35

Implementation

35.1. HOW SHOULD WE MAKE AND WHAT SHOULD WE LISTEN FOR?

Having so clearly marked out the limits of our study, it would seem that we were generalizing without crying, “Beware.”1

Moving on in this way from objects to their implementation is surely tantamount to going beyond the limits we had determined for ourselves? Since we thought we should, and could, make a clear distinction between composition and the discipline of music theory, why change our minds? Are we going to add to the question about the use of objects another question, even more unwise, and particularly presumptuous at the level of materials, the question of ultimate meaning? In other words, having written about the musical object without being willing to write a single note, are we going to tackle music itself, its beginnings and its ultimate purpose?

We are indeed going to do this, immediately making clear the limits of our ambition but also accepting responsibility for what we do.

First, it would be difficult to see how a piece of research of such importance could be put forward without instructions for use. We have said often enough that the study of material was indispensable only because of its involvement in musical organization. As for the choices that emerge thereafter, we will not take sides.

At least we should say clearly what these might be. We think, moreover, that these choices determine which, of all possible musics, we intend to make and play, its performance potential, its communicative qualities; these choices, in turn, depend on the intrinsic properties of the material, which determine the particular relationships and functions it can take on. This is the subject of this chapter.

So we must allow the theory to go thus far. If, in the next (and last) chapter, the author happens to go a little further and exceed the limits he has set for himself here, this is a matter of temperament and vocation. After such an arduous scrutiny, it is tempting to give a few opinions: to recommend reasonable aims, identify contradictions and dead ends. This can be done without embarking on a pointless and often harmful aesthetic debate: it is a question of indicating not preferences but possible musics.

35.2. ON THE RIGHT USE OF A MUSIC THEORY

If in this book we have never used the symbols of traditional theory, it is not because we despise them. Assuming that everything they represent was already well known and had nothing more to teach the reader, our intention was not only to describe what these symbols do not show but precisely to put him on guard against this particular symbolism. We should not forget, for example, that mathematics has often preceded, prepared the way for, made possible, the discoveries of physics. Its role is not limited to putting a phenomenon into an equation; it suggests new experiments to researchers, provides a medium for their imagination. Notation plays a similar part in music. We can see this tendency in action in the propensity musicians have at present to rely on it to calculate their scores, and we cannot be angry with them for seeking to predict music with a little more method and “rigor” than their ancestors did in their absolute devotion to their inspiration. But the tools must work properly, and the figures must not be rigged. In any case, a careful examination of the bases of the calculations themselves cannot be wrong.

In sketching out a “generalized” music theory, going way beyond the immediate needs of present-day composers, we had two applications in mind: one concerns musics that are “different” from our own (ancient or non-Western), where it is our contention that the present way of deciphering them is poor, crude, and inaccurate as long as we apply the Western frame of reference to them; the other concerns musics yet to be invented, which clearly preoccupy musicians of our time. The moment has come to test these out.

First we will see how this new way of looking at music might enable us to explore musical civilizations. Then we will see how present-day developments can be explained by it and how it reveals a number of methodological errors; so we hope that, by broadening their vision, we may be able to free composers’ imaginations.

Before going any further, we should immediately point out a contradiction that usually remains latent in contemporary musical thought. The latter, in fact, looks at music in two alternative ways. It is supposedly an expressly cultural language, which finds its meaning only in use: so in contemporary developments we see an extension of the traditional system, which involves an attachment to these signs. But people also refer to acoustics, physiology, parameters, the response curves of the ear; that is, they postulate a natural explanation for music, which they seek in organizational formulae (mathematics) or the properties of sound. This means that we come back to the central problem of the essence of music: is it natural or cultural? From the very beginning we have recognized this dualism, and in every concrete instance we have found its mark. The serious thing here is that most composers do not even seem to be aware of the problem and dwell in ambiguity. In short, when it suits them, they do not hesitate to go without any warning from one side to the other.

35.3. ATTEMPT AT AN EXPLORATION OF TRADITIONAL MUSICS

Rather than go backward to the past, starting from the most highly developed Western system, we propose to discover the musics of the various civilizations through their origins. We can imagine that they develop from the resources available to homo faber, always precisely situated in time and space. Yet, instead of excavating his remains with the same care that archaeologists show for fragile pottery, perishable varnishes, and unstable glazes, we turn the field over with a bulldozer, which is nothing other than our piano (forte), steel-clad and rosewood-finished. So strong is the faith in our own musical signs that it seems impossible to approach other civilizations, which are, in fact, often unreadable, in any other way than through these signs, which then leads us to describe their development in terms of tetrachords. But tetrachords can only apply to civilizations whose offshoots we are and that in their time made the choices that are ours. There may be others. The story of music should be related in ages: bamboo or skin age, fiber string age, bronze and cowbell age. We may imagine that then the struggle between sounds of determined pitch and complex sounds was not so unequal and that consequently musique concrète is not such a bad route back to the sources. Eventually, we discover that the music we so improperly call “traditional” is practically contemporary with the modern, technological period, preceding the electronic age by only a few centuries.

We, on the contrary, intend to take a more universal approach to musics. An authentic analysis of these should rest on the type of comparison of sounds we have suggested, by classes, genres, and species, first raising the question of the historical choice of a class of dominant perceptions when a genre of sounds is being played. Here we discover “in embryo” one or several interactions of values when a particular characteristic of sound delivers them. So it is very easy to explain how primitive civilizations—unable to develop harmonically and having no well-determined registers, which depend on refined instrument making—should have turned not only to rhythm but also to evolving and complex sounds, in short to all the objects described in our typology.

The exploration of non-Western musics also reveals two main “states” of objects or at least the fact that some of these musics turned to the continuous as well as the discontinuous. Here Asia gets its revenge; in these musics it is very difficult for us to appreciate both sounds that vary from one degree to another and also intermediate notes that in our mother tongue are wrong (even if exquisitely so) and that Asian people must surely hear with a different ear. Our notation of this language (in discontinuous degrees and duration) will thus miss the essential, seeing as important what is not, and vice versa. The question is not how to transcribe these languages into our alphabet but how to discover the functions of their own musical objects and the original organization these bring about. It goes without saying that this must involve varying criteria, trajectories, and a particular dialectic of the perceptual field for this purpose, developing a particular natural relationship culturally among practitioners of this music.

Finally, and only then, comes the question of calibrations, always stupidly presented as essential and prerequisite. They are, as might be expected in our vocabulary, only examples of species. We will probably find that they, too, have a balance between the natural and the cultural.

35.4. CALIBRATIONS OF VALUES

We had promised not to discuss calibrations of values, because in a treatise that deals only with the description of the object, we were not in a position to do so. In fact, we find ourselves in a very one-sided situation between the attention given to some values, the central theme of impassioned discussions, and our neglect of the others (since some values are not even acknowledged and the relationships the perceptual field allows them even less so). So we fall between two schools: the excessive competence of Western musicians in the so-called chromatic calibration and our incompetence in those we can only glimpse. The important thing, however, is to point out the plurality of calibrations and to condemn the tendency to bring them into line with the calibration in degrees, as if this were the model, both natural and cultural, for all the others. This tendency is all the more absurd as it coincides, historically, with the rejection of diatonicism.

In this chapter we will at least endeavor to clear a terrain cluttered with very different problems, which have usually been conflated. We will distinguish between

• the natural phenomenon of the main harmonic degrees,

• the cultural phenomenon of the scales based on these,

• the frame of reference formed by these scales,

• leaving out of our discussion the exploration of harmonic rules, which themselves can be deduced from the above.

A program such as this is very similar to those that have been expounded by more competent researchers than us.2 We have absolutely no intention of discussing this question all over again but only to attempt a brief foray into the natural foundations of music, limiting its scope to musics “of tonic pitch.” Moreover, we will be happy simply to explore the possible origin of the diatonic scale. We cannot but be surprised, in fact, at the ever-greater divide between musicians of equal good faith but firmly lodged, it seems, in one or other of the warring camps where the problem of consonance is concerned.³

Pythagoras, according to Jacques Chailley, did not “make it his aim to determine the intervals produced by preestablished relationships, but he was struck by the coincidence between previously known intervals and relationships between string lengths.”⁴ So here we have an experimental finding and not an a priori construct. “Of course he does not know the principle of harmonics, discovered only in the seventeenth century, and sees only string lengths, therefore relationships between consecutive sounds, which he transforms into simultaneous consonances only by means of an a posteriori thought experiment.” How can a string be divided? Into two halves of course, but then? The simplest fractions after this are two-thirds and three-quarters. And so we obtain the fifth and the fourth, and we notice, with Chailley, that tone is not defined “as the relationship between harmonics 8 and 9, but as the difference (relationship) between the 2/3 fifth and the 3/4 fourth.” The string length relationship corresponding to the tone is indeed: 2/3:3/4 = 8/9. For Chailley, the mastery of degrees happens progressively. “By ending direct observation at the number 4, Pythagoras is simply conforming to the state of consonance of the primitive ear at the first stage of its progress from level to level. . . . Thus the framework of a Pythagorean melody cannot be the perfect chord C E G C. It is usually C F G C, and to the very end of the Middle Ages every Western melody is Pythagorean.”5

35.5. SIMPLE RELATIONSHIPS

The debate generally gets off to a bad start because people seem to put forward “simple relationships” as a sort of metaphysical justification. We need to take a closer look.

Two experimental facts establish what we called in book 3 “correlations” between the physical phenomenon and musical perception. It seems that no one has ever properly identified that the two facts are different or that they are correlative rather than explanatory. The first “fact,” the Pythagorean experiment, can be verified by pupils in the string classes in our conservatories. When a cellist goes up the scale on the C string, he divides the string successively into fractions respectively equal to 8/9, 5/6, 3/4, 2/3, 3/5, in order to play D, E, F, G, A after C on the open string (and we wisely stop there, before the “leading” note, and for good reason).

What Pythagoras had neither seen nor heard was discovered in the seventeenth century, and Helmholtz worked out the theory of it a hundred years ago; it is something completely different: the same string (and not the strings next to it on the lute or the fractions of the C string divided up by the cellist’s finger) vibrates like a spindle for the fundamental, but also in two, three, four, five, and so on spindles, revealing the existence in the same “tonic” sound of a series of harmonics, whose comparative frequencies are like successive whole numbers.

The two phenomena (the old and the new) are so different that they can be isolated. “Pure” electronic sounds with no harmonics show only the first correlation between frequency and degree if we make them go up the scale.

Now, even though the way these two distinct correlations tally appears remarkable to the physicist, it is only convincing musically through a general consensus. If we want to rewrite history, we deny this consensus. And so these days we observe two contradictory (and largely uncompared) attitudes on the part of physicists and musicians: the former continuing to attach the greatest importance to consonance, the latter not caring a damn.

The discussions about all this are therefore far from achieving unanimity, even among scientists, because of the prevailing uncertainty about the perception of harmonics. Some ask, What role can they play, since we can’t hear them? Others remark that, as harmonics are different from one timbre to another, consonances must be subject to change. Helmholtz’s classification is challenged by another, related it is true, based on the (subjective) perception of additional or differential sounds N1+N2, N1−N2, and so forth.

It is in Professor Winckel’s6 writings that we find the most positive contribution.⁷ “Helmholtz,” he says,

had already drawn attention to the similarity of harmonics in consonant chords. The notion of residual sound enables us to see that there is also a degree of similarity in the residual fundamental; that is, we can find identical components coming from two different intervals. . . . The view that sinusoidal sounds would give the same sensation of consonance has now been invalidated after a series of experimental demonstrations. Natural sounds show a coincidence between residual harmonics and hence a greater degree of similarity. The effect of consonance is therefore proportional to the number of harmonics, that is, the richness of the timbre. So this effect is weaker for chords on the flute than on the trumpet.⁸

This remark corroborates what we have said: consonance is not a relationship in itself but depends on the objects present and, since they are assumed to be tonic, on the structure of their timbre. The perception of intervals does, indeed, rest on facts and classifies them in a certain natural order.⁹

Even if the fact is confirmed in this way, the explanation itself is not always given. This is because, misled by the schoolboy axiom—an error expounded again and again—that we hear tonics through the fundamental, we cannot really understand the purpose of these harmonics we cannot hear, or that we hear in the form of timbre, in the reasons given to explain consonance. Now, we demonstrated in book 3 that as a general rule the perception of tonics involved the whole of the spectrum, and we were surprised that this observation, which we were not the first to make, had so little impact. So it is otiose to ask whether we hear harmonics or not;¹⁰ it is harmonics, their series, perceived as a whole (a musical object precisely) that reveal the tonic to us. From this starting point the explanation becomes convincing: when we compare two sounds, we are not comparing two numbers (their simple relationships would not necessarily explain a law of perception) but two “structures,” which have a greater or lesser number of “shared” as well as “different” features. The permanence-variation law thus applies to the most basic phenomenon in music: the intervallic relationship. The more points two of these structures have in common, the more apparent is their consonance (melodically at first, then harmonically). The fewer they have, the less natural is their relationship (these harmonic structure relationships are represented visually in figure 46).

So we can now understand more clearly why the theory of scales has remained so elusive. One of the reasons for the ambiguity is that so-well-taught error that tonics are perceived through their fundamental; the other is too much naturalism: theoreticians would like to base the Western scale entirely on the natural phenomenon of consonance. Because they cannot, they sell the whole thing down the river. He who wishes to prove too much . . .

35.6. REFERENCE STRUCTURES

It is beyond our remit to look any further into the origin of scales and to decide for good and all whether the seventh degree is a convention. We know enough about it to say that this is highly unlikely and to state that musical civilizations will diverge profoundly from here, perhaps attaching the most intense significance to this one degree of freedom: so the leading note is well named. From the above facts we can also identify the origin of the diatonic scale in three perfect superimposed chords or, again, the so-called Pythagorean scale in the sequences of fifths; all very logical but constructed as a complement to natural data. Finally, once these degrees are given, the freedom to take one rather than another as the tonic for a mode is just a question of choice, tradition, and conditioning. So we go from a few fundamental natural elements to a quite different order of facts, obviously cultural, developed through the most rigorous learning processes.

So we have two categories of very different problems, depending on whether they involve natural or conventional reference structures. This difference is not generally perceived, and for good reason, since the idea of a fundamental dualism does not even cross people’s minds. The examples we are about to give will endeavor to explain each type of problem in turn.

First we will look at the problem of the change in cultural references at a high level of development and formulation. Atonalism, just like the Chinese scale, rejects diatonicism. But these three systems also have some degrees in common (used in different ways, it is true), apparently arising from that minimum of natural bases that we have just been discussing. How does this serve them, or does it limit their freedom?

We will start with atonalism.

The term indicates that it rejects tonal reference. Better still, the rules for the use of the twelve sounds without omission or repetition guarantee this. Here we have a conventional level of complexity, where it is certainly difficult to alter spontaneous reference but where earlier developments in tonality had prepared the way through successive transgressions. There are still degrees, however, that are harmonic in the atonal scale, and it is difficult to deny their effectiveness, which—in our view—is of natural origin.

The recourse to the value of intervals is, moreover, implicit in atonal music—for example, in the creation of series by inversion. Also there are two ways open to atonalism. One consists in reincorporating intervallic functions outside diatonicism,11 the other in getting rid of them and going imperceptibly and, as it were, unconsciously from distinct, tonic pitches to “blocks of sound,” which come under our definition of “complex mass” and no longer allow chromatic relationships to be heard. Between the two, there are short-lived musics, and ambiguities between the intervallic relationships and gradations (not the degrees) of a pitch register, presenting the same type of nuances as the register of intensities.

We can give a striking example of the ambivalence or contradiction between using and simultaneously rejecting the harmonic register. From the standpoint of a generalized atonalism, people go so far as to reject the octave relationship and contemplate calibrations of sounds, from low to high, based on a choice of proportions independent of any traditional interval. This is technically possible in instrumental music and even more easily so in electronic music. So there is every chance—the tonal or consonant context being absent and also thrown into disorder by the complexity of the blocks of sound or the rapidity of the features—that the listener will no longer listen harmonically but according to the calibration of mels: the true (perceived) intervallic relationships between high and low are not now those from inverting or transposing, still in favor in serial music, but those determined by working out intervals in mels. Thus, Paul Pedersen gives as the equivalent of motif (a) in the midregister, not the same notes transposed into the bass register (b) but the equivalent motif in mels (c), a group perceptually nearer to the initial motif (a).¹² The composer is probably right on this point, but then it is the writing down that is likely to mislead. For, continuing to read in the key of G or F on a harmonic staff, we always attribute a (harmonic) value to these notes. They no longer have one; they are merely signs for performance, like piano keys or instrumental fingering. They are no longer simply inadequate symbols that mask additional contents but signs that have lost all value. Worse than an illusory sense of security, they give false ideas and misinformation about the merchandise. Just as the physicist refuses point-blank to write decimals when he only knows the approximate value of their magnitude, so the musician should reject as false currency signs that no longer correspond either to what we hear or even to the relationships he is claiming to determine. Thus, even if we have decided to get rid of a conventional structure such as tonality, we continue, in fact, to return to the calibrations involved, and this on the two levels of making and hearing. We continue to produce harmonic sounds and notate them on a staff, and we pretend to hear them (or we endeavor, with the help of the score, to find them), without noticing that this may be either impossible, because of new contexts, or unjustified, because of new choices (see fig. 43).

FIGURE 43

This duality of planes does not occur in our second example, where harmonic perception, instead of being blurred (or negated), is reinforced. The Chinese scale (according to the most scholarly description of it) is also constructed on a series of fifths but limited to the first five. All its degrees are identical to ours and its intervals simplified. So they will not present any problem for natural perception: on the contrary their calibration, too obvious, will appear as follows:

C    G    D    A    E

which gives the scale:

C    D    E    G    A

or this other mode:

A    C    D    E    G

This last structure is remarkably symmetrical: two minor thirds frame two tones and form the following group of perfect fourths and fifths:

The strength, the “meaningfulness” of such a structure is very evident to Western ears. Instead of finding a neutral scale or a reference structure like the Chinese, we hear a motif. Also all Chinese melodies, for us who are differently conditioned, are only variations on a theme, insistent and repetitive, the pentatonic theme related to our own scale. The musical meaning in a traditional system therefore rests on the perception of differential structures.

This all-too-brief and very sketchy incursion into the domain of scales, in the penultimate chapter of this treatise, clearly demonstrates that it is ending precisely at the point where the debate most often begins. We hope it will at last inspire the reader to generalize the idea of the musical and also to set a boundary stone. At the basic level where we have chosen to be, the question of scales does not, in fact, yet arise: music theory defines the basics of musical perception, and so stops at the criteria for this and the interaction of the potential relationships among these criteria. Musical theories, which underpin particular musics, affirm the taste of civilizations: the choice, out of all possible structures, of those that will serve as their frame of reference.

35.7. LISTENING TO CONTEMPORARY MUSICS

Now we will count time not in millennia but in decades. In our day we are witnessing the confrontation between two tribes. The first is composers who construct musics a priori on precisely calculated scores. As these composers sometimes possess an overtrained ear (and here we must acknowledge the progress of the Western ear, at least in a specialized sense of making and hearing), they have some chance of hearing their music as they have written it. The other tribe is (uninitiated) amateurs or (experienced) enthusiasts who both have nothing but their ears. Scandalized or interested, they generally hear something different from what the composer intended for them—the same thing that arouses their repulsion or their interest. Then come the elect (this is us, reader), in the minority but enlightened by a modest revelation: we also only believe our ears but ears trained over several years in the practice of the types, classes, genres, and species in the generalized theory of music. Here, independently of any organizational analysis (and of any aesthetic allegiances or dislikes), we practice musical dictation: we are capable of deciphering these, and other non-Western, musics. We even occasionally observe strange similarities between the former and the latter (which, from our point of view, is by no means a criticism). We feel uneasy, however: our reasons for appreciating these so-well-calculated compositions are not the same as their composers’ reasons: we can see a divorce between what they intended to write and what we were able to hear.

This is where, in our opinion, the debate should take place; the communication between composer and listener and their shared interpretation of what is “given to hear” could be made very much clearer if this were so.

Several of us have in fact practiced careful listening to contemporary works, whether orchestral, electronic, or electroacoustic. We have applied our typological rules for identification to them, our division into classes, genres, and species, which, moreover, these “dictations” from experience have led us to revise constantly, bringing them to their—still quite rudimentary—state in the present study. We can say that this analysis is fruitful and, in any case, gives an account of reality in a better though other way than a symbolism that is both inadequate and persnickety. Even if we have been reluctant to elevate such analyses prematurely to the level of composition, we are convinced that they are possible, indispensable even, and certainly very different from the working schemas of performance scores.

To recapitulate the methods and the findings of these exercises in “musical translation”:

(a) We identify objects in the works, and we carefully observe whether they emerge in the classical way through traditional values or if they form new aggregates because of the complexity of the perceptual criteria involved or the continuity of their variations. Generally speaking, this is how musical objects define themselves in relation to the continuity or the discontinuity of the musical fabric.

(b) We also recognize the types of objects the composer chooses in a particular work, and this, of course, stems from the way he uses the orchestra or instruments. In general, these do not play note by note any more, and it takes only a moment to discern the composer’s preference for webs, iterative sounds, rapid varying objects, cells, and so on.

(c) Independently of this typology, often characteristic of a composer’s “style,” we will have identified the genre of sounds he favors and the main permanence-variation relationships he uses. Of course, this is where the listener’s agitation is the greatest, an agitation shared, let us be in no doubt, by the composer himself. The latter may very well have worked everything out on paper, but where the results are concerned, he is usually in a state of uncertainty unless, fanatically obsessed with his own ideas, he is resolved to hear only what is on the performance schema he has finally learned by heart. We are sorry for him. We can only advise him to go back to the classical gesture of the painter, who stands back to see the effect.

(d) So, then, the listener will always turn to his natural reference structures, developed by his own conditioning. The contents of his listening then become very personalized. He hears in detail or in “bulk.” He may refer to what is too well known or be taken aback by too much strangeness.

(e) We are talking here about listening from beginning to end in memorizable sequences that do not necessarily coincide with phrases. What is certainly important is that the work should communicate a meaning that will be examined at greater depth on further listening, which is always essential. But what is this meaning (or these possible meanings) at the level of the overall form?

We can see that we have just gone round the cycle of “quadrants”: identification of the state of objects or types in (a) and (b), perception of the genre of fundamental relationships in (c), measured against reference structures in (d); finally, in (e) we come to the question of meaning—that is, of the work as an overall structure, which rests on the whole preceding framework.

35.8. A PRIORI MUSICS

Unfortunately, analyses such as these are not at all convincing to anyone who is not trained in reduced listening and has not attempted to use this training to decipher works. We would wager, however, that when a sophisticated public, or at least an experienced composer, listens to a modern work—without being party to the score—they do hear roughly what we have just more clearly outlined: dynamic or harmonic forms, the stuff of which sound is made, developments of matter or color, dust clouds or traceries of sound, profiles, and webs. The difference between the two approaches is that the one we are recommending, made at the level of perception, does not aim to be anything other than a description of the objects perceived (and not a justification of their organization), whereas note-by-note analysis, based on the score, generally claims to do both things simultaneously: to describe what the listener is perceiving, while at the same time justifying the validity of the work. The debate that for years has pitted serial music against experimental music certainly reflects this difference in perspective.

We will look a little more closely at the two typical variants of a music justified a priori in this way—the score and the blueprint—leaving to theoreticians the task of upholding their theses.

We will begin with an analysis of a passage from opus 31 by Webern, as presented by Michel Fano:

Four different blocks of sound: six initial and six final sounds in similar and contrary series with their homeomorphism seen in pairs, I and II, III and IV:

FIGURE 44

as is the permanence of the variant (in dotted lines) for the two pairs. Furthermore, on each of the four blocks, a transformation—timbre, register, intensity, duration—an example of which on block IV is shown below:

FIGURE 45

In the latter example (Bar 48), block IV being only a component of a 12-tone complex.

Fano continues:

Where we observe the persistence of certain invariants—not necessarily affecting the same parameters—the result is successive distortions of an identical sound block, a homeomorphic character i.e. a bi-univocal and bi-continuous transformation of its components.

Even if a whole collection of blocks that are themselves homeomorphic gives a similar number of different sounds, we will nonetheless be dealing with a single figure.

Moreover, if we isolate the transformation variants in the various blocks we will identify a group of operations (in the group theory sense) which, freed from their individual sound blocks, will have an influence on other organizational planes, thus creating an isomorphism of structures whose series will turn out to be the law of composition.

All we need to add is that only a diagonal intermingling of structures (and not a juxtaposition or a superimposition) will lead to a torsion of the entirety at any particular moment by bringing about the essential interactions that will affect all the groups, without which any formal attempt is likely to remain fruitless.13

It is not we who have done the italicizing but the author, and we are grateful to him for it: there could not be a better opportunity to explain the similarities and differences between this method of analysis and our own. First, the permanence-variation axiom, although couched in highly abstract terms, will have been recognized; the “single figure” refers to permanence, and the “different sounds” are the possible variants of this. As for the “block of sound” that is being worked on (a term not defined in any other way), it doubtless refers to something more general than a chord since it is given another name: why not what we call “musical object”? But even if we notice the transfer of block IV on to other timbres, we are told nothing about the nature of this transformation; as for the “diagonal intermingling” that ensures the perception of the “entirety,” how does it work? In other words, Fano’s explanation seems to us to be extremely accurate as far as musical writing is concerned, but it stops there and takes hardly any account of what is “given to hear.” Now this is where our investigation starts; what, with this judicious organizational formula, are the justifications, the perceptible effects, as much on the level of this group of “blocks of sound” as of the development of the entirety?

35.9. SERIAL GENETICS IN ELECTRONIC MUSIC

Before continuing the discussion, we will examine the other way serial music operates: Stockhausen’s method in his 1953 Electronic Study No. 1. We admire many other works by Stockhausen, where the instinctive inspiration is, in our opinion, infinitely better than the explanatory systems he recommends. We are less impressed by the text we are about to discuss now. We should, however, give him credit for having shed light on the assumptions behind a theoretically conceived electronic music. Finally, we should make it clear that the experiment described in this text deserves closer technical examination on account of its serious nature.¹⁴

We do not want to quibble with the author over his use of sinusoidal sounds, or of any particular procedural detail; all that concerns us here is his overall attitude toward the musical:

Starting from the optimum auditory field, the fact that sounds will tend to move toward a nonexistent frequency on the one hand and an infinite frequency on the other will be felt proportionately as these sounds tend toward either infinitely small amplitudes or infinitely short durations. In other words, taking into account the physiological conditions of listening in the low and high registers, the perception of the shortest duration and also thresholds of intensity (pain and audibility thresholds), we have acknowledged that there is a frontier, nevertheless quite relative, beyond which the tendency toward a soundless, timeless absolute is implicit. Could this one day be made perceptible? Thus serial structure will suggest a rotating sound world, with no possible development: the essential, the tendency to move toward thresholds, will be implied in the creation of each series: concepts suggesting tension, such as “beginning,” “development,” “end,” “middle,” or “final” will be abolished; past, present, and future will be one and the same.

FIGURE 46. Harmonic structures.

FIGURE 47

FIGURE 48

We can see several initial assumptions here, as well as a reference to Fletcher’s curves (which give the frontiers of the absolute). The composer could just as well have tried to compensate for the deterioration of sound sensation at the limits of the audible; on the contrary, he has chosen to accentuate this fading away. Thus he postulates a “rotating” (we would say “rounded”) domain, where the usual tensions, particularly those between pitches, tend to disappear and where as a result time, it is hoped, will be abolished (?). Furthermore, superimpositions of pitch will create timbres: “by using simple intervallic proportions (harmonic proportions), timbre will simply be the result of their combinations.”

So everything depends on the series of the chosen proportions. This is where we must pause in contemplation; this is the Elevation, the moment of pure performative authority, of supreme freedom: it is decided that the series will be as follows:15

The implacable law will now apply to the entire creation of the work: the general illustration of the frequencies used, the grouping of sound complexes, the variant of these groupings by “modulo-permutation”; for the latter, it is true,¹⁶ a second sovereign act occurs in the form of an organizational series, chosen “because it is asymmetrical and determined by the overall formal concept.” This magic formula is:

4    2    3    5    6    1

One more detail: as it is necessary to “make a clear distinction between the individual timbres of each complex by means of dynamic degrees,” complexes of frequencies will be made by means of the following dynamics, corresponding to each number:

1: flat profile;	2: flat and resonance;
3: crescendo;	4: crescendo-resonance;
5: decrescendo;	6: decrescendo-resonance.

However arbitrary these various choices may be, we can rely on Stockhausen to have reduced his authorial interventions to a minimum. The idea is, in fact, clearly asserted: “When a series of sound complexes were used in my two latest works, a contradiction emerged between the use of preestablished spectra (instruments) and the application of the serial structure to the timbres. A solution to this problem can be found by working with sinusoidal sounds, for the timbre will be defined by the number of sinusoidal sounds that make a vertical complex and by the intervallic proportions between these sounds and their respective amplitudes. Composing with complexes defined in this way amounts to integrating timbre into polyphony by the very fact of bringing them into play.”

There is certainly something fascinating (like self-harm) or absorbing (like totalitarianism) in this ferocious quest for the compulsory link, for integration at all costs, for the development of the whole from an initial cell that could be—and soon will be for others—taken from chance itself. Unfortunately, all the facts of perception we have discussed in this treatise run against such a concept of musical genetics. Furthermore, if Stockhausen, as he admits, has conceived “a real aversion to the dead-end experiments with ‘sound objects’ made by the musique concrète group,” we should in turn acknowledge—in all friendliness, why not—our no less real aversion to the sort of experiment we have just been discussing. We should at the very least take note that these are two implacably opposed attitudes toward the musical.

We could interpret Stockhausen’s position as a salutary reaction against worn-out ideologies, an essential return to concrete principles. Even then we ought to retain aspects of the scientific spirit, adherence to the real, mistrust of hypotheses, instead of giving in to a mimicry of numbering and measuring. Now a physics of musical listening based solely on Fletcher’s curves, which ignores the most elementary facts of perception, even those acknowledged by other physicists, can only lead to formulae for manufacturing instructions. It is our turn now to denounce a self-satisfied and deceitful aspect of the most blinkered amateurism.

Michel Fano’s analysis of Webern’s “sound blocks” is, in our opinion, just as obsolete. We have acknowledged the idea, already familiar to us, of a balancing act between permanence and variation. But, whereas we take our information only from listening, Fano confidently deduces a law of composition from a formula, basing his analysis on the score alone. Certainly, this varying element in unvarying structures has a good chance of being perceptible. If we set out to verify it, we find a—highly interesting—experimenter’s hypothesis. If this is imposed as a law justifying composition, it is through blind obstinacy and the confusion of three levels: elementary perception, referentiality, and meaning. Using the pretext of the nominal permutation of a note or the transferral of the block to other instrumental timbres, they want to make us say at one and the same time:

(a) that we can perceive this formula,

(b) that it is has a frame of reference, and

(c) that with further perceptions of its variants it can form the basis of the structure of the work.

This is too much for such a narrow base. It is unfortunately often possible to observe in contemporary thought a refusal to see this upward movement and a taste, as it were, to keep to lower level determinist systems. We really must try to understand why. This is what will lead us, in the next chapter, to raise the level of debate.

35.10. OUTSIDE THE SERIES

Let us go back to language.17 The phonological level is the only one that does not refer directly to meaning, except to give access to the signifying levels of lexis and syntax. Lexis and syntax make up a code, with which every speaker must comply under pain of not being understood.

But as soon as this speaker combines words following the rules, he says something, which knowledge of the code alone would never allow us to expect. Once the thing is said, we check that the utterance conforms to the code and actually respects the linguistic rules. But the content of the message and its literary, poetic, philosophical, or scientific value belong to the writer, the poet, the philosopher, the scientist, in short to the users of the language, speakers or listeners, who concentrate on the meaning while forgetting the rules that allow this meaning to be transmitted.

Whether music is a language or not, it appears impossible not to recognize these three levels. The most everyday musical analysis, even the most inaccurate literature on music, distinguishes at least implicitly between theory, syntax, and the work, which has a meaning. We need to know whether this distinction still exists in contemporary musical thought. Are we the only ones who think this way?

“Grammar is not language,” Luciano Berio writes, “but only one of its dimensions. In a language continuity such as our own, we could not possibly have a single grammar, but many ideas and possible levels of ‘grammaticality,’ independent of any idea of semantic signification. The word comes later. . . . That is why I consider the concept of serial music as something linguistically indefinable—the opposite of a complete language. This concept may perhaps be useful to give a generic description of a tendency toward grammatical plurality and multiplicity, or to designate part of the chronology of the most important musical events of this century.”18

This sentiment is echoed by Pierre Boulez, who first of all sheds some light on those notorious “sound blocks” discussed by Fano (chords or objects?):

In reality, there is a great deal of ambiguity in the use of these chords, which are “sound blocks” and can become “whole” objects, the timbre and intensity then being an integral part of this combination: this is where we would call for the creation of a hyper-instrument whose sounds would be a function of the work itself. This links up with the present concerns of electronic music, where this goal is pursued with pure sinusoidal sounds; however, in most cases until now, a timbre that appears as such is very rarely achieved by superimposing sinusoidal sounds: we are more likely to obtain refined harmonic effects. The aim of research should be to try to analyze under what conditions, whether with electronic sinusoidal sounds or this hyper-instrument, a combination of existing instruments, the ear can really perceive a timbre that results from these, and is not a simple add-on.¹⁹

Point made. So we come to recognize a unit of perception until now given the all-purpose name “sound block,” which would be a “whole” object indissolubly linking together pitches, timbres, and intensities.

“The misunderstanding that dogs us and that we must be terribly wary of,” Boulez continues,

is confusing composition and organization. A coherent system is, in fact, a prerequisite for any composition. . . . But the web of possibilities made available by this system must not be simply set out (on the page) and considered to be enough in itself for the requirements of composition. Indeed it seems that, out of a “religious” respect for the magic power of number and the desire for an “objective” work depending on a much less uncertain criterion than the composer’s free will, and out of some thought still about a contemplative mode of hearing, we are abandoning the task of composing to organizational systems.

We ought, on the contrary, to see the work as a series of rejections in the midst of so many probabilities; we must make a choice, and herein lies the difficulty so well sidestepped by the express desire for objectivity. It is precisely choice that constitutes the work, repeated at every moment of composition: it will never be possible to reduce the act of composing to the fact of juxtaposing these nascent connections in one immense set of statistics. We must safeguard this inalienable freedom: the constantly hoped-for good fortune from an irrational dimension.

These are important lines. They should enable us to distinguish between personal inspiration, which we do not share, and methodological conclusions identical to our own.

That from an aesthetic point of view Boulez bases his choices on “rejection,” whereas we base ours on “expectations”; that the word contemplation is pejorative for him, whereas, if there is still any trace of a preestablished harmony in the series, that it should be contemplated is precisely what we would ask; that, finally, he sees what is inalienable in our freedom as “the irrational,” whereas for us freedom is reason—all this is of little importance in our present discussion. In fact, from the methodological point of view the idea that there is a distinction between sonority and musicality, between the experience of the ear and of the mind, and between the planes of the perception and use of objects, which we have argued time and again, is acknowledged here (although vaguely, and as it were secondarily).

We could simply shrug our shoulders at all this: what is the point of these arguments over method? Provided a musician has talent, he will get by; the main thing is that he makes music. True, but must we then go back to the cult of personality, after castigating the libertarians for this for so long?

35.11. THE THREE TIERS

The details of the discussion on new bases for music about to take place here, although very ancient and fundamental, are, in fact, very poorly understood. Certainly, we share the opinions we have just quoted, but we are scarcely any further on. If we accept that there are “several levels of grammaticality,” then we must conclude that these days we have no fundamental rule for music, or at least no generally accepted musical rule base that would constitute what was, for several centuries, the “common fund” of the musical language system. First of all, therefore, there is confusion between the levels linguists call phonology and morphology. If new frames of reference are in the process of being formed, then it is amid the most impossible tangle of stereotypes and neologisms. If, moreover, we need to distinguish between organization of materials and composition, this is because there is a higher level of meaning, to which organization itself is subordinate. Now, in the traditional system, we could clearly see these three tiers of musical language. At an “acoulogical” stage, which was so well integrated that it seemed as if it were immutable, with no possible variants, was a certain number of sounds made by a limited instrumentarium defining a “musical” completely purged of “sound.” Then there were the structures of music theory; and over and above these were the structures of scales whose hybrid origins we have briefly mentioned, the whole melodic-harmonic code that we have put aside as being beyond the remit of a music theory, but which very clearly constitutes practically the whole traditional frame of reference. Finally, there were the works with their internal regime guaranteeing the meaning, like the meaning of a text, about which we said that it did, indeed, depend on the language system but in its essence eluded it. What is left of all this today, and who is openly asking questions about it?

This is why we have deviated from present-day problems, which seemed to us to be wrongly presented, and have analyzed the traditional system. We have made a distinction here, and we still attach great importance to it—because it is unusual—between the theory of harmonic sounds and the theory of scales with its various consequences. And above all, we have certainly not deduced from what is above what we vainly expected from it: a more rational harmony or rules for new languages. Similarly, when we suggest parametrical relationships, and—ultimately in a true spirit of empiricism—link together various arbitrarily chosen values, it is simply an instinct (which should be tested experimentally) that justifies the new choice and ordering of objects; there is nothing to prove that this is getting us any nearer to the final level of meaning or even that we can be reassured about musical perceptions at the elementary level of objects. We were able to work at the strictly linguistic level to devise new codes or syntaxes, but we still need to see whether they will be perceived and to test out what contribution these new utterances make. In other words, we should be able to test out every new, relatively arbitrary, musical system at its two extremes: materials, for the structures actually perceived, and ultimate meaning, where perceptual structures, always rather general, come into play. These reflections show the futility of a single frame of reference or a unitary generic schema: what is below can neither give rise to what is above nor account for it.

35.12. MUSICS

This plural has often been used in the course of this work. The reader will have understood that it refers to the variants presented by musical civilizations. But they were implicitly referred back to “Music,” thus arguing a common ancestry for all these musics, as once we argued an original language system, the common ancestor of all language systems (an idea now abandoned for language systems but certainly not for music, owing to the importance of natural data in the phenomenon of music). So it remains, it seems, to clarify from the variants what this common ancestry is. This whole treatise has endeavored to answer that question. At least it has finally recognized two shared features of all traditional music: a fundamental, more or less developed, harmonic relationship between pitch and timbre and a staging over three successive levels (objects, frames of reference, and meaning).

A quite different aspect, a quite different plural, now appears. It is the common ancestry itself that is in jeopardy in two ways. We have already mentioned the first, which consists in introducing relationships other than harmonic between objects, which is masked by present-day notation. But more important still is the abandonment of any shared reference system, and this, indeed, seems to be the result of the development of serial musics latterly. Our entire critique of a priori systems has, in fact, been made with a view to finding justifications for the musical both below and above serial schemas. Below, it would be verification from authentic perceptions, confirmed by an experimental approach or an artistic practice. Above all, it would be verification through a dialectic resulting from differential structures, in accordance with “implied” reference structures.

Even if we still hold to our criticisms attacking the absence of perceptual bases for most serial formulae set up a priori, we do not think that every music is absolutely required to have conventional reference structures similar to the traditional melodic-harmonic code. But then this music must renounce the status of our usual musics. Polemics aside, this is what we would suggest to clarify the idea of “variant schemas” suggested by Boulez. In effect, from the moment when the relationships between the distinctive features of sound are perceptible, and set up as musical criteria through an artistic decision gradually adopted by society, why should we not arrange objects directly in structures, going straight from the “acoulogical” level to the level of overall organization, as a building is constructed according to the logic of the materials, and not a discourse arising from a code? There is no objection to this, but we must be aware of what we are abandoning. Saussure’s essential idea for defining language systems is differentiation (“in a language system there are only differences”);20 similarly, the traditional musical language system is only a language system because we have forgotten sound, almost as much as in the language of words. It is by reference to tonality and modality that musics are listened to. And the proof of this is given by the extraordinarily different meanings attached by an Indian, a European, an African, or a Chinese person to a particular melodic structure (e.g., Indian morning and evening modes; major allegro for us, not for the Greeks). In this context we find a remark taken from linguistics by Theodor Adorno: “the material of composition is as different from the composition itself as spoken language is from the sounds at its disposal,” and this is what makes him also say that “the psychology of music is problematic.”21

Now, when we abandon the melodic-harmonic code and put forward “variant schemas,” it is because meaning is no longer being sought through differential structures: meaning must be found in the work itself, its internal proportions, as with a building. This is where Adorno’s statement is most unfortunate. We have never had more need than at this time to understand the object as material whose psychological properties are becoming essential, since we no longer have a code to assimilate and go beyond its immediate meaning toward a conventional signification. Adorno’s is a crucial remark, therefore, the importance of which will not escape those who recommend a music based on “variant schemas”: no one has more need than they for a music theory that is realistic and completely restructured from new experience.

But this is not all. Suppose now that the middle tier between the two outer tiers of meaning and fundamental perceptual structures has disappeared, at least as far as its strictest and best-known conventions are concerned. We must then look for meaning in the assemblage itself, in a completely new coherence between forms and material. Compared with the former music, a music such as this brings with it two simplifications: its perceptual registers are less refined but more “natural” (dynamic or color perceptions, much more apparent to the ordinary ear, are associated with harmonic perception); in addition, the disappearance of the conventional tier makes these musics more universal (as may be the case with a building, which is always more comprehensible to a foreigner, even if only more or less, than the native language system). So it is important to agree about terms, about what we call “music”: we should, in fact, have two words or else take the plural “musics” to refer not only to relative differences in the code but to a divergence that is now radical on the level of both elementary materials and meaning.

But it is not enough to mention these differences in nature; we must also identify differences in means. The image of a building substituted for a language is an opportune reminder. While it has always been possible to hum traditional music, it seems that the shape of contemporary music relies much more on gesture.22 What are these instrumentaria, very different daughters of the voice and hand?

35.13. TABLATURES

Here we return to origins of a sort, not a primitive stage used as an allegory but the perfectly clear origins of the present situation. Primitive man must have spelled out his sounds by any means at his disposal; we, who have all of them, must adopt a similar stance: to decipher those relationships between sounds that lead to one music rather than another. For it is not from a new instrument that we must now expect music; on the contrary, it is our quest for a music we desire that will make us invent instruments appropriate for it. It is no longer a question of scrambling an ill-matched orchestra together but of defining a tablature. We are using this old word in the absence of anything better to describe the development of an instrumentarium that would be more than instrumental technology developed at random and subject to every whim. The definition of tablature given by Machabey, “the representation of musical sounds specific to a particular instrument or category of instruments,”²³ refers, in fact, to something different from a technology of means; it is almost an analysis of contents. More broadly, tablature should describe the value relationships available to the sounds from a particular group of instruments. A “representation of musical sounds” such as this would, in the final analysis, be nothing other than an analysis of “genres of sounds,” which we spoke about in earlier books.

It will not do to have experienced the extraordinary discovery of the universe of sound if we end up getting lost in it. As anything is possible at present, through analysis or synthesis, now is the moment to vigorously gather together chosen ways and means with a specific end in view. But what will we choose out of such abundance? Our aim is, precisely, to establish a little order and to reach a conclusion.

Ultimately, there are two extreme types of tablature: a “harmonic” type, where all the sounds have tonic pitch, and a “complex” type, where there are only nonharmonic mixtures of natural or artificial frequencies. Making a bold guess about what may happen in the future, we could say that every new sound instrument will more or less borrow from one of these systems and will strike the ear in one of these registers (or both at once, if the instrument is mixed).

35.14. MUSIC AND MACHINES

In the quest for means, what is the role of electronic machines, whether for composing scores or synthesizing sounds? We should make a distinction between synthesizers, devices for making sounds out of encoded electronic data, and calculating machines, which can process musical information in the same way as any other information. In both cases we may well expect to have to make preliminary choices, since we must give the machine a set of instructions. We will leave aside the question of machines used in automatic composition, which are suitable for research dealing with a completely encoded musical language. It is at the elementary level that we, who are focused on the material, are seeking to use machines—synthesizers as much as calculating machines in association with them.

Synthesizers are very flexible instruments for dealing with the combinatory initiative of a composer, but, as we know, they start from first principles that are quite different from those of musical experience. So it is lack of experience in knowing the right set of combinations to give the machine that has led experimenters to the failures we have discussed. Not that the machines themselves have no limitations of their own (perhaps they will never have the subtlety and sensitivity of a crafted sound), but electronic synthesis has suffered mainly from the simplistic ideas held by musicians about sound and the crude or arbitrary models they devised. Hence the need to undertake a thorough study of natural sounds, which are still very poorly understood and to stop reducing them to combinations of parameters.

How, under these conditions, can we use an instrument made specifically to combine parameters for the purposes of music? This is where the calculating machine may well outstrip the synthesizer. We think we need to give the synthesizer not a few crude and raw data, as Stockhausen used to do, but a very large quantity of data, and certainly instantaneous parametric data, to form each sound. Synthesis would then appear not as the gratuitous act of an inventor, or a composer’s whim for “rigor,” but as the equivalent of preliminary analyses, as has always been the case with technologies. The analysis we have recommended in this work consists in observing natural sounds or, if they are artificial or have never been heard before, observing perceptual criteria, which can be combined in innumerable original ways. The natural sounds would then be models with properties that could be reproduced or developed by the machine, capable of continuously “nourishing the sound” in the same way as the performer himself. This seems to us to be what is not only possible but also desirable, even if not profitable.24

There is little likelihood, however, that this direction will be taken because of the two tendencies to be oblivious to the psychology of perceptions and to be too ready to hand over to machines the problem of choices and the quest for values, which is ultimately only the concern of the musical consciousness in the context of a personal and group experience. We will certainly need several decades more of furious research into machines before researchers, brought to their senses by the rebuffs of determinism, consent to go back to their own resources and, as we have suggested, admit to the necessity of a preexisting music theory.

35.15. THE TWO MUSICS

In the light of the two types of tablature defined in section 35.13, we find two “main” musics, which divide the common stock into two main branches. One, based on harmonic pitch relationships, has all sorts of cultural variants, each with “three degrees” of complexity: they are the musical languages known to date. The other, based on nonharmonic relationships, brings elementary perceptual structures and the overall form into direct contact with each other through “variant schemas.” This branch leads to a music that (for the moment) has only two levels of complexity and is more like a building.

Of course, we are talking here about extreme examples (pure musics). We are more likely to come across transitional types, with a mixture of reference structures and variant schemas, chromatic notation and no authentic notation at all, in the most perfect ignorance of the distinctive features of sound and the musical registers perceived in practice.

In fact, depending on which of the two tablatures it is dealing with (or it may be a mixed type), the ear relies on one or the other perceptual pitch field (or both at once), which are marked out differently, orientated differently—one precise and the other not, one cultured and the other not. So we have two musical registers: one structured, the other amorphous; one repetitive, logarithmical, calibrated, the other only linear, approximate, nuanced.

In the same way, we can find two contrasting pairs of structures on the plane of intensity: structures that are uncompromisingly rhythmical, with fixed spacing, and dynamic structures that indicate the presence of sounds. We should add that sounds will have to be arranged in two large groups: homogeneous (or perceptibly homogeneous) sounds where the downbeats match the upbeats of the silences, and formed sounds where perception is different—the rhythm of the spacing, marked by impacts, no longer conforms to the laws of their internal duration, and the perception of this is anamorphosed.

So if we leave aside the question of timbres for a moment and concentrate, as in pure music, only on the dimensions of pitch and intensity in relation to duration, the two variants of music will share four relationships in the perceptual field, two by two. We have already identified a “harmonic field,” chromatic in classical terms, where the location of tonic objects takes place, and a “colored field”25 (by analogy with the visual appreciation of colors), to denote that other way of situating nonharmonic sounds (thick or complex) by means of approximate nuances going from the low to the high register. We will also give the name rhythmic field to the field of perception of spacing and the name dynamic field to the field that integrates profiles. The four relationships on which pure musics are based are thus as follows:

• harmonic field, with tonic objects,

• colored field, with complex objects,

• rhythmic field, with spacing or homogeneous sounds,

• dynamic field, with the impact of formed sounds.

35.16. THE CONTINUOUS AND THE DISCONTINUOUS

These four relationships assume the use of discontinuous objects described by means of pure, unambiguous criteria: tonic pitch or complex mass, homogeneous duration or impact. The theory of traditional music has always considered sounds as fixed, determined by the instrumentarium, unvarying through time; this is still the case here, except for objects that come under the last criterion, where the fluidity is masked (at least in traditional music) by a reassuring keyboard (piano) or a completely evanescent sound (string pizzicato). Now suppose we have fluid objects where these four criteria evolve in continuous variation. What will happen? Can we perceive new relationships? Doubtless, but we must look at them more closely. Our initial observation is that a glissando of pure pitch will not appear as anything other than a sound of complex mass evolving in pitch; conversely, a sound of complex mass going up the harmonic degrees in a scalar fashion creates intervals in conformity with the harmonic calibration. Moreover, an intensity evolving in duration, no longer anamorphosed as in an attack, but clearly perceived as in a swelled sound, is nothing other than a generalized dynamic profile of the object, now perceived as a dynamic trajectory. Consequently, although the perceptual criteria for these various objects are very different (a fixed complex mass is very different from a glissando, an attack very different from a willed dynamic profile), we can see that once more we come back to the two perceptual fields, colored and dynamic, as a general mode of perceiving. All this can be summed up in a diagram describing six sorts of fundamental relationships between the objects presented to our ear and perceptual registers, in the knowledge that, depending on the speed of development, relationships in the continuous oscillate between the memory of old and the originality of new perceptions:

Objects presented to the ear.

This comparison gives two important results; it encourages us,

(a) on the one hand, in our ordering of objects, never to confuse the opportunities to employ either the repetitive register, eminently suited to the abstractness of formulae and figures, or the linear register, much less “musical” but very similar to a plastic register (visual, kinesthetic). We can see the enormous confusion on scores as soon as notations valid for the second column are applied to objects in the last two columns;

(b) on the other hand, to understand how to go from one music to the other by changing types of objects or, what amounts to the same thing, by changing duration modules, as described in chapter 14.

On this last point we will go into more detail. We will start with the most classical music. At the level of notes, which are the basis for optimal memorization, a discontinuous material is used. On the contrary, on the level above, phrases, the continuous is brought in: the linking of instrumental features, the development of nuances, melodic development. As we have paid due attention to ear time and bulk in the field, we are assured of good memorization, and the perception of the most precise relationships, in short, the best “yield” from the perceptual field suitably occupied by distinct aggregations.26

Imagine, on the contrary, that we have a music that uses continuous or complex sounds. On the one hand, it has glissandi or masses that are neither situated nor calibrated in the harmonic perceptual field. On the other hand, it gives melodic or dynamic trajectories that did not exist before. This music has therefore chosen both other objects and other perceptual qualities, which we call “plastic.” It could even be insinuated that it seeks its meaning where the previous music evaded it. Suppose, in fact, that a classical type of music is hugely slowed down: phrases will vanish over the horizon of memory, and discontinuous sounds will expand and give rise to attack profiles that turn into dynamic trajectories, drawn-out sounds, otherwise imperceptible, and so forth.

In a way these two musics are focusing on two different uses of the duration of the object; “plastic” music adopts the level below the other music as its distinctive level, after expanding it into a normal memorization module. At the higher level, on the contrary, this new music made of elements in continuous variation, where timbres and values are fused together, finally forms macro-objects, not phrases. At the level of expression we come back to the discontinuous: a series of objects that should find its meaning in an interobject relationship and not in relation to the classical reference structures for the discontinuous, which at this level of complexity are completely lost from view.

35.17. POLYPHONY AND POLYMORPHY

Obviously, we have greatly simplified the fundamental relationships in the perceptual field, studying them in only a few types of objects (in general deponent, as the reader will have noticed). But most objects figure in both fields, with more or less prominent or nuanced dominants. Hence the importance of tablature, and of where its resources are directed. Depending on which tendency dominates, we will have a more “musical” or a more “plastic” music. One of the musics chooses the most subtle field but has to be careful about the suitability of its objects on pain of being unintelligible; the other chooses the most instinctive field (since it organizes itself naturally in a similar way to our other sensory registers) and relies on a general sense of proportion related to the dynamics of gesture, movement, muscular tension, and so on.

But we have left out that embarrassing partner, timbre. How can we include it in this overview? We can do so by introducing a third pair of types, arising from the fact that musical chains are multifarious, and can give the very classical alternative of counterpoint and harmony,27 which we will generalize in the expression “polyphony-polymorphy.” In fact, either we want to emphasize the coexistence of discourses that are both distinct and connected, and separate the “voices” through the artifice of instrumental timbre (the distinct voices of the traditional orchestra) or the independence of the parts of the fugue (the counterpoint of a single timbre); or we want to bring the constituent elements more closely together, do away with these voices as isolated protagonists, and reintegrate what they contribute into the web of a general metamorphosis: first, we turn to harmony (and so to orchestration that fuses timbres together into general chords or phrases); then we fashion orchestral objects by cutting out (the pointillism of timbres within the same form); or, finally, we fuse them together, not now to form dynamic trajectories set with timbres but to obtain blocks, iridescent sound stuff (polymorphy).

A music that gradually fuses its “voices” thus moves little by little from one perceptual field to another: it becomes polymorphic, and it is very clear that the development of an increasingly loaded harmony, which gradually blurs intervallic and timbre relationships, has always been one of the tendencies of traditional music.

So it seems that we can distinguish four poles in the way music is implemented, cardinal points that could help us situate the various domains of musical organization through illustrations similar to those in chapter 18.

These main tendencies would then be:

It seems that Western development ran through the cycle in this way: if indeed a more and more harmonic music (4) has naturally succeeded the original polyphony (1), complicating and mingling contrapuntal relationships (1 → 4), we end up, also naturally, with a transitional music such as serial music (4 → 3), a music perceived as a series of objects linked together in the most logical way possible (3). But it may be that this logic is not convincing enough, while a polymorphic relationship between several chains of objects (2) would reestablish meaning, as in a building where a particular form has no meaning in itself but takes on meaning within the whole. We often speak about a new dimension in music (wrongly called “spatial”); this is nothing other than a polyphony of chains of objects that, in the absence of instrumental clues, can only be distinguished by their spatial localization.

35.18. MUSIC AND AESTHETICS

Thus, through questionable systems and despite errors of principle, music is developing in the direction we have indicated: new relationships between objects, new problems of form and, perhaps, a music that is radically different from traditional music.

Admitting this, however, amounts to a considerable change in attitude. First of all, we must let go of all exclusively natural or cultural prejudice about the foundations of music. This means ceasing to pull it in all directions, from scientific determinism to linguistic structuralism. It means allowing hybridization, the merging of disparate elements and hence an interdisciplinary approach. It also means identifying the different planes and the levels of complexity in musical organization, which are currently almost never perceived, and thus questioning many premature claims to success. We must also have the will and understand how to welcome the most divergent experiments, which all carry a share of the initial draft, and endeavor to be not conciliatory and eclectic but full of curiosity and willing to experiment. We must also follow our preferences: working out a method or going straight to the results.

We could then turn our attention to aesthetics, to which artistic requests, for the most part unfinished, are addressed with the comment “Return to sender.” We are then relieved of responsibility and would end up turning a welter of ignorance and idleness into a sort of specialty. Similarly, when chemistry was in the doldrums, chemists came up with the idea of phlogiston, an unknown fluid that leaked out of bodies and that, it was believed, could be studied separately, independently of its material medium.

We have pinpointed two lines of research that, in fact, involve aesthetics, provided that aesthetics is understood from the outset as a crossroads between disciplines. One of the questions focuses on the most general structures common to all the arts; the other focuses specifically on music inasmuch as it explores the specific domain of sound perceptions.

So this is quite different from a friendly chat. We need to consult a whole body of knowledge to gather together the “bundle of criteria” for a reasonable study. Since we believe in science, why not adopt the rational approach to something that so clearly borrows from physics, linguistics, and mathematics? But, at the same time, how can we not ask questions about the particular development of the musical, which so mysteriously links the psychology of perceptions and the psychology of the depths of the human mind?

A refusal to do so would be difficult to explain logically. Nevertheless, we must say that an interdisciplinary perspective demands conditions and a working approach that run very much counter to circumstances.

35.19. MUSIC AND THE DISCIPLINES

An interdisciplinary project is always ambitious because of the areas of expertise that need to be brought together. Either a single researcher must take them all on board, in the knowledge that he will only be an amateur in each (this has always been the author’s feeling and regret), or he must get them to come to him, which is possible in theory but like jumping through hoops in practice. Research organizations would have to adopt some original viewpoints very far removed from what justifies their activities at present. If we managed to do this, we should come across new difficulties. It is, in fact, at the limits of areas of specialization that we discover almost unexplored territory and find an interdisciplinary project. If we try to go that way, we find it is attitudes, much more than the contents of disciplines and the specificity of languages, that now diverge.

Specialists all have their own way of understanding things; they all have a system of reference and thought; finally, they all have their faith. It is not enough for one to take a few steps toward another—for the philosopher to become a bit of a physicist or the mathematician a linguist; we are talking about something quite different from versatility. It will rapidly appear necessary for researchers from different disciplines to decide on more than a shared objective: the shared object of their listening (since we are dealing with sounds) and their thinking (since we are dealing with meaning). We have shown the importance both of secondary disciplines for gathering musical data and of the choices that must be made as soon as the first tentative steps in typology are taken. It is possible for well-disposed individuals to get to this point under the leadership of a philosopher rather than any other mentor. We are thus unambiguously focused on the individual. We do not allow the object to be diverted from this encounter. In short, to go back to our schoolboy schemas, on the figure showing the three possible intentional directions (see section 8.9) the chosen direction is, at the bottom, gravity, self-examination, and, in a word, contemplation of the object.

But who contemplates the object, if not man! The above approach still involves an “individual”: not altogether a man. It is still the external man, taken as an object in the world, and still the anatomy lesson: a wrapped-up mummy, a stuffed man, homo sapiens, who is as like a real man as a waxwork in the Grévin museum. The musical and that man will never live happily together. It is up to us to be filled with the feeling that dare not say its name, the respect for humanity that comes to us from the domains of ignorance and fear.

To pursue music without situating it, without taking into account the problems of the times, the ideas of the moment, the vocation of art in general, would be to believe in a music in itself. We have just examined it at its very beginnings, but its meaning is also to be found in the remotest distance, near the ultimate goals.