonal line towards a note = play that note directly after a preceeding one . Adiagonal line away from a note = that note must be followed directly by another.A vertical line down from a note = play simultaneously with the next sound (bothattack and release)...If a line to a note is broken by a number followed, after a colon, by a zero (-2 :0-)... thatnumber of seconds of silence intervene before the required coordination.-J = play after a previous sound has begun, hold until it stops.2~ = start anytime , hold till another sound sta rts, finish with it.L_,= start at the same time (or as soon as you are aware of it) as the next sound,but stop before it does.

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SOUND, GESTURE AND SYMBOL 2 0 3p = start anytime, hold till another sound starts, continue holding anytime after

t that sound has stopped.Horizontal lines joining two notes = a legato from the one to the other...Larger numbers on a line between notes: if black = that number of changes of someaspect(s) of the sound before reaching the next no te; in red = that number of changes ofthe timbre of the first note before reaching the next one...X = high in some aspect."1

Thus, for instance, the first symbol on the upper left side of page II,/ ?. t directs the performer to first play any loud sound; then, while holdingthat sound, to change two aspects of it (volume and timbre for instance); and,finally, to move smoothly (legato) to another sound which must be high insome way. In contrast, the symbol near the lower right corner of the pageJf \ directs the performer to play his first sound only after he hea rs one ofthe other players produce a sound. H e is to hold his sound until the other stops,ending as close as possible to it. In addition, while holding his sound he isinstructed to change one aspect of its character (for instance, it might getlouder or softer). After this first gesture is completed he is to move directly andsmoothly to another p itch which is itself to be followed directly by one moresound produced by himself or any one of the other players.

In listening to this music one is immediately struck by the fact th at severalrenderings of the same no tated gesture rarely, if ever, produce patterns whichare recognizably similar. "The complexities of this notation are directed lessat an arrangement of sounds resulting from the performer's actions than atthe conditions under which their actions are to be produced". (Behrmafi,1976,p. 89). Thus, the notated symbols never determine any particular me-lodic con tour nor any other specific type of sonic configuration. Rather, all thatis ever defined symbolically is a complex of interactions between the per-formers. As the composer himself puts it: "People sometimes ask, why don'tyou just specify what you want and be done with it? I do Actions areindicated..."2)

What one hears are the gestures themselves, gestures which are usuallytaken for granted as the means to an end but which are here drawn out as anend in themselves. Thus, for example, the idea of playing together () takes onimportance as an act initself.Each perform ance is guided by carefully mani-pulated behavioral patterns which do not generate products and, as such, do

') ChristianWolff For 1,2 or 3 People,(Peters Ed. N .Y. 1964), p. 1.2) ChristianWolff record liner notes, "John Cage and Christian Wolff (Mainstream Records,MS 5015), p. 2.

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2 0 4 THOMAS DELIOnot signify anything beyond their essential characterization as behavior. In thismusic one ceases to distinguish between signs and signifiers forms and thebehavior which engenders such forms. This work is not so much a constructionin sound as a situation of action and response defined abstractly throughsound. What is perceived as form is the ensemble of these interactions whilethe aural result is understood as merely one particular sonic projection of tha tform. Clearly, that "dialectical interchange" by which form and meaning areengendered is, in this music, embodied within the very substance of its audiblestructure.

It is significant, also, that, in Wolffs music those activities which arerepresented on the page are usually activities of coordination. In his worksactions are intimately tied to responses. First of all, within the framework ofFor 1,2 or 3 People it is quite probable that often, while one performer isresponding to another the third may be shaping his next gesture in response tothe first. Even m ore revealing is the fact that, by and large , the actions nota tedare themselves responses. In this the com poser identifies th e notions of action



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SOUND, GESTURE AND SYMBOL 2 0 5and response as inseparable. Actions are themselves responses which, in tu rn,generate further responses from others. Acting affects and is, at the same time,itself affected.

"The enigma is that my body simultaneously sees and is seen. Tha t which looks at allthings can also look at itself and recognize, in what it sees, the "oth er side" of its power oflooking. I t sees itself seeing; it touches itself touching; it is visible and sensitive foritself.Itis not a self through transparence , like thou ght, w hich only thinks its object by assimilatingit, by constituting it, by transforming it into thought. It is a self through confusion,narcissism, through inherence of the one who sees in that which he sees and throughinherence of sensing in the sensed..." (Merleau-Ponty, 1964, p. 162-163).Robert Ashley's orchestral composition in memoriam ...Crazy Horse(1964) suggests striking similarities to the Wolff score. Significantly, how ever,those ideas which both works share in common are dealt with in very differentways and therefore represented graphically through very different systems ofnotation. Two pages from the score are reprinted here (Figs. 3 and 4). Theinstructions read, in part, as follows:



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2 0 6 THOMAS DELIO"...for 20 or more wind or string or other sustaining instruments in five or more groupsof four or more instruments per group.The instruments of each group should be as closely related as possible.Each group plays from one page of the set of 32 pages. Beginning at any radius theplayers count around the circle allowing one unit of silence for each numbered radius. Asustained sound quality of the appropriate kind is called for upon reaching a radius onwhich there are number symbols. The inner set of symbols (inside the oval dot) allots adura tion to this activity. The ou ter two sets of symbols specify alternative radii from whichto proceed after this duration of activity. Each group decides in advance (in any manner)which direction or schedule of directions it will follow.The m easured units are given for the orchestra as a whole by the conductor and are

determined continually and freely by him.All numbers (durations and radii) are given in sums of the following symbols: = 1;~ = 5 ; o = 10.Individual performers determine what is to be played on the basis of their group'sobligation to produce a certaindensityof sound at a certain radius. Plans for assigningvarious radii or directions of movem ent to subtle differences in density can be worked outin advance. H owever, it will be sufficient if the performance involves only the two extremesof ensemble density: as pure (harmonious) as possible; (or) as noisy (dissonant) aspossible. Any division of the score into semi-circles can be interpreted to represen t thesetwo extremes of density.Individual performers should choose their sounds spontaneously and begin playing atthe beginning of a specified duration of activity. Within any dura tion, th en, as soon as allmem bers of the group are playing, individuals may continually adjust (change) the ir soundactivity toward achieving a better realization of the ideal density.The concept of "density" is intended here to include all aspects of the sound infor-mationproduced by the ensemble (group), not just density of harmonic spectrum. Thusthe term " pu re " means... unanimous, similar, redundant, synchronous, integrated, etc.,...in describing the perform er's actions (sounds) and implies (1) a lack of individuality amongthe parts and (2) a high degree of redundancy in successive actions . Conversely, the term"no isy" means... dispara te, dissimilar, chaotic, asynchronous, divided, etc.,... in describing

the perform ers' action (sounds) and implies (1) a greater individuality among the parts and(2) a high degree of moment to moment change in successive actions". (Ashley, 1967, p.42).For the purpose of clarification, the same two pages of score are again re-produced, an notated in such a way as to facilitate reading and interpretation(Figs. 5 and 6).First, it should be noted tha t the configuration of symbols within the largenum bered circle is exactly the same on both score pages . The only differencebetween these two pages is the placement of this inner configuration withrespect to the outer circle. For example, the configuration of symbols foundbeneath position seven on the numbered circle on page I is found beneathposition twenty-three on page II. All the configurations on page I are shiftedclockwise sixteen positions on page II.

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SOUND GESTURE AND SYMBOL 207

Symbols within the inner circle determine the duration of each soundactivity. These range from three unitsoftimeinlengthtothirteen unitsoftime.The symbols betweentheinnerandouter circles de term inethe twopossiblepositions alongtheouter circletowhichone maymove after performingagiven sound event.Asnothing concerning this mat terisstatedin thescoreit isassummed thatone maymove clockwiseorcounterclockwise alongtheoutercircle.

Forthepurposeof clarification, the following exampleisoffered. If anensemble withintheorchestraisreading pageI itmay beginon anypositionalongthenumbered circle.If itdoesnotbeginon aposition which has symbolsbeneathit theensemble proceedstomove silentlyineither direction untilitreachesonethat does.Let usassume thattheensemble beginsonpositionfifty-nine. It then moves clockwise, following the conductor's beat untilitreaches position sixty-four.Atthis po inttheensemble beginstoplayandmustcontinue playingfor sixunitsoftime. W hen this segmenthasendedthegrouphastwooptions.It maymove eithertoposition fortyor toposition twenty-eight alongthenum bered circle.If itchooses fortyitmust immediately playforsix unitsoftimeandthen proceedin amanner similartothat just described.Ifhowever,itchooses twenty-eight whichis asilent position ,itmay then p roceedin either direction alongthenum bered circle untilitreachesaposition withsymbolson it. Allmem bersof each ensemble must follow thesame routethroughthescore.Theensembles themselves, however, move independently.The scorehas twoparts:one theverbal instructions, determine,in averygeneralway thekindoftransformationsto beused;theother,thegraphicsymbols, co-ordinate the activities both withinandamong thegroups.Forexample,thecirclesinFigs.5 and 6have been bisected into semi-circlesto oneof which isassigned thequality ofpureorharmonious and theother,thequalityofnoisyordissonant.Assuch,onpageI anysound eventin theupperhalf isto beinterpretedasnoisyandany eventin thelower half as pure . Thus,ifan ensemble reaches position sevenitperforms for nine unitsoftimeandduring that period strivestomakeavery noisy sound.Ifafter thistheensemblemovestoposition thirty-sixitwill playforthirteen unitsandduring that timestrivetoplayavery pure sound.Significantly, theindicationsofnoisyandpuremay beinterpreted in avarietyofways:

pure vs. noisy(harmonious, simple) (dissonant, complex)unisons vs. dustersine tones vs. complex tones




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wide registral vs. close registralspacing spacingregular rhythmic vs. irregular rhythmic

patterns; one patterns; varyingdynamic level dynamic inflections

Concerning these notions of pure and noisy sound quality it is important torecall the composer's own comments on this subject in the instructions:"Both of these terms describe antipodal, "ideal" densities that the ensembletries toacW eved uring theco urseo faparticu lardura tionofa ctivity.. .it should be noted that it willdefeat the purpose of the performance to play detailed "realizations" of densities. Thepreparations for performance should exclude neither the fortuitous initial densities thatare the sum of the sound ingredients that the individual players have chosen spon-taneously, nor the process involved in the player's attempt to work in an ensemble towardthe "ideal" extreme." (Ashley, 1967, p. 42).



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SOUND, GESTURE AND SYMBOL 2 0 9

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2 1 0 THOMAS DELIOAny realization of this score must, first of all, be understood as an

exploration of the different ways in which these two ideal densities can beachieved by each ensemble of instruments and, ultimately, will be a com-mentary on the nature of both the types of instruments involved and thecharacters of those performing as they interact within the constraints of acontrolled ensemble situation. For example, an ensemble of violins or oboescan never achieve as pure a sound as an ensemble of flutes or recorders. Forone thing, at soft dynamic levels flute tones are reduced to a sine tone-likepurity which can never be approached by the other two instruments. Similarly,an ensemble of recorders can never produce as noisy a sound nor even thesame type of noisy sound as that of an ensemble of trumpets, the recorderbeing incapable of the violent dynamic contrasts nor the loud volume levelsavailable to the trumpet. Clearly, then , the nature of each type of instrumentwill be a major factor in determining the ways in which the ideal densities a rerealized and, moreover, will actually determ ine the limits and character of theimagined "ideals".

Another factor which directly affects the unfolding of the piece is theindividual capability of each performer in manipulating his instrument andinteracting within an ensem ble situation. His control over the instrument andhis ability to respond to the o thers in the ensemble as they together shape theirtotal ensemble sound will be of singular importance to the shape of eachperformance and, of course, will also dramatically affect the ensemble's abilityto achieve the quality of sound required.

Ashley's composition juxtaposes the different ensembles as they striveindependently to achieve their particular densities. Each sound event of thepiece begins with a random mass of sound and m oves toward one of the two"ideals". Each event captures, sonically, thestriving of some ensemble toachievea certain sound. As the initial sonority is sounded, each player begins toadjust his own playing in response to what the others are do ing. Of course, asnoted above, the ideals may each be realized in many different ways. So, thecharacter of the sound result achieved at the end of each sound event will bedetermined by the ways in which the members of the ensemble react andinteract with one ano ther as they guide each other and the whole toward somesort of realization of the ideal. Thus, each sound event is not so much a sonicshape asan unfolding interaction. The ideal itself is not so much of interest forits own sonic qualities. Nor, indeed, is the form the sum of a succession of suchsonorities. Rather, the ideal is a goal the repeated and varied strivings forwhich are, in the end, what are heard as form.

As the piece is about the striving for some unknown the notation is



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SOUND, GESTURE AND SYMBOL 2 1 1purposely ind eterm inate. Since it is a true ensemble piece, the activities of eachperformer must be coordinated an d, thus, the graph arises. As th e object is notso much the creation of a specific sound but the striving for a particular soundquality the composer resorts to a rather suggestive verbal description inti-mating the qualities toward which the ensemble is to propelitself.What arenotated , then , are first, verbally, the goals to be achieved and then, graphically,the framework within which the ensembles work to achieve those goals.Sounds themselves are never notated, no r, in fact, are they even the subject ofthe piece. Rathe r, once again, what the composer does notate are, verbally, anideal to be striven for and, graphically, the framework for an ensemble ofinteractions.

II. PLURALISMA great many of the transformations in musical notation over the past twodecades seem to have arisen from the desire to introduce various notions ofmultiplicity into musical discourse. "M an himself is being forced to reestablish,employ and enjoy his innate 'comprehensivity." (Buckminster Fuller, 1969,p.44). Such a revolutionary conception of form in turn necessitates the devel-opment of an approach to notation capable of symbolizing a total range ofstructures rath er than any single sonic shape. Th e evolution of formal schemeswith the po tential for m ultiple realizations has directed composers to seek newmethods of notation enabling them to incorporate their striking visions ofmultiplicity and comprehensivity.Neyrac Lux (1978) is a work in five movements for solo guitar by thecomposer/theorist Pozzi Escot. Both the notation and the structure of itssecond movement (Fig. 7) are particularly revealing. The score is no tated fullyon one page of manuscript containing two sets of symbols. In the center of thepage are three collections each containing seven pitches all of which arenotated on a circular musical stave. On the upper right side of the page is asingle sequence of numbers arranged in a zig-zag pattern and partitioned invarious ways by its alternating vertical and horizontal arrangement of bothsquare and round shaped enclosures.

With respect to the central part of the socre the circular staff - one isinstructed to num ber th e three collections in any order. T hus, the seven pitchesbeam ed together on the upp er left part of the circle might be labelled collection2;that of the lower left, 1; and, that on th e right, 3. However, it is imp ortant tobear in mind that any other labelling is equally acceptable and may be variedfrom performance to performance.

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2 1 2 THOMAS DELIO

Figure 7The num ber series in the upper right hand corner of the page is to be read asusual from upper left to lower right and consists of only the integers 1,2 and 3.Most striking is its visual presentation within an alternating succession ofvertical and horizontal boxes and circles which suggest the following par-

titions: 1 2, 3, 2, 3 1,3,1 2,1 3,2,3,2 1,2,1 3Furthermore, it seems clear that the central pair 2,1) are singled out as ofspecial importance since these are contained within a circle and all othergroupings are contained within boxes.Beyond this, only a few very general indications concerning th e duration ofthe m ovement and silences surrounding it are given. At the top of the score theindication of one m inute and thirty-tw o seconds is given as the total length ofthe movement. Below, just to the right of the circular staff is the markingsixty-three seconds which is to be the actual duration of playing time. Theremaining thirty-three seconds are silent and are used to sep arate this move-ment from its predecessor and successor (twenty-one seconds preceding andtwelve following).

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SOUND, GESTURE AND SYMBOL 2 3In performance the various elements of the score are put together in such a

way that the three pitch groups, now labelled in some way as one, two and threeare played successively in the order designated by the sequence of numbers.Tempo, the speed at which the tones are played, is determined by the onetiming of sixty-three seconds given in the score. This is the total duration of aperformance and within only this general constraint the performer sets histempo. Similarly, no dynamic indications are marked into the score as thecomposer believes that these will be determined quite naturally by the speed,order and registral placement of the notes within each group. In general, noinstructions are included as it is the composer's belief that the score visuallysuggests the structure which it represents as well as a mode of realizationrelevant to that structure.The entire m ovement is constructed from the additive num ber series 1, 3,4 , 7 , 11, 18 1+3 = 4, 3+ 4= 7, 4+7=11, 7 + 1 1 = 18). From this series thecomposer determines the following information

a) There are3pitch collections each containing 7 pitches.b) The number sequence contains 18 elements partitioned into 7 groups, two eachcontaining1, 3and4elem ents. One g roup contains only two elements the pair in thecenter. Thus, the visual separation of this group from the others suggests its actualstructural isolation from the fundamental series of the piece.c) The unique nature of this2,1pair which stands in the very center of the series suggests afurther division of the partitioned series into halves:

7 2323 131 (27) 3232 121 31 4 3 4 3 1Each halfcontains3 groups, one each of length1, 3, and4.Thus, as the notationsuggests, the central pair, serves a pivotal role in the composition's organization.

Central to any exploration of the notation em ployed h ere is the fact that thethree pitch collections can be ordered in any way desired. As such the move-ment is left open to multiple interpretations and from one performance to thenext its form will be encountered in a variety of different sonic garb. Thework's notation suggests this separation between form and materials quitedramatically as the three pitch collections are presented apart from the num berseries by which they are shaped. Moreover, the multiplicity which such aseparation implies is also captured graphically in the circularity of the musicalstaff itself an unambiguous image of plurality. Thus, in several ways, thenotation of this piece depicts quite vividly an image of structure created so as to

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2 1 4 THOMAS DELIO

Figure 8

admit any num ber of equivalent sonic representations. It is a striking vision ofabstraction and of that sense of universality which such abstraction engenders.Significant parallels are suggested to several works of the visual artist SolLeW itt. In his drawing for Wall Markings(1968) (Fig. 8) LeW itt outlines whatis essentially a score which, with the exception of certain details, suggestsamazing similarities to the second movement of the Escot guitar piece.WallMarkingsconsists of two systems, as the artist refers to them , (ou tlined on theleft side of Fig. 8) and two very different modes of realization (listed along thebottom of Fig. 8) . Each system is to be articulated visually by both of these setsof graphic materials. LeWitt's drawing, then, contains within its framework

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SOUND, GESTURE AND SYMBOL 2 1 5two very different visual realizations for each structure which it proposes. Assuch, the work also seems to demonstrate a certain independence of form frommaterials, and points to many of those same notions of abstraction and mul-tiplicity which were encountered in the notation and music of Pozzi Escot'sNeyrac Lux.Reflecting many of these same concerns, as also revealed through itsnotation, isVariations/ / (1961) of John Cage. The score for this piece consistsof eleven separate transparent sheets, six having straight lines and five havingpoints."The sheets are to be superimposed partially or wholly separated on a suitable surface.Drop purpendiculars by means of any rule obtaining readings thereby for 1) frequency, 2)amplitude, 3) timbre, 4) duration , 5) point of occurrence in an established period of time,6) structure of event (number of sounds making up an aggregate or constellation).A single use of all sheets yields thirty de terminations. W hen, due to 6), more are necessary,change the position of the sheets with respect to one another before making them. Anynumber of readings may be used to provide a program of any length." (Cage, 1961, p . 1).

Figure 9Any realization of this score is the resu lt of a particular configuration fashionedfrom some superimposition of these sheets (Fig. 9). The sonic structure re-sulting from such a superimposition will invariably be that of some statisticalcorrelation of several distributions of sound elements.

For the sake of clarity, examples will be drawn from a simpler scoreconsisting of fewer components than the original. In this situation, constructedby the author, a score with only three lines and four dots will be used. Bysuperimposing these elem ents the configuration found in Fig. 10 might arise.

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2 1 6 THOMAS DELIO

Figure 10Here the dots and lines have been labelled, respectively: d1;d2, d3and d4; and,1,, 12and 13.The dots represent sonic events and the lines are given assignments assonic param eters. Let us say, for instance, that 1, = duration, 12= pitch, and13= volum e. If a dot falls close to l j it represents a short sound, close to 12a lowsound and close to 13a soft sound; far away from 1, a long sound, far away from12a high sound and far away from 13a loud sound. Since there is no point ofoccurrence param eter in this example it will be assumed that the performer orperformers may read through the dots in any order. With respect to thisparticular configuration then, it seems clear that there will be three times asmany short sounds as long and three times as many low sounds as high sincethree dots fall close to 1 and 12and one far away. Also, there will be threetimes as many loud sounds as there are soft since only one dot is close to 1 3while three are far away. This information is summ arized in the chart shown inFig. 11. The structure of this composition, then, consists of three distributionsof dots, one distribution over each line.

It is important to no te, however, that there are actually two aspects of thisstructure (this configuration) which have been revealed through the chart.First, one should note tha t the to tal available range of each param eter has beenpartitioned into only two general areas: close (soft, short, low) and far (loud,long, and high). Second, a density ratio of 3:1 has been determ ined. A s such,over the course of any reading of this particular realization, one of the twopartitioned areas of any param eter will have th ree times as many sounds as theother.

los far

Figure 11

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SOUND, GESTURE AND SYMBOL 2 1 7Next, it should be observed that the configuration also determined a

specific correlation among those distributions. Roughly speaking, the majorityof sounds will be short, low and loud w hile only one-third as many will be long,high and soft. More precisely, the 3:1 density ratio is assigned to the twopartitions of each parameter in the following manner:duration:

pitch:

volume:

(short/long)3 : 1

(low/high)3 : 1

(loud/soft)3 : 1

This particular assignment of the 3:1 ratio to the three parameters tends togroup, on the one hand, all the short/low/loud sounds together and, on theother hand, all the long/high/soft ones together. These groupings follownaturally from the respective densities of occurence within the partitions of th evarious param eters. In other w ords, there are three times as many short/low/loud sounds as there are long/high/soft ones:short/low/loud : long/high/soft3 : 1

Thus,the specific assignments of the density ratio to the th ree sets of partitionsresults in a correlation among the elements of those partitions.To su m m arize :///^ , the total available range of each param eter is partitio-ned into two broadly defined regions (low-high, soft-loud, short-long) as aresult of the configuration of dots over each line;second an association ismade between members of these pairs (short/low/loud, long/high/soft) as aresult of the configuration of the lines; andthird a density ratio is determined(the result of which will be the sounding of three times as many sounds of theshort/low/loud type as there will be of the long/high/soft type). The final auralresult is, then , that of a statistical distribution of sounds over several param e-

ters and one specific correlation of those distributions. If several performerswere to read through the configuration several times there would soundapproximately three times as many short/low/loud sounds as there will belong/high/soft ones . The order of performance of the dots is irrelevant and willin no way alter this outcome since the overall statistical results will remainunchanged despite the particular order in which the sounds are heard.

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2 1 8 THOMAS DELIOIt is, however, important to recognize that the score does not fix any one

such configuration. Ra ther, th e composer presents as his score the materials bywhich any such configuration may be fashioned. As such, the score containswithin it the full range of all possible configurations of six lines and five dotsand, consequently, the full range of statistical structures to which these con-figurations give rise. Thus, it cannot really be said that any one specificstatistical structure is the structure of Variations II. Rather, the structure ofVariations II is the complete range of all such statistical complexes madeavailable by the composer through the score. Indeed, with respect to thisnotion it would seem significant that Cage allows the use of many differentrealizations of the score within any single performance (see instructions: "A nynum ber of readings may be used to provide a program of any length." (Cage,1961,p. 1). Clearly, then, each performance may contain many suggestions ofthe work's inherent multiplicity as it may freely sample from the range ofstructures which the composition's supra-structure engenders.Cage has integrated into the structure of his piece the very processes bywhich that structure evolves. Moreover, the realization of these processes isleft open, to be completed by those assembling a performance.VariationsII ,then, is one large, comprehensive system which itself represents the totalaccumulation of its many constituent realizations. As such, the score repre-sents a structure in potentia as it symbolizes, graphically, not just one specificstatistical distribution but rather the mechanism for constructing an entirerange of such distributions."A composer who hears sounds will try to find a notation for sounds. O nethat has ideas will find one tha t expresses his ideas, leaving their interp retationfree, in confidence that his ideas have been accurately and concisely no tate d."(Cardew, 1974, p.III). Though many composers who have striking and re-vealing insights still do employ traditional notation, it seems clear that, withrespect to the music of the past two decades, an era has emerged w herein thenotation of method often takes prominence over the notation of sound. Thishas led to a flourishing of creative energy devoted almost exclusively to thediscovery of unconventional m ethods for notating musical compositions. As aresult, recent compositional activity has witnessed a shift in emphasis awayfrom the creation of sonic structures tow ard the creation of more precise waysof notating activities and attitudes. This change, in turn, has brought to light amultitude of hitherto unexplored facets of our perception, creation and un-derstanding of musical structure.

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SOUND, GESTURE AND SYMBOL 2 1 9REFERENCES

Ashley, R. "in memoriam. . .Crazy Horse",Source Ma gazine, Composer/Performer Ed., Davis,California, 1967.Behrman, D. "What Indeterminate Notation Determines"Perspectives on Notation and Per-formance, Benjamin Boretz and Edward Cone ed. W. W. Norton Co., N.Y., 1976.Buckminster Fuller, R.Operating anualforSpaceshipEarth,Simon and Schuster, N.Y., 1969.Cage, J. VariationsII , (Henmar Press Inc., 1961), p. 1.Cardew, C.TreatiseHandbook,Peters Ed., London, 1971.Merleau-Ponty, M.ThePrimacyo f Perception. Northeastern University Press, Evanston, Illinois,1964.Merleau-Ponty, M.The S tructure ofBehavior Beacon Press, Boston, 1967.Thomas DeLioDept. of MusicUniversity of MarylandCollege ParkMaryland 20 742, USA

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