Tempus Ex Machina PDF

 

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Tempus ex Machina A composer s reflections on musical time Gérard Griseya a  Dept. of Music, University of California, Berkeley, California, U.S.A.

To cite this Article Grisey, Gérard(1987) 'Tempus ex Machina:  A  A composer's reflections on musical time', Contemporary Music Review, 2: 1, 239 — 275 To link to this Article: DOI: 10.1080/07494468708567060 URL: http://dx.doi.org/10.1080/07494468708567060

 

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Contemporary Music Review,   1987,   Vol. 2 pp . 239-275 239-275

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© 1987 1987 Harw ood Academic Publishers GmbH Printed in the United Kingdom

Tempus ex M achina: achina:  A

com composer' poser'ss reflections on musical time 1 1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

Gérard Grisey

Dept.   o f Music, University  o f California, Berkeley, California, U.S.A. (composer)  (composer)

This article is divided into three sections (the skeleton of time, the flesh of time, and the skin of time) and clearly distinguishes conceptual (or Chronometric) time from perceptual (or psychological) time. The author firstly liquidates a few theoretical avatars such as rhythmic symmetry and then proposes a scale of complexity for duration that goes from order to disorder. The most important point is then addressed, namely, the absolute relativity of temporal perception which has become a function of the quality of the sound objects and the difference between successive objects. The degree of pre-audibility becomes the true musical substance of the composer. In the last section the author sketches out some problems of memorization as well as the complex relations that exist between the several times of the listener, the performer and the composer. KE KEY Y WORDS conceptual time, perc eptual time, rhythmic symm etry, relativi relativity ty of temporal perc eption, pre-audibility, scale ooff complexity.

The skeleton of time Definition By skeleton of time we mean the temporal divisions that the composer use s to organize organize so un ds. Without being immed iately iately d iscerni iscernible, ble, at best merely sensed beneath the "flesh of time", this infrastructure nonetheless retains an attraction for twentieth century composers, no doubt because in its relative simplicity it gives us the illusion of operational efficiency. The unit of measurement for this infrastructure is chronometric  time, e.  e.g. g. the secon d.

Rhythms and durati durations ons Two approaches to rhythm may be identified: a) by relating it to a given pulse, the meter, in the form of a periodic reference point. Into this area falls the rhythmic writing of Stravinsky, Bartok, Bart ok, jazz etc. Each rhyth m is perceived in its qualitative qualitative relationship to meter (on the beat, off the beat) but also in its quantitative relationship to me ter (longer or shorter th an the beat).

 

24 0   Gé rard Grisey

b) Without a reference pulse we are no longer talking of rhythm but of durations. Each duration is perceived quantitatively by its relationship to preceding and successive durations. This is the case in the rhythmic writing of Messiaen and of the serialist school. In fact, a micro-pulse allows the performer or conduc tor to count a nd execute these duratio ns, but it only exists as a way of working an d ha s no perc eptu al reality. The more complex the durations (combinations of fractions of the unit), the more our appreciation of them is only relative (longer or shorter than ) 1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

Question: Doesn't Indian music achieve a synthesis of two systems: the first taking into account rhythmic macrostructures (talas), the second dealing with rhythmic subdivisions (rapid combinations of long and short notes)? c) To remain consistent with the use of the second system, it seems unlikely that our quantitative perception could extend to the totality of durations that a piece of music comprises, but rather to a few durations adjacent adjace nt to the one w e are in in the process of perceiving. One can also imagine an oscillating rhythm in which the meter itself would fluctuate constantly. The moving reference point becomes its own objective and rhythm is abolished in favor of fluctuations in the pulse is one of the aims of my piece fo forr six percussionists  Tempus  e x M a c h i.n This a .   2 is

Som e theoretical avatars avatars and their importance Twentieth century composers, like those of the fourteenth and fifteenth centuries, have speculated considerably about durations. They have applied to time the pro portion s identical to' those on e finds in spatial concepts: prime numbers (Olivier Messiaen), the golden section (Bela Bartók), the Fibonacci series (Karlheinz Stockhausen), Newtonian binomials (Jean-Claude Risset), and also stochastic procedures: kinetic theory of gases (Iannis Xenakis). Xenakis). Though useful as methods of working, such speculations still fall far

s h o r t o f s o u n d a s i t i s p e r c e i v e d .  .   Th e y b e c a me ri d i c u l o u s w h e n o u r e ld ld e rs e n d e d u p c o n f u si n g t h e ma p w i t h t h e l ie ie o f tthh e  land.

Let us look in passing at some theroretical avatars of the twentieth

century. a) The notion of smooth (unmeasured) and striated (measured) time described by Pierre Boulez (1968, 1971) is merely the invention of a conductor bereft of any phenomenological awareness. Who perceives the differen difference ce b etw een tim e divided u p periodically periodically by a meter (se (seee Igor Stravinsky's definition, 1942) - or, if one prefers, by a virtual pulse maintained by the composer/musicians - and smooth time, without a pulse, if the rhythms which overlay it are there precisely to destroy all feeling of periodicity?

 

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24 2   Gérard Grisey

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a

Three examples: Gruppen for  for thre e orche stras by K. Stockhau sen (1963 (1963): ): the tem pi ha ve a great structural importance. Who perceives perceives them? Lontano for  for o rchestra by G. Ligeti Ligeti (19 (1969) 69):: The te m po 's on ly im portance is as a point of reference, meant simply for conductors and musicians. Who perceives it? On the other other hand,   S t i m m u n g for six vocalists by Stockhausen (1969) show s us that only some elementary, even primary rhythm s give us the very clear possibility of perceiving the tempo of these rhythms. If, therefore, the pulse is not expressed, we will rem em ber th at only a few simple rhythms make the perception of a virtual pulse possible, whereas others disguise it for the sake of ambiguity and the mesmeric feeling feel ing of of pure d uration , witho ut a reference reference poin t. In the  the latter ca atter  ca se, in the a b se n c e o f a n y st a n d a rd , e a c h d u ra t i o n c a n o n l y b e c o m p a re d w i t h t h a t //tt h o se

preceding  i t,  and ou r apprehe nsion of the preceding  the du rations is thus m ore global global and more relative. Perhaps because of this, the tempi in my music seldom have a structural value. More often, they serve to compress or expand a musical sequence, and it is therefore the total duration of this sequence which is structurally important, and not the unit of measurement. Sometimes, however, tempi which become the basis of an elementary periodic structure take on a phenomenological value: see Fig. 1 above,   T e m p u s e x Machina x Machina   for six percussionists. (1981).

b) Let us move on to another avatar: The notion of retrogradable and non-retrogradable rhythms (Olivier Messiaen, 1956) or, similarly, that of rhythmic symmetry and asymmetry "(Pierre "(Pierre Boulez, 1971) 1971).. Again, such a distinction, distinction, wh atever its operational value, has no perceptible value. It shows the level of contempt for or misunderstanding of perception our elders had attained. What a utopia this spatial and static version of time was, a veritable straight line at the center of wh ich th e listener sits sits implicit implicitly, ly, po ssessing

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not only a memo ry but also a prescie prescience nce that allows allows him to appreh end the symmetrical axis the moment it appears Unless, perhaps, our superman were gifted with a memory that enabled him to reconstruct th e entirety of the du rations so that he could, a posteriori, classify them as symmetrical or not ... Or un less this w ere, once ag ain, the busin ess' only of the specialist specialist w h o   reads   a s c o r e . . . We can see clearly that, like the distinction between smooth and striated time, such distinctions only assume a phenomenological value in a limited number of cases that have yet to be defined; in this case, only short and simple rhythmic cells would make such a classification possible. W hat a spatial view of musical time - b ut also w ha t anthro poce ntrism there is in this image of a ma n at th e center of time, a listener listener fixed fixed at the

 

A composer's refl reflections ections o n musical time  2 4 3

very center of of the work to wh ich h e is listening listening On e might say that a truly Copernican revolution remains to be ffought ought in music . . . To return to the idea of rhythmic sym metry: if if, for long sequ ences ooff duratio ns, the sensatio n of of symm etry is unrealistic, unrealistic, it it non etheless seem s to me that there must still exist a means of creating such a sensation. Since the piece of music and the listener are two entities in time, we

w o u l d h a v e t o i m a g i n e   a n a n a mo rp h o si s t h a t w o u l d a l t e r t h e sy mme t ri c a l st ru c t u re s i n su c h a w a y t h a t th th e i r b l u rrin rrin g i n t he he me m o ry w e re re a d j u ste ste d .

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

Unfortunately, we are far Unfortunately, far from from p rocessing the psy choacoustic data for for such an operation, but it is not unthinkable that we might eventually arrive at them. With sequences of short durations, it would seem that we are more apt to recognize a symmetry by groupings rather than a genuine symmetry. In the way that we do not perceive single frequencies but attempt to group them in formations, so does the same apply to durations.

Let us take the followi following ng sequence: J J J J* J J J We would tend to group

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because once we perceived perceived it we wou ld attach the short note to preceding or successive successive one s.

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because of the perceptible importanc e of the repetition of the first group

andnot: j j   }) 

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Repetition is mo re salient Repetition salient tha n inversion or symm etry, to such a poin t that it can in certain certain cases assist assist the pe rception of these latter.

For example, the sequence J J

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(symmetry

by group) wo uld certainly certainly seem mo re symmetrical than th e fir first st sequen ce quoted. With this reflection I have slipped unawares into the areas that form the subject of the next section. Back then to our skeleton

 

24 4   G érard Grisey

Categories

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

In place of the arbitrary and generally dualistic categories which have been use d in an attem pt to cla class ssif ifyy d uratio ns: short/long, ternary/bina ry, rational/irrational values, symmetry/asymmetry, I substitute a scale of complexity - no doubt equally arbitrary - but which has the advantage of reverting to the phenomena of musical times as they are perceived and allowing a continuity to be grasped. Information theory, such as that presented by Abraham Moles (1966) could be of assistance here. From the following table w e can construct a   c o n t i n u u m t hhaa t c a n be found in   th e classification of  o f intervals  ( by their degree o f d i ssonance)  (byy ssonance) a n d o f timbres (b the extent   t o  which they  a r e non-harm onic). a)   P e r i o d i c  c 

maxim um predictability

ORDER

b )  1) 2) c)  c)   1)

average predictability predictability C o n t i n u o u s - d y n a m i c  c  contin uou s acceleration acceleration contin uou s deceleration slight predictab ility D i s c o n t i n u o u s - d y n a m i c  c  acceleration or decele ration by stages or by elision 2) statistical acceleration or deceleration d)   Statistical zero predictab ility Statistical   complete redivision punpredictability punpredictabili ty of durations maximum discontinuity e)  e)  

D ISORDER

Smooth rhythmic silence

Befor Bef oree go ing over the elem ents of the table point by point it shoul d be made clear that all sounds can be given a duration. By duration, musicians have too often intended a limiting meaning, such as the rhythm ic expression of an attack attack transient. Climaxes of of dynam ic curves, changes in timbre, sound quality and vibrato, or, more generally, the actual form of a sequence or sound, constitute as much material as one can rhythmically express. In the course of revising the present essay, Stephen McAdams drew my attention, quite rightly, to the fact that the degree of complexity as defined by information theory has very little to do with the degree of structuring and th e way in which this structuring structuring is actuall actuallyy understoo d by the listener. It is true that perceiving the degree of complexity is neither as simple

nor as linear as the prec eding table migh t suggest. Between the perfectly perfectly predictable and the perfectly unpredictable, the degree of complexity seems to follow one or several curves whose peak(s) are entirely the

 

A composer's refl reflections ections o n musical time  2 4 5

result of the musical context and the perceptual capacities of each person. One of the most arduous tasks for the composer will be to determine up to what complex affects non-negative way. Onpoint either side ofstructuring such a point areperception two polesinofa boredom due to a lack or saturation of information, but this threshold is not any less dependent upon the complete subjectivity and responsibility of the composer. a)  a)   P e r i o d i c 1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

1) We d o not consider periodicity as either basic material nor as the uni t of rhythmic structure, but the most simple, most probable phen om enon; it iiss temp ting to see it as an ideal po int of reference reference for for th e percep tion of  as is is a sinusoidal soun d for the p erception of pitches, but no t at all all time, as time, the a priori foundation foundation of a hierarchical system. We wou ld ha ve as well the same attitude to consonance. However, if as Abraham Moles explains so well, "the notion of rhythm is linked to that of expectation" (1966), absolute, mechanical periodicity tires the listener as much as a ceiling or wall composed of perfectly equidistant tiles. We have all noticed ho w the periodicity of the syn thesizer or com puter in its perfect perfect redundancy merely induces boredom and inattention. The whole art of the composer who works in an electronic studio, analogue or digital, consists of making this excessively redundant material mo re flexible flexible.. 2) In 1973, 1973, with respect to a work called called simply P simply  P é r i o d e s ,  II introduced the notion of fuzzy periodicity. This involved composing periodic events which fluctuate slightly around a constant, analagous to the periodicity of our heartbeat, breathing or footstep. The rate of deviation can be almost inaudible (what jazz players call call "feeling" "feeling")) or, if if it is mo re m arked, perceived as a slight hesitation in the periodicity (cf. expectation aroused in the music of Gagaku). I noted with great enthusiasm that here I was dealing w ith one of the areas of research carried out at IRCAM by David Wessel, psychoacoustidan and composer. During a stay in Rome I was given to read the studies made b y a team of German archeologists on the Greek temples of Paestum. The measurements of the pieces carved in the coffered ceilings showed an amazing variety in their repetition. The length of the pieces varied, if I remember rightly, between 23 and 29 centimetres Question: What amount of systematic or statistical phase difference must be programmed to make electronic periodicity 'live' without also destroying the feeling of periodicity itself? The psychological importance of periodicity no longer has to be demon strated. Psychoanalysis Psychoanalysis teaches us tha t neurosis  neurosis  is  a repetitio n: if if is a

 

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

 

A composer's reflections reflections o n musical time  2 4 7

In this connection I would mention Mozart, who with his unfailing psychological insight portrays in   D i e E n t ffüü hhrr u n g a u s d e m Serail  a character at the height of a neurotic delirium: Osmin see Aria No 19: "und die Hälse schnüren zu, schnüren zu, schnüren, schnüren, schnüren ..." The m usical discourse is liter literally ally,, halted: the s ou nds twist a nd turn indefinitely, caught in the trap of an obsession.

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

In serial music, rhythmic or harmonic periodicity, having been dispensed with, is made infinitely haunting by its very absence. The octave, another form of periodicity, was disturbing to the point where one could dream of non-octaviated spaces (Wychnegradsky, Várese, Boulez). To the contrary, repetitive (or minimal) music in some way embodied the "return of the repressed object". This type of periodicity, similar to those found in numerous African musics, seeks a state of trance by annihilating time. We shall see later on how this hypnosis works. Neith er of the ab ove stages app lies to us . Periodicity Periodicity is irreplaceable; irreplaceable; it allows a pause in the music's unfolding, the suspension of time and, sometimes, a redundancy helpful to our powers of comprehension. When the musical structure demands it, we use it for its intrinsic qualities, avoiding both rejection and obsession. 3 b )  C o n t i n u o u s - d y n a m i c 1) For the perception of duratio ns, logarithm ic curves certainly certainly hav e an imp ortance equal to the harm onic spectra whi ch determ ine the timbre timbre of of a pitch. The perception of the dura tions is actually actually governed by the sam e law as that of pitches and intensity: the law of Weber/Fechner, which may be roughly expressed as: S =   k log E Where S is the sensation (or the psychological dimension), E is the excitation excita tion (or the physical dim ension) and   k is a constant value w hich conditions the relationshi relationshipp betw een an augm entation of S and a given given augmentation of E Sensation therefore varies roughly as the logarithm of excitation.   himself,

As everysensation musicianofhas been able to see for an equivalent difference whatever the duration,  to onemaintain must have a longer difference between long durations than between short durations. In addition, the spontaneous acceleration of a musician is always of the logarithmic type. 2) To mak e th e tran sition fro from m period icity (c (cf. f. Fig. 3) to acceleration or deceleration, it is only necessary to add or substract a factor to a given duration (arithmetic (arithmetic progressio n of the first first,, second order, etc; cf. cf. Fig. 4 ) or to multiply or divide this dura tion by a factor factor (geometric progression; cf. Fig. 5).

 

24 8   G é r a r d G r iiss e y Order of eventsi  v S

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

Time Figure 3

Peri Periodic odic durations .

Order of events  A

8"

6"

Time

Figure 4   Arithmetical progre ssion. Order of events 5

Time

16"

Figure 5   Geometri Geometriee progression.

 

A composer's  reflection's o n musical time  2 4 9

In order to visualize these accelerations and decelerations, we represent on the ordinate the order of events and on the abscissa the projection of these events in the temporal axis. These "cu rves" bring a great flexibility flexibility to the tempo ral distribution of

s o u n d s w h i l s t c o n ttrr o l llii n gg   t h e d e g re e o f t e n si o n a n d t h e sp e e d o f t h e p ro c e sse s.

Replacing the order of events by the order of the frequency

1 1 0 2    e  n  u  J   2 1   8 1  : 1 1    :  t  A   ]  y  r  a  r b i  L    y  t i  s  r  e  v i  n  U    &   l  a  n  o i  t  a  N   h  s i  w  e  J [    :  y  B   d  e d  a  o l  n  w  o  D

components axis by ina the linear frequency axis, may well be and madethe to time correspond, realm of timbre, to these spectracurves with different degrees of harmonicity. (Such inharmonic spectra are produced by certain instruments - the piano, for example - but can also be produced electronically by methods such as frequency modulation). It is these progressions which orientate the evolution of the sound positively or negatively, which from then on is no longer static and

n e u t r a l b u t   d y n a m i c a n d c h a rg e d w i t h d i re c t e d m e a n i n g .

3) Psychologically the acceleration of durations reinforces the progressive blurring or fading of sounds that takes place in our memory: the longest events memorized are also the earliest. Through acceleration, the presen t is m ade m ore dense, th e arrow of time at full full speed, an d the listene r is literally  propelled  towards something which he does not yet know. The arrow of his own biological time and that of musical time, added together, cause a complete loss of memory. By contrast, the deceleration of durations contradicts the fading of sounds: the shortest events memorized are the earliest. A slowing down induce s a sort of of expectancy expectancy in th e void of the present. He re it functions functions as a rebalancing of forgetfulness, the most salient densities being the earliest. earli est. With deceleration, deceleration,   th e listener   i s p u l l e d b a c k w a r d s , since   since the arrow of musical time had somehow turned in the opposite direction. But because our listener also perceives that the arrow of his own biological time had n ot cha nged course, he will oscilla oscillate te indefini indefinitely tely betw een these two senses of time going in opposite but concomitant directions, in a sort of state of of   t e mp o ra l su sp e n si o n .

Our mind rapidly tires of this game. As with "infinite" acceleration where differences end up confused in the window of the present, our perception no longer being sufficient, durations that are too long and too slow to come no longer allow a comparison of the sounds with one another, and fatigue our waiting. In this connection we m ay refer refer to the m arvellous film film by W erner Herzog, "Aguirre". The temporal structure of the film seems to be based on a continuous slowing down, the events becoming fewer and further apart until the end, even as the tension of the viewer grow s. This füm füm should also be seen fo forr its evolutionary structure (density of events, behavior of the principal characters, photography, lighting, etc.) Empirically we have observed that we tolerate a long acceleration followed by a short deceleration rather than its opposite (a short acceleration followed by a long deceleration). Why?

 

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 n  w  o  D

CHËÊ Figure 6   From Parfie/s for  16 or 18 musid ans (pp. 38-39).

 

risey 252   Gé rard G risey

Is it a matter cf a for form m that relates to us physiologically? physiologically? Or p erh aps it

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is precisely this double sense of time and the void of expectation, in which the rarefaction of events keeps us suspended, that we can only tolerate for a limited time, whilst by contrast the vertigo induced by acceleration makes us forget Chronometrie duration? To conclude, let us remember that acceleration and deceleration, just like periodicity, form part of our daily experience: cardiac and respiratory rhyt hm s which d eterm ine the different different pha ses of of sleep subject subject us to those phenomena every night. On the other hand, a new science, chronobiology, is in the process of revealing a series of temporal images of man correlative to the purely spatial anatomical image. It is certain that musicians will have much to learn about these multiple periodicities: daily, diurnal, nocturnal, monthly or annually, as well as their synchronization. Question: Where is the threshold of perception between periodicity on the one hand and acceleration or deceleration on the other? In other words, what is the shortest perceptible acceleration or 4

deceleration? c)   D i s c o n t i n u o u s - d y n a m i c To avoid too great a predictability - something for which one might occasionally criticize logarithmic curves - two types of acceleration and deceleration remain for which an equivalence can be found in filtered spectra (suppression of certain areas of harmonics) and in spectra composed of completely inharmonic, and therefore unpredictable, partíais (bells and gongs, for example). 1) Accelerations and decelerations by step which skip entire sections of the curve in order to immediately introduce the state of a sou nd as it wa s to be at a later later mo me nt (Fi (Fig. g. 7). Order of events,

 n  w  o  D

a

b

d e

Time

Figure 7 Acceleratio Accelerationn by elision.

 

A  composer s reflections o reflections  o n musical t usical  t i me  253 25 3

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Order of eventsi 10 9 8 7 6 5 4 3 2 1 Time Figure 8

Statistical Statistical acceleration.

Such a phenomenon would be perceived either as a simple discontinuity, or in the best of cases as a compression of the acceleration process, the listener re-establishing the formal link which exists between a, c, e in Fig. 7. 2) Statistical accelerations and decelerations which proceed from a positively or negatively orien ted d iscon tinuity (Fig. 8). The Gestalt of a temporal sequence thus determined remains orientated vectorially whatever the statistical meanderings. Excluded from the global form, pure chance is thus limited, held back in some way; the general dynamism takes over. It does not follow, however, that our perception is automatically able to work out the orientation of such a sequence. If the curve is too long, or if the ambitus of the differences in durations or in rhythmic densities is too large, we will pay greater attention to the surprise of the moment than to the actual sense of the sequence. Excessive discontinuity and excessive information focus our attention on the present moment, prevent us from taking any kind of retrospective view, and put a mute in our memory Of course, all types of superimposition of different curves come into the category that we have just defined. However, it is no longer so much a matter of imagining different curves as in the preceding category, than of composing with continuity and discontinuity, with dynamism and stasis, an unstable and perpetually renewal play. Here we encounter the principle of uncertain-

bi l itit y , t y i n per cept i on:   w h a t w e g a i n i n d y n a m i sm w e l o se i n u n p re d i c t a bi a n d v i c e v e rs rs a .

 

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Questions: 1) What specific relationships must the sound contents   a  and c (Fig. (Fig. 7) have so tha t  a  a n d  c  are perceived, not as a simple discontinuity but as an   elision, a comp ression of  a-b-c  into  a -c i Such faults exist in geology which permit the immediate reconstruction of the continuity of opposing strata.

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2) Find a law law defining a relationship b etwe en the total dura tion of the sequence and the range of the statistical variations of microdurations, as we perceive and memorize clearly the positive and negative sense of the sequence. What is the threshold at which the perception of this vector definiti definitively vely g ives way to the p erception of 5 the discontinuity of the present moment? d)   Statistical Like a veritable Like veritable wh ite noise of durations (Cf Cf.. Fig. 10 ), th e probabilisti probabilisticc distribution of a vast scale of durations leaves us no possibility of prediction. The degree of disorder is at its maximum. Absolute discontinuity will only hold ou r attention for for an extremely limited time. Even if it is possible to color with a little energy such a region of

f r equency of whi t e noi se, i f   mu st b e p o ssi b l e w i t h in in d i sc o n t i n u i ttyy t o o rg a n i ze i sl e ts ts o f c o n t i n u i t y .

t h is is a b so lluu t e

e)   Smooth To this picture we can add (non)-rhythm, seamlessness or lack of all temporal division. This "seamlessness", this absence of durations can Durations  ¡i (secs) 0.5 _

0.4 _ 0.3 _ 0.2 _ 0.1 _

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15

20

Order of events

Figure 10 "White noise" of durations. The reading of durations for events numbered 5, 10, 15 and 20 are approximately 0.31, 0.18, 0.38 and 0.22 seconds, respectively.

 

A composer's ref reflecti lections ons on musical time   2 5 7

either be entirely perceptible, the rhythms being only operative, or can be perceptible   a n d  conceptual, a rare case of of the total absence of any event, single sound or rhythmic silence. Question : From From wh at threshold is a duration n o longer longer appreciated as such - which would make it unfit for rhythmic combination?

Conclusion

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The categories categories that w e have jus t defined defined do n ot have to be li limiting. miting. Like Like musical parameters, they are only a reference for the reader, a sort of axiom which permits us to tackle the problem of durations. We can sense that between these categories there are other classifications possible among which we will discover new ones, and so on, indefinitely. We have, on the other hand, voluntarily left aside all combinatory systems realized by the composer, which defy all classification. Such a schema is never affixed exactly to musical reality, which is infinitely more complex. To more closely approach this musical reality, we will pass on to the "flesh "flesh of time" time" w here sou nds , like living living cells, cells, will will come to inhabit and envelop the temporal skeleton with their density and complexity. To close this chapter on temporal structures I am tempted to paraphrase St. Just ("Revolution must stop at the perfection of happiness ") by saying that  s t r u c t u r e , wh atever its complexity,  m u s t s t o p

at the perceptibility of the message.

The flesh of time Definition Hav ing tried to class classif ifyy the qu antitative aspec t of musical time in o rder of complexity, complexity, here are some guidelines for a more qualitative qualitative approa ch: what I call the flesh of time. It is certai certainly nly the case that that I have often ad vanced explorations in th e direction of this present section. In fact it seemed to me virtually impossible to ref reflect lect on structure s of musical time witho ut imme diately touching on phenomenological and psychological aspects. The flesh flesh of of time is is the unac kno wled ged part of musical comp osition. osition. It is thus that we un derstand such phrases as: "The rest is up to the musicians " "This can't be learned." or perhaps "It's a matter of intuition." However, if we believe blindly in the intuition of the musicians, we believe equally equally blindly that this can be deve loped as patiently as the art of good reason. Subtler and more nebulous than the preceding section, it is here 'a qu estion of appro aching the imm ediate percep tion of time time in

 

i s ey ey 25 8   G é r a rrdd G r is

its relationships with the sound material. The same temporal skeleton may be enveloped and therefore perceived differently according to the way in which the volumes and weights of the musical flesh are distributed . To a greater extent than for the skeleton of time, we will be attentive here to the relativity of any temporal structure from the moment a sound materializes it.

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By including not only the sound but, moreover, the differences perceived  between  sou nds, the real material of the com poser becomes the degree of predictability, or better, the degree of "preaudibility". So, to influence the degree of preaudibility we come back to composing musical time directly - that is to say perceptible time, as opposed to Chronometrie time. Karlheinz Stockhausen had already anticipated the importance of this by using for certain works   (Carré   for four orchestras and four choirs, 1971) what he called the degree of change   (Veränderungs g r a d )  )   (1963,  1967, 1971, 1978). This notion is itself the direct outcome of information theory. I believe that the composer who wants to give time a musical value must focus on this point. It is no longer the single sound whose density will embody time, but rather the difference or lack of difference between one sound and its neighbor; in other words, the transition from the know n to the the unkn ow n and the am ount of inf informati ormation on tha t each each sound event introduces. In his composition class Olivier Messiaen said that it was necessary to have at least two sounds, or a silence and a sound, in order that there be music V. Nabo kov w rote on this subject: subject: "Mayb e the only thing that hin ts at a sense of Time Time is is rhythm ; not the recurre nt beats of the rhyth m bu t the gaps between two such beats, the gray gap between black beats: The Tender Interval. ..." (1969). This brings us back to "composing around space", rather like sculptors (cf. Henry Moore) whose hollows are not holes bored into the material, but forms in negative around which the volumes are articulated. Let us imagine a sound event,   A ,  followed by another event,  B . Between   A  an d B exist existss wha t one calls calls the density of the present, a density which is not a constant but which expands and contracts according to the event. In effect, of the difference between   A  and B is virtuallyy nil, in other w ord s iiff the sou nd B is entirely virtuall entirely predictable, time seems to m ove at a certain spe ed. By contrast, iiff the s oun d B is radi radicall callyy different diff erent,, and virtually unpredictab le, time time unfolds at a differ different ent spee d. There must exist holes in time, analogous to what aeroplane passengers call "air pockets". Chronometrie time is never obliterated,

 

A composer's reflecti reflections ons  o n musical time  2 5 9

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but our perception of it can overshadow the linear aspect for a more or less brief instant. Thu s, for for example, an unex pected acoustic jolt causes us to skate over a portion of time. Sounds perceived during the ensuing moment of readjustment - a moment which is necessary for us to regain a relative equilibrium - no longer have anything like the same emotional or tempo ral value. This This jolt jolt wh ich d isturbs the linear unfolding of time an d which leaves a violent impression in ou r mem ories, mak es us less likel likelyy to grasp the shape of the musical discourse.   T i m e h a s  contracted. On the other hand, a series of extremely predictable sound events gives us am ple allowance for for percep tion. The slightest slightest event acquires an importance. Here,   t im i m e hhaa s e xp xp a n d e d .  It is m oreo ver this sort of predictability - this expansion of time - which we need to perceive the microphonic  structure of sound. Everything happens as if the effect of a zoom lens, which brings us closer to the internal structure of sounds, was on ly able to functi function on by w ay of an op posite effec effectt in relation relation to time. The more we expand our auditory acuity to perceive the   microphonic world, the m ore we draw in ou r temporal acui acuity, ty, to the point of needing fairly long durations. A law of perception therefore comes into play which could be f o r m u l a t e d t h u s :   t h e a c u i t y o f a u d i t o ry p e rc e p t i o n i s i n v e rse l y p ro p o rt i o n a l t o t h a t o f t e mp o ra l p e rc e p t i o n .

can expenlained by a simple of energy ism,kno wnis, fo forrThis exam ple,also thatbethe ergy consu me d bytransfer visual percep tion. It (fil (film, TV) such that in order to have a satisfactory auditory sensation we must increase the sound level (Grisey, 1978). This brings us closer to applications of the principle of uncertainty formulated by quantum physics which here is "a principle of limitation of information receivable from the outside world" (Moles, 1966).

Duration and microphony A s  a  result of the extreme expan sion of time, time, w e arrive arrive at the very hea rt of sound whose material is revealed by the effect of an inordinate magnification. What remains of the dynamism of global structures when, with our ears riveted to the   i n t e r n a l  dyn am ism of sound s like the eye to a microscope, we become deaf to every   macrophonic   event, or more precisely to all forms of relationships linking these events: melody, harmony, articulation, rhythmic gesture etc..., in short, all that traditional Western music proposes? Let us imagine o urselves, like like the h ero of C. Castan eda 's wo rk (197 (1975) 5) contemplating the water at the edge of the river, then progressively, men tally redu ced to the size size of of the molecules of of water until we o urselves become molecules; we wou ld certainly certainly be surrounded by an u nhe ard of

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