Ericson JMT Winter1963

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Yale University Department of Music

Time-RelationsAuthor(s): Robert EricksonReviewed work(s):Source: Journal of Music Theory, Vol. 7, No. 2 (Winter, 1963), pp. 174-192Published by: Duke University Press on behalf of the Yale University Department of MusicStable URL: http://www.jstor.org/stable/843108 .Accessed: 06/02/2013 15:32

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Time- Relations

Our sense of time, both in music and in other activities of ourwaking life, depends primarily upon the mental faculties ofmemory and attention. Without awareness there are no per-ceptual events, and

memory bridgesthe

gapsin time when our

attention falters. Memory and attention make it possible forus to anticipate the future. Because human beings are able toremember and anticipate they have created time and its cate-gories: past, present, future. Of these categories the mostinteresting (and the one most misunderstood) is the present.We know the present exists - it is "now". We live in it, likea fish lives in water. If one were a fish it would probably be

[This paper was read at the 1962 Symposium of Contem-porary Music sponsored by the School of Music, IllinoisWesleyan University, Bloomington, Illinois. i

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ROBERT ERICKSONdifficult to define water, and it is no easier for us humans toconceptualize the flow of our existence.

Alfred North Whitehead writes, in The Concept of Nature:"What we perceive as present is the vivid fringe of memorytinged with anticipation". The phrase might seem to imply thatthe present hardly exists, but that is not the point he is makinghere. He is emphasizing the fluid and on-going quality of ourtime perception; the fact that the present is a vivid fringe doesnot mean that it must be instantaneous. Whitehead's choice ofthe word, fringe, implies extension of some sort; and this vividfringe, the psychological present, as it is usually called, al-

ways has thickness, duration. It is variable from quite long toquite short, and the present should not be conceivedof as somesort of dimensionless slit past which time flows. There are



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no durationless instants in perception.

Precisely because it is a dynamic unity and because it is char-acteristically variable in duration the psychological present isfundamental to our sense of the flow of events, and, I believe,the most important single factor in our sense of rhythm.

The psychological present is a true unity, a perceptual unity,but it is fluid, moving, stretchable, like an accordion. Thereis nothing static about it. In the phrase, "a present is the vividfringe of memory", one is presented with the possibility of theblending of one present into another, and a moment of intro-spection will demonstrate that the blending may also involve anoverlapping of presents. So the conception of psychologicalpresent by no means implies only one happening per givenpresent. Our mental faculties are such that we can sense adiversity of events within a unified present. Take the exampleof driving an automobile in traffic: during the time it takes meto shift from one gear to another I may, and I often do, feelthat particular time span as a unit; yet, during that time I mayalso be aware of many things - cars coming toward me at var-ious speeds, others hovering close to my speed and movingslowly in relation to me; and I may even be somewhat awareof the motion of other events, such as the flight of birds orpeople walking. Within a present one does not focus attentionon everything at the same time; some motions occupy the cen-

ter of my attention when I am driving and others recede to be-come background or potential foreground; moreover, fore-ground and background elements are constantly changing. Thismight sound like a description of chaos, except that we do itevery day. From experience we know we are able to sense anumber of events within a unified present. In the gear shiftingsituation there are events which are quite slow and events whichare quite fast. My perception of that present, and the numberof motion elements I am aware of, will depend largely upon the

focus of my attention. Further, it is well to keep in mind thatthis particular present cannot exist all by itself. The shiftingof gears will be part of a larger organization of overlapping,rather hazily defined presents, and this larger organizationmay offer a number of different time series to my attention.

The phrase, time series, implies some sort of order. Timeordering in science, social life, and in music too, relies upontime counted in regular units of some sort. The size of thecounting unit in scientific work can be

anythingfrom a

lightyear to a microsecond. In ordinary human activities the sizeof the unit is determined by the perceptual situation and the



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fact that the unit must be smaller than the event. Thus slowerevents may have longer units. The unit size, whether fast orslow, has limits determined by our physical and neurologicalmakeup.

Scientific work and ordinary human activities both use counting,but regular counting in human time perception is by no meansthe same thing as the kind of time measurement we use clocksfor. In scientific method an event cannot be described withouta conventional and convenient scale of measurement. Percep-tual time is rigorously excluded, as it must be. But our de-pendence upon clocks in our social and scientific activities,and the rationalized assumptions about time which our clock-dominated life fosters, can blunt our sensitivity to the richnessand variety of our potential time experience. Our clocks mayeasily lead us to believe that minutes and seconds are somehowultimate time particles, and that psychological time is illusoryand of no moment. On the contrary, psychological time is pri-mary to life, and therefore to art. Not everything in this lifecan be counted out. Beyond the practical and social world ofclock ordered events there is the inner world, the world offeeling, the musical world, where we live - in a swirl of over-lapping presents, a flux where events happen at a multiplicityof unit speeds, where the units themselves are subject to dis-tortions, and where uncounted episodes, unit-free durations,are a large part of our experience.

Our sense of time comes closest to clock time when we areexperiencing a regular succession of perceptually eqial units.When the units become very very long the experience becomesthat of unit-free duration, unless it is filled in, broken up intosmaller units, which may form the long duration by addition.When the units become very short they blur into texture. Thetexture, in turn, may be experienced as unit-free or it may beformed into perceptually manageable units, depending upon themusical

situation.

These special cases aside, when we experience the regularsuccession of perceptually equal units we have the effect oftempo in its traditional sense, and the question might be put,"Is tempo of some sort a necessary condition for musical or-ganization?" I do not believe it is. In my opinion the notionof strict tempo, so suitable to much of the music of the 17thand 18th centuries, needs to be replaced by a point of viewmore in keeping with contemporary experience and more har-monious with new attitudes toward other musical dimensions.



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I do not mean that there is no room for the tempo concept incontemporary music, but older, rigid ideas about tempo havebeen changing for 150 years, and our theoretical constructsshould take these changes into account. For example, tempodoes not necessarily disappear in music, or in our other timeexperience, when events are ordered in unequal units. Stravin-sky's Danse Sacrale is an excellent example of unequal unitmusic which preserves tempo of a sort, and in our everydayexperience of motion and the passage of time we often feel atempo or pace in a series of events, even though the eventsmight not be ordered in a strictly regular way. Think of base-ball, where one game might be fast paced and another excru-ciatingly slow. We are certainly sensitive to perceptual regu-larity, but we are also able to "average out" rapidly shiftingvelocities and durations.

The reason that tempo is preserved in Stravinsky's Danse

Sacrale and much other contemporary music (for that matterin much traditional music too) is mainly because we are ableto perceive ratios between durations. Whole number ratiossuch as one-half, one-third, one-fourth, two-thirds and three-fourths are easily within our capabilities and have been usedin music for centuries. Much of our traditional notation isnothing more than a system of symbols for expressing thesesimple ratios. Higher number ratios, such as one-fifth, one-sixth, one-seventh, four-fifths, five-sixths, six-sevenths, are

more ambiguous; they may reduce to perceptually simplerratios, depending upon the musical situation; or they may beperceived as incommensurable, especially at slower speeds,and therefore will be sensed as unit-free durations.

Much of our time experience is of this character, hoveringbetween ratio and unit-free duration. This is the time of ourunclocked real existence. Time experienced in this way asduration, as an uncounted psychological present, ambiguous in

the sense that it may, with a flicker of perception, be experi-enced as ratio, exists in traditional music only under the signof the fermata and the pause, and at the whim of the performer.This is excellent as far as it goes, and I do not in any way wishto narrow the region of the performer's freedom; but any musicwhich takes as its point of departure the belief that rhythm ismore than the pounding of a trip-hammer will be likely to ex-ploit this aspect of our time experience too, to use, organizeand control unit-free durations, especially those which havean ambiguous relationship with ratios, in order to

bringthem

into the composer's domain.



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I favor a music which addresses itself to our whole range oftime perception. I havetried to show how regular units, ratiosof irregular but commensurable units, incommensurable unitsand unit-free durations are all important to our experience oftime, and I have hinted that time clicked off in perceptuallyequal units was by no means the only facet of our time experi-ence which may be useful in music. But I do not wish to leavethe impression that perceptually regular units are no longer avalid and valuable rhythmic device. It is not a question ofmerely substituting irregular and incommensurable elementsfor regular and commensurable ones. It is rather that con-temporary music would be impoverished if it limited itself tothe regularities and ratios bequeathed to us from the 18th cen-tury and earlier, and transmitted largely through notationalconventions which reflect attitudes about life far different fromours.

This century has seen striking changes in musical rhythm.Before 1920 the door to a new rhythmic world was opened byStravinsky and Bartok, each using his own brand of irregularbut commensurable units; and jazz music, with its typical ir-regular, occasionally incommensurable and unit-free durationsagainst a background of rigid regularity. For example, in thethird movement of his Fifth Quartet Bartok uses several typesof irregular units. The irregularity is reflected in the timesignatures, 4+2+3 for the scherzo and 3+2+2+3for the triointue, 8 8 for the trio.Melodic and harmonic events support and emphasize theseeighthnote groupings, making each measure irregular; but be-cause of the fast tempos (the scherzo moves at 46 measures tothe minute and the trio at 60 per minute) and because of thestrict patterning, one perceives that, although there is irreg-ularity within the measure, the measures themselves are allof equal length and similar pattern. Therefore, regularitymoves up a level and includes the irregular units in a slowermoving regular unit. What the composer gains, over and abovea more

interesting background pattern, is the option to synco-pate in a more varied way than was possible in the traditionalregular meters.

There is regularity of another sort here too: the eighth noteacts as a counter, filling in the half, the quarter and the dottedquarter. A rigid counter, used to produce irregular lengthsby addition, is a common device of 20th century music. Inthis movement the steady eighth notes help to reinforce thefeeling of smooth flow, but the speed of the eighth note is sofast, and the patterning is so consistent, that attention focussesmostly on the higher levels of phrase and period.



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There is no such regularity of the larger unit in Stravinsky'sDanse Sacrale*1. It is no accident that this composition iscited so often for its irregular meters and original phraseconstruction, and Stravinsky is right when he remarks*2 inone of his conversations with Robert Craft that no composer,to his knowledge, has extended the idea of variable metersfarther.

In the Danse Sacrale the measures of 2/8, 3/8, 5/8, 2/4, and3/14 produce rhythmic phrases of varying length which reflectthe irregularity of the metering on higher levels of phrase andperiod. There is patterning, but it is much richer in incidentand far more unpredictable to the listener than Bartok's irreg-ular patterning, because instead of fixing the irregular patternin a meter, as Bartok does, Stravinsky constantly reshuffleshis metrical units.

To a composer for whom "the barline is much much more thana mere accent, and I don't believe it can be simulated by anaccent, at least not in my music", *3 meters are not a notationalconvention; they are as much musical materials as chords andtimbres, each meter carrying its particular character and in-dividual pattern potential. An analysis of the music shows thatStravinsky never destroys the metrical sense, and never usesthe meter as a mere aid to counting. The composed ordersyncopates, displaces and supports the potential of expectation

in specific ways, thematic to the composition, and therefore,significant differences between notes taken "on" and "off-of"the beat. The figure carries different connotations inthe forms, 3 'f i and

.

Changes of meter, as inp) 7 , a shift from 3/8 to2/4, or from 3/4 to 5/8, or between any of the eighth note andquarter note meters imply, and require for their proper pro-jection, a change of beating unit. The character of the motion

cannot be adequately expressed in any other way. It is the veryessence of the music. Only in the piano four-hand version didStravinsky reduce all the meters to a single unit, the 16th, andin that version much of the disjunctive quality of the music isleft unexpressed.

Throughout the movement the two beating units, quarter andeighth, are linked and related. All situations of an eighth notein conjunction with an eighth rest, whether in 2/8, 3/8 or 5/8meter, are potential paths to the quarter note meters. Thefigure Lfl is the usual path to an eighth note meter. Theresult of having meters on two levels, with paths between



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levels, is a field of meters. The field (I use the word in thesense of a field of operations or a milieu) consists of two levelsof duple and two of triple, together with 5/8 which appears asa real meter:

2/4 3/45/8

2/8 3/8

When composing my Duo for Violin and Piano I was not thinkingabout fields of meters or any other kind of field; I was workingintuitively to produce the kind of music which I imagined. Iknew that I wanted a quality of motion less tempo-bound thanwhat I had previously composed. I had always used accelerandoand ritardando in my music to ameliorate the "tickiness" of arigidly held unit and to help establish the fluidity of motionwhich I wanted; and for the Duo I hit upon the compositionalidea of combining certain musical events in disjunct but com-mensurable tempos, which sometimes would integrate with eachother without any single tempo dominating, and at other timeswould be connected by means of accelerando and ritardando.What this turned out to be was a field of tempos.

The chart, Example 1, outlines the principal tempo changesand changes of beating unit for the first movement. The mostimportant relationships are between 44 and 66, ratio of 2/3;between 44 and its double, 88; and between 66 and 88, ratio3/4. The other tempos are primarily nuances, but there isa hint, hardly more, of 40-60-80, which within the context ofthis movement acts as a slight ritardando of the 44-66-88, butwhich assumes more importance in the second movement; thetempos, 52 and 56 are mostly related to the opening materialsof the movement.

Measures 65 to 82, Example 2, illustrate some of the ways in

which integrations between tempos are used, and some of thefunctions of accelerando and ritardando. To lead into the ex-ample, from measure 65 to measure 70 the music moves inmeters of 9/16, 2/16 and 12/16, with the beating unit shiftingfrom eighth to dotted eighth. At measure 70 there is a changeof meter to 5/4, with thematic materials associated with theopening of the movement (and more particularly, with theirdevelopment) except that the tempo is faster. In measure 72and 73 the quarter note accelerates to 88, but at the same timethe spacing of events is broadened. Between measures 74

and75 the tempo changes abruptly from 88 to 66. It would havebeen perfectly possible to notate measure 74at the tempo of



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66 to the quarter note, because if =88 then l66; and if =66thenI= 88. But I wanted the half note triplet units to be takenfrom the beat of 88 to the quarter, and I do not believe I couldhave achieved the kind of intensity embodied in this particular"off the beat" feeling in any other way.

From measure 75 through measure 76 the quarter note slowsdown to 44, touching the lower end of the tempo field. In meas-ures 77 and 78 it accelerates to 56, then drops back through 44to its nuance, 40. Measure 78 begins a reminiscence, in thepiano, of an important idea, and suddenly the violin starts offwith its equally important material. The shift to 9/16 meterat the rate of 66 to the ., allows building the material associatedwith the quarter note 44 into the 66 tempo*4. What is involvedhere, and in the whole idea of building one tempo into anotheris not a mere notational game. It is a very different thing,musically, if a 32nd note, for example, is taken as part of aquarter note beating unit or as a part of a dotted eighth. Thebeating unit and its speed are primary musical categories. Anynote length is in itself neutral and carries no specific meaning.It must be referred to a context which includes the speed of thebeating unit, the position of the note in that unit, its articula-tion and its relation to other durations, not to speak of timbre,harmonic and melodic considerations. That is why there seemsto me to be something incomplete in what is usually referredto as additive rhythm, where all lengths are made commen-surable through one ultimate counter. The counter and its ad-ditive durations are only part of the whole rhythmic situation;the divisive idea is equally important. We are able to per-ceive shorter durations as fractional parts of a beat. In musicboth kinds of experience are likely to be happening concurrent-ly, usually as elements in some larger process.

From the experience of composing the Duo, and trying to un-derstand what I had done, I realized that I had worked mainlywith the actual durations of various note lengths relative toeach other, to a counter and to a beating unit. During the com-position of my Chamber Concerto, which followed the Duo, Ifound myself working with a larger number of tempos and coun-ters, and I had a strong compositional desire to integrate allmy speeds, counters, accents and durations in a nonrigid way.Therefore, I tried to be conscious of the various durations ofall the note values I happened to be using, at whatever tempoand beating unit, and I found myself turning away from hierar-

chical rhythmic relationships toward a rhythm of constantlyemerging and changing patterns of relationship.



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Looking back at the Chamber Concerto, especially its finalmovement, it now appears that the term, field of tempos, whichdescribed the action of the Duo fairly well, is not very appro-priate. It is too narrow, and it Carries connotations which donot seem to reflect the musical reality. What I was involvedwith in this movement was actually a field of durations, somestable and regular, some unstable and irregular, where rela-tionships between durations, beats and counters changed inmore complicated ways than the term tempo field could ex-press. To convey some information about the way that I usedthat field of duration, and something of how the various musi-cal elements interact, I have made two charts. The first chart,Figure 3, gives a rough approximation of the number of meas-ures at a certain unit, relationships between the speeds of thevarious beating units and the disposition of the passages of ac-celeration and deceleration.

The chart shows that the duration 36, and its double, 72; 63and its double, 126, are the most used tempos, although in theactual music no tempo has any special perceived priority. Ifanything has a special importance it is the duration 72, (notthe tempo, the duration) which is more central to my concep-tion than the chart indicates, because one of the important ideasof the movement is a" semi- steady" duration of 72. The semi-steady 72 is a sort of fluctuating and intermittent constantwhich threads through the movement. How it is built into beat-

ing units of different speeds may be illustrated by a section ofthe movement comprising measures 316 to 360. The chart inFigure 4 is a rhythmic skeleton of these measures. Thenotes in the little square boxes, in measure 316 and later, areperformed according to the rule, "play any time during thebeat exceptat the beginning". The brackets, beginning in meas-ure 317, indicate built-in-durations- for example, inmeasure318 the number 7 under the bracket means that seven sixteenthnotes added together produce the duration 72. Notice that thesevens are not the only lengths involved; nines and fives aresignificant too, as are the doubles and triples of seven. Atmeasure 333 the semi-steady 72 motion is interrupted; it be-gins again at measure 351, where the semi-steady 72 is main-tained through the accelerando. Thus, from measure 316 to360 there are built-in lengths of 7/ 16ths, 5/16ths, 4/16ths and3/16ths, all producing 72's, some of them steadier than others,depending upon the speed and acceleration of the beating unit.Throughout the movement there are many places where thesemi-steady 72 is expressed, but other semi-steady lengthsare important too, and sometimes these are used to produce"written in" accelerations and decelerations.



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The meters of the movement are mainly 4/4 and 2/2. Only afew other time signatures are used. Many relationships whichmight have been notated as rather complicated fractions ofbeats in a strict tempo are handled by changes of the beatingunit. But my motive was not simply a desire to create a prac-ticable notation. The beating unit and the ratios between speedsof beating units are integral to the music and my conception ofits flow. Therefore the wide range of speed in the beating unit,from 24 to 126, is neither an accident nor a matter of conven-ience. For me, a beat is a present. It is the mental and per-ceptual "now". A beat is a unity, and it is no less a unity whenit happens to be accelerating or when the flow of beats is fluc-tuating. I used this range of beating units in my ChamberConcerto in order to organize a flow of presents.

The ratios between the various beating speeds are important,but equally important to me are the "irrational" situationswhere the beat is speeding up or slowing down, because in suchsituations wonderfully delicate rhythmic nuances may be ex-pressed. The irrational relationships, controlled of courseby the steepness of the acceleration or deceleration, are per-haps more important to me than the ratios between speeds ofunits, which are the obvious aspect of my field of durations.Especially when the beat is speeding up or slowing down, semi-steady durations can create a composed irregular regularitywhich for me is the essence of growth and emergence.

By composing without splitting the idea of regular-irregularinto two parts, a kind of unit-free rhythm becomes possible.Sometimes durations which are close to being unit-free aremeasured out in beats. In measures 344 to 350, Figure 4,where there is a long ritardando on a single note, is such aninstance, and there are other similar situations throughout themovement. Sometimes the semi-steady motions are heard incontexts which, though measured, are on the fringe of unit-

freedom. The disjunct beating units toward the end of themovement, (Figure 3) especially when the ratio between themis other than that of one-half, one-quarter or one-third, andwhen the tempo of the beating unit is slow, will tend towardunit-freedom. Other elements which lean in this direction arethe notes placed in boxes, such as those at the beginning of thechart, (Figure 4). As I mentioned earlier, they carry therule, "play at any time during the beat except at the beginning".They are used usually to produce a harmonic cloud or to sep-arate background materials from

more precisely measuredforeground elements. The amount of "irrationality" is, ofcourse, controlled by the speed of the beating unit. All the



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boxes shown in Figure 4 are eighth notes with a steady beat-ing unit, but there are places in the movement where boxesare used with acceleration and deceleration, and there are alsoboxes of other note lengths.

The theorist runs a special risk, especially in these days ofscience and scientism, of reductive thinking. He must try toavoid the temptation to sweep under the rug those recalcitrantelements which do not fit his theory. Rigor and logic havecreated some theoretical edifices which are remarkable intheir consistency and beautiful in their own right - but irrele-vant. It is nice to be clean, tidy and elegant, but it is good tolet the dirt show in a theory if the dirt is there.

Time relations cannot, of course, be separated from othermusical dimensions; indeed, many insights about rhythm havecome about precisely because of the increasing inseparability

of the various musical elements. Today harmony and timbreare a single category, and tend to merge withmelody and coun-terpoint into a broader musical idea which as yet has no name.We are involved with a many-faceted totality, in which all themusical relationships are imbedded in time in a unitary way.This is perfectly natural: the separation of music into variousdiscrete elements has never been very satisfactory anyway,and has been perpetuated mainly by the notorious conservatismof the music curriculum.

One feels and thinks and imagines in a unitary way, and it iswithin the context of this unity that time relations should bediscussed. I do not possess the conceptual framework neededto analyse in this unitary way, although I recognize that this iswhat needs to be done, so I have done the next-best thing: Ihave focussed upon time and rhythm because they are integralto and inseparable from the whole musical event.

In the 18thcentury, time,

itappears,

couldbe separated fromthe events which took place in it. Time, very much like 18th

century space, was considered to be absolute, infinite andhomogeneous. It is no longer possible today to think in termsof events clicking along an imaginary yardstick measuring outto infinity. This notion, with its abstract, spatialized conceptof time, its knife-edge present and its rigid and therefore stat-ic notion of periodicity, belongs to a past world.

Time, for us, is unitary with events, whether in science, inart or in ordinary life. There is no knife-edge present in hu-man perception, and apparently there is no longer such a con-



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cept in contemporary scientific thinking either. The essen-tially circular and rigid periodicity of 18th century time is be-ing replaced by different periodicities, which turn out to beanalogous to our bodily and mental processes.

Biological periodicity is heterogeneous and unstable, but het-erogeneity need not imply chaos. Events (including musicalevents) flow, and we perceive them in a constantly fluctuatingpsychological present. This present, in all its variety, itsoverlappingness, its heterogeneity, is nevertheless a unity,and in it we grasp the flow while the flowing is going on. Thisability to grasp, to staticize, is important; we perceive thefluid and dynamic qualities of time, but the act of perceptioncreates stabilities too. We need these stabilities for a numberof reasons. So far as music is concerned, certain stabilitiesare essential if we are to enlarge the simple present. I havesaid that a beat is a present, but I hope I have made it clear

that in principle beats can be any length, up to very long. Ifwe keep in mind that memory, with the fixing of memory traceswhichmemory implies, is essential to our perception, then thenotion of a beat being a present may be seen to include poten-tial larger presents formed from the continuing overlappingprocess.

Consider a line of melody as we listen to it: we remember thesignificance of what has passed, sense the unfolding of the mel-

ody, and during that unfolding create a sense of the anticipatedwhole. The anticipated whole changes as we listen, becausesome of our anticipations will be confirmed and others will not.If all our anticipations were reinforced by the melody it wouldbe likely to be heard as a dull tune indeed. Our changing an-ticipation is therefore not static, but it is a stability in theflow; we do staticize but the flow is not arrested.

When I direct my attention inward to contemplate my ownself. .

.I perceiveat

first, as a crust solidified on thesurface, all the perceptions which come to it (from thematerial world. These perceptions are clear, distinct,juxtaposed or juxtaposable one with another; they tend togroup themselves into objects. .. But if I draw myself infrom the periphery towards the center. . .I find an alto-gether different thing. There is beneath these sharply cutcrystals and this frozen surface, a continuous flux, whichis not comparable to any flux I have even seen. There isa succession of states each of which announces that whichfollows and contains that which precedes it. In reality noone begins or ends, but all extend into each other. [Bergson]



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When Bergson refers to the perceptions from the materialworld as frozen, solidified, juxtaposable, he points to the"thingness" of these perceptions. These frozen and juxtapo-sable things are memories of objects and thoughts about ob-jects, a class which could include musical objects too: themes,harmonies, sections of compositions, musical wholes. Whatis interesting here is that Bergson is using spatial words rath-er than time words to describe these "perceptions", in thatway conveying, if I am reading him correctly, the sense thatthese things, which as he says may be juxtaposed, have aquality which is different from that of the flux of time. Hemakes a black and white contrast between the surface "percep-tion" and the mind's center, but it seems to me that the imageshould contain not only fixed and frozen elements, but melting,slushy and liquid elements too, a range between crystallinestasis and the flux. If we extend his thought to include recog-nizable musical objects which may melt into flux - the objectsthemselves susceptible to change - then we can have relation-ships between the surface and the center. With this modifica-tion, his description of the flux as a succession of states, witheach state announcing the next and containing the last, is themost realistic description of how we listen to music that Iknow; and when he adds that in reality no one state begins orends and that they all extend into each other he is describingthe way in which a well equipped listener comprehends a largemusical organisation.

How these states extend into one another has been expressed inmore detail by Whitehead in The Concept of Nature. He de-scribes the complexity and overlappingness in terms of whatwe could think of as a group of tempos:

The difficulty as to discordant time systems is partlysolved by distinguishing between what I call the creativeadvance of nature. . .and anyone time-series. We habit-

ually muddle together this creative advance, which we ex-perience as the perpetual transition of nature into novelty,with the single time series which we naturally employ formeasurement. The various time-series each measuresome aspect of the creative advance, and the whole bundleof them express all the properties of this advance whichare measurable.

In this bundle of discordant time-series, any one strand maymeasure something of nature. Whitehead's

emphasisis

uponthe bundle; the error we make is to muddle nature into a sin-gle scale of time measurement. The creative advance of na-



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ture simply will not reduce to a single time-series. Some ofits properties may not be measureable at all. This view oftime, with its acceptance of flux, and its nature experiencedas perpetual transition, is harmonious with today's modes ofthought and feeling in both science and art.

If, then, we wish to compose music in which events are some-times contemporaneous but not simultaneous, in which thereare occasionally clouds of tones, in which velocities are shift-

ing and irregular, in which the traditional categories of melody,harmony, counterpoint, timbre and rhythm have a unitary re-lationship, then a view of time such as Whitehead's, with itsperpetual transition of nature into novelty, its fringe-like pres-ent and its creative advance of nature is, I believe, a true andproper one for us.

r e f e r e n e s

SThere are three available versions of the Danse Sacrale. When he composedthe dance Stravinsky could play it but did not know how to write it down. (Sat-urday Review, Dec. 26, 1959, "Apropos Le Sacre du Printemps"). His firstrevision was for the performance of 1921, some measures being shortened tomake the music more manageable for the conductor and clear for the orchestra.

Stravinsky felt that the shortening alsq clarified the scansion of the music.Whether this applies specifically to the Danse Sacrale can be only a guess be-cause in the Saturday Review article cited Stravinsky says that he possessesthe only copy of the 1913 original score.

The 1921 revision is the probable basis for the edition published by BooseyHawkes, B&H 16333, which is in common concert use, and from which mostrecordings are made. The composer's version for piano four-hands, pub-lished in 1926, represents either a return to the original score of 1913, withits longer barring and meters in 16ths, or a new conception. The most recentversion was made in 1943, "mainly to facilitate performance by means of aneasier-to-read unit of beat:'

2 Stravinsky, I. and Robert Craft, Conversations with Igor Stravinsky (Double-day & Co., Inc., New York, 1959)123.

3 Ibid., 21

4 The piano part is moving at 49.5, a nuance of the 44 tempo.

Documents

Ericson JMT Winter1963