30

Theory of Homogeneous Sounds

Criterion of Mass

30.1. EXPERIMENTAL MATERIAL

The most well-defined, most rigorous, and most easily analyzed typology of homogeneous sounds is often the most difficult to find materials for in practice: we need sounds that remain the same through time. They have no form, contribute no new information in the course of their duration. We accept sounds of this type from any origin, traditionally musical or not. So we will find sounds that are or are not tonic but, generally speaking, no noises (which in most cases are certainly not without form). The most ordinary, least-interesting example is electronic white noise, with which everyone is familiar: this is what in the studio or in electronic technology is called “hiss.” It is, indeed, a homogeneous sound, the exact opposite of tonic sound (as it occupies the whole tessitura): for statistical reasons every moment of listening is the same as the one before. These circumstances are to some extent reproduced in applause, water falling, or pebbles being poured out—indeed, in any agglomeration of sounds provided they are varied enough and their distribution in the tessitura and time follows the laws of chance. The accumulation of all the sounds in the world would doubtless be a white noise, which explains our distaste for this perfect disorder.

If we only had the scale of traditional sounds and the vagueness of white or similar noise (even when they are cut into “slices” of so-called colored white noise by filters) to explain the concept of mass, we should not get very far. This doubtless explains why mass is so underrepresented as a sound criterion. What is so poorly perceived, however, is glaringly obvious. Despite their nominal pitch, some of the most traditional sounds, such as tonic sounds, incontrovertibly present masses that are not perceived as occurring at discrete points. The low notes of an organ, for example, or a sustained double bass or bassoon note compared to middle-register or high notes on the same instruments, or other instruments on the same tonic, already suggest the term mass rather than pitch.

A tonic sounds on the note but is a bulk in the tessitura: physicists’ frame of reference for the spectrum cannot tell us whether our ear can detect a certain thickness in the sound, apart from its nominal frequency. Suppose we play three or four adjacent notes in the medium or high register of the piano: does this package have a greater or smaller mass than a single low sound? Even if the answer is inconclusive, the question still has meaning: mass is a perceptual criterion.

Then we could think up some comparisons. Since we are able to cut out slices of white noise through filtering, could we not compare the above sounds with these thickness samples? Such an experiment, seductive in its simplicity, nearly always comes up against differences of genre: we perceive here a fundamental, crowned, as we say, with a thick timbre, there a package of frequencies without timbre. In fact, comparisons like these amount to asking ourselves to compare an invertebrate with a vertebrate. So there are several classes, or genres, of massive sounds.

In the sense of prose composition we could think of constructing thick sounds on a predetermined model. Thus, Luc Ferrari built up superimposed layers of sustained violin sounds that formed perfectly homogeneous wefts. Why “wefts”? people will ask. Aren’t they chords? We must be very clear about the word. We can use the term chord as long as there is a possible resolution—even a difficult one—into constituent musical objects. As soon as resolution is impossible, it is because a new perceptual criterion has appeared. Contemporary music is full of these false chords, these packages of notes written on the score with the greatest care but that in the overwhelming majority of cases the ear clearly cannot resolve. The works we are thinking of are therefore not based on the nominal pitches of these notes but on the mass of the sound objects created in this way. It is better to acknowledge this state of affairs and use the term mass than to pretend to hear what no one can any longer perceive. But how?

By way of introduction to and illustration of our discussion, we will examine how far and with what vocabulary musicians and physicists deal with sound qualities that do not come directly from classical scales or measurements.

30.2. ANALOGICAL CRITERIA FROM TRADITIONAL MUSICAL EXPERIENCE

When evaluating tonic sounds, musicians habitually describe them using the following analogies:

1. Their volume. Generally speaking, a high sound will seem less extensive than a low sound. But, again, a clarinet sound will appear “narrower” than a flute sound of the same pitch. Here we come back to the dimension of amplitude, independently of the tonic quality, which gives us to understand that all tonic sounds are discrete.

2. Their timbre, which will be dark or light. Timbre here denotes a quality of the notes and does not refer to the instrument; thus, a violin or a voice can sound light or dark. We would say that here timbre is understood as a value and not a characteristic. We can say, however, that the bassoon is generally dark, while the oboe is light.

3. A musician will also say of a sound that it is rich or poor. These qualifiers will be applied equally to the timbre, with the same ambiguity as above. A singer can produce sounds that are hollow or full, with or without timbre. The flute has a poorer timbre than the clarinet. What does this mean, except that we can perceive a greater or lesser complexity, a fuller or less-full texture?

4. It may happen that even a rich timbre does not come across, is muffled, has no radiance, no brilliance. And so we say that a violin or a voice comes across to a greater or lesser extent, probably depending on whether the partials reinforce each other when the sound is produced or whether it strikes the ear that receives it in the registers where it is most sensitive.

30.3. SCIENTIFIC CRITERIA: ADDITIONAL PROPERTIES OF PURE SOUNDS

We intend to “reclaim” some work done by physicists on sensations, which seems to have been totally forgotten by even the most acoustics-obsessed musicians, set on retaining only the three perceptual dimensions of frequency, level, and time in pure sound. If they had done their homework, they would know that experimenters such as Rich, Stumpf, James, Koehler, and, more recently, Gundlach and Bentley, Zoll, Halverson, Dimminck, and finally Stevens, have kept up a continuous inquiry into properties of pure sounds other than pitch, intensity, and duration. These authors acknowledge the existence of additional qualities because of the fact that the properties of perception depend as much on the characteristics of the receiving system as the stimulus: so we are indeed dealing with objective properties, but they are highly likely to elude experimentation, owing to the imprecision of analogies and the conditioning that the listeners we consult about them cannot avoid undergoing. It is not so much the quantitative results of this research that interest us here but the curiosity that motivated physicists, without being explicitly aware of it, to take an approach similar to experimental music, though still applied to the least suitable material: pure sound.

The work to which we allude, summarized by Woodworth, concludes that, putting aside duration, simple (sine wave) sounds have the following qualities:

1. Sound strength (intensity) increasing with the level (decibels or phons), and at equal level varying in a complex manner with the frequency (Fletcher’s curves);

2. Pitch, rising with the frequency, and perceptibly, although to a lesser degree, affected by the level;

3. Volume, increasing with the level, and at equal level diminishing with the frequency;

4. Density, increasing with both the frequency and the level.

More precisely, where pitches are concerned, physicists distinguish two sorts of calibration, depending on whether the evaluation is harmonic, by comparing simultaneous tonics, or melodic, when the sounds are heard successively and outside the harmonic context (we then obtain the calibration in mels). In the first case the main reference points (octaves) are repeated over increasing frequencies as powers of 2; in the second (mels) octaves are ignored and the sound spectrum is considered in its entirety as a sort of fabric more or less stretched out from the lowest to the highest register. In practice these two types of evaluation almost coincide in the medium register and diverge in the low and high: from the point of view of mels, the high octave of the piano is worth only “half” a medium octave; this proportion becomes even smaller in the very highest register (see section 10.7).

We find, however, that with increases judged to be equal, the qualities of volume and density are linked to inverse variations of frequency (see fig. 35): at equal intensity the participant finds a low sound “more voluminous, less dense” than a high sound; for him to judge them to be of equal density, the low sound must have a greater intensity than the high sound; finally, these sounds do not seem to him to have the same volume until the high sound is louder than the low sound.

FIGURE 35. Densities and volumes of pure sounds. Relationships between volume, sound strength, density, and pitch at different frequencies, this being compensated for by a difference in the intensity of the stimulus. The rectangular framework represents the physical dimensions of intensity and frequency, the curves indicating the relationships when the volume, density, etc. are equal. With the curve labeled volume, read, for example, that according to the average from several participants the following stimuli gave sounds of equal volume: 400 cycles at 56 dB; 450 cycles at 58 dB; 500 cycles at 60 dB; 550 cycles at 62 dB, or thereabouts; 600 cycles at 63.5 dB, approx. Same reading for the other curves. Thus a sound of about 508 cycles at 64 dB is considered the same pitch as the standard 500 cycles at 60 dB. (Adapted from Stanley Smith Stevens, “The Attributes of Tones,” Proceedings of the National Academy of Sciences of the United States of America 20, no. 7 [1934].)

What are we to make of these observations? First we note that they are all expressed in a vocabulary of analogies that finds its origin in references that are only “notionally” auditory. Here, however, we can distinguish two situations: in the first the analogical terms continue an established tradition, terms such as pitch and intensity. We can hardly reproach an experimenter for using abstract terminology so widely employed in so many other fields of sensory or kinesthetic activity. In the second situation the analogy is far-fetched, and we may question its real value and effectiveness: what characterizes the concept of volume compared to density, and how can we so easily separate these perceptions from the notion of intensity? Surely these qualities are much more linked to a mode of operation? This would not be at all surprising, as we know that structural relationships depend on the order and frame of reference of the comparisons.

To clarify our thoughts, it may be useful to compare them with a remark by Stevens on the results we have mentioned above:

So we are faced with four types of different responses, the result of the interaction between a two-dimensional acoustic stimulus and a multidimensional neuroperceptual system. The method used in these experiments gives the participant a role rather like a measuring device detecting zero: the instructions given to him at the start of the experiment “tune” and “condition” him to detect differences in a particular field of his domain; then he adjusts the stimulus until the difference disappears. What we must point out is that the participant can respond in four different ways. The fact that each type of instruction may lead to a response that is a function of the two physical variables of the stimuli may make us think of a two-dimensional type of experiment; but the fact that there are four different responses shows that we should be able to find at least four characteristic pathways in the nervous system at the exit from the cochlea.1

In our eyes, however, these experiments and the results obtained have the advantage of using objective methods to underline ways of perceiving sound that are mostly or totally ignored by those who wish to find “scientific” support for a particular aesthetic theory; and so, it seems to us, they open up a point of contact with the interests of the experimental musician.

30.4. METHOD OF APPROACH

It was perhaps necessary to refer back to the problems raised by musicians and physicists, and the specific terms used in their inquiries, in order to put our approach more fully into context.

Far from refining instrumental timbres, or the somewhat uncommon subtleties of the perception of pure frequencies, we are extending our field of investigation into sounds in general, and we intend to cover the groundwork on what we call the criterion of mass in homogeneous sounds by making a large number of comparisons, as we have already stated several times:

1. By comparing all possible sounds we have defined general types of sound masses (cf. Typology).

2. How do these perceptions divide into musical classes when we examine homogeneous sounds in general?

3. How do they most frequently group together to form musical characteristics of mass, which we will assign to different genres of homogeneous sounds?

4. How, where species are concerned, can these criteria of mass be situated or calibrated in relation to the scales of the musical field?

30.5. HARMONIC TIMBRE AND MASS

There are two extreme examples, as we saw at the beginning of this chapter: the tonic sound of musicians and the white noise or colored sound from electronic generators. We have called what continues throughout duration matter, in tonic sound as well as white noise, and obviously in all intermediate cases (cymbals and sustained notes, packages of indistinguishable notes, etc.).

At the end of numerous experiments on sounds we propose that listening to sound matter should be conducted with these criteria: a mass criterion properly speaking, a harmonic timbre criterion (as distinct from timbre in the sense of instrumental source),2 and, finally, a grain criterion subsuming sustainment. We will look at this last point in chapter 32.

We will use the term mass for the quality through which sound installs itself (in a somewhat a priori fashion) in the pitch field, and timbre for the more or less diffuse halo and more generally the secondary qualities that seem to be associated with mass and enable us to describe it. This is an approximate, entirely empirical, distinction that, as we will see, allows for all sorts of osmoses. Our aim is precisely to proceed by a series of approximations, not by setting up dogmatic categories. How, then, do we apply these concepts?

• with traditional tonic sounds we quite naturally distinguish between pitch and timbre: so we return fleetingly to tradition;

• with pure sounds the analogies chosen to indicate the associated qualities mentioned above, volume and density, are linked to their mass;

• in most cases, nontonic sounds, mass is less easy to perceive, but what we do not locate as an integral part of mass is still a timbre, and this is so whatever the listener’s training or the sound context. In effect, depending on his level of skill, his attentiveness, and also the environment of the object presented to him, the listener can distinguish between mass and timbre in a whole variety of ways. For example, a bell will be situated at a different pitch (evaluation of mass) depending on the tonic with which it is compared; or again, it will seem to be composed of tonic or complex sounds (of indeterminate pitch) depending on the listener’s aptitude for unraveling clusters of sound. Similarly a metal sheet giving a homogeneous sound can seem to be a confused mass or, on the contrary, a superimposition of tonic or vague components, with the whole perhaps surmounted by a high-register harmonic with its own particular timbre.

Consequently we intend to use the two criteria of mass and harmonic timbre in conjunction with each other, considering them rather as connecting vessels, with the exception of certain specific examples where the attribution seems beyond doubt given the classical nature of the sounds and the strength of listening habits. (We know, however, that for Helmholtz timbre and mass actually did “communicate” if he could indeed resolve a tonic into its harmonic partials.)

30.6. CLASSES OF MASS IN HOMOGENEOUS SOUNDS

We will distinguish seven classes of homogeneous sounds (fig. 36; cf. fig. 41, box 12).3 At the two extremes we will put sounds with pure frequency (class 1) and white noise (class 7): the sounds best and least suited to the perception of pitch. Roughly, we could say that toward the top of the figure the listener’s reactions will be in keeping with traditional musical conditioning (harmonic intervals, successive octaves) and toward the bottom, in accordance with the calibration in mels that we spoke about above (here, to refer to his perceptions, he will use analogies—for example the “white noise” image—since no term from traditional theory will help). We should point out that these two modes of perceiving pitch are independent, and we should not expect to find examples where perception follows an intermediate law; rather, in doubtful cases, we will obtain two sorts of simultaneous perceptions.

FIGURE 36. Classes of textures of mass and harmonic timbre.

A cymbal clash gives a sound similar to white noise, centered on a particular zone of the tessitura: nodal sounds such as these will be situated above the box for white noise (6). Tonics on traditional instruments, less pure than sinusoidal sounds and colored with a characteristic timbre, will be placed symmetrically below the box for pure frequencies (2). Several simultaneous cymbal clashes centered on different zones of the tessitura will constitute a cluster with nodal elements that can be isolated: we will call this a nodal group and place it above nodal sounds (5), in the same way that we will situate tonic groups below isolated tonics, their traditional chords, which can be resolved into their constituent notes, being the simplest example (3). Finally, a central box will be reserved for ambiguous sounds—for example, gongs, bells, metal sheets, and so forth—which, depending on the sound context, are perceived either as nodal sounds or groups of nodal sounds, some of them so narrow that they sound like tonic notes or as more or less clear tonic groups surrounded by a complex halo. Such sounds deserve to be evaluated from the point of view of both traditional intervals and color analogies. We will call them channeled sounds.

30.7. CHARACTERISTIC OF MASS: TEXTURE OF A SOUND

We have just seen how to perceive sound in terms of mass: typologically according to whether the sound is fixed or variable, and morphologically according to whether it is tonic, nodal, or channeled. These various classes of mass seem very general as soon as we find ourselves in front of a real sound: they crudely summarize too many sound experiences. When we move up into the sections for the musical, we ask ourselves two questions: one is about describing the criterion of mass in relation to the properties of the perceptual field, and the other is about the possibility, if not of describing particular examples, at least of identifying the main genres of sounds in terms of their mass.

The popular expression “a bit like” expresses this idea of the character of a sound very well. For it does more than name the example: piano, metal sheet, bell, electronic sound, and so forth; it generalizes it; it states that a particular sound, over and above the specific example, can present itself as representative of a general structure. If I play packages of notes that give a thick mass on the piano, I will no longer hear the tonic sounds, no longer analyze the chord, but I will do more than appreciate a width of more or less vague thickness. Between the chord where I resolve the tonic sounds and the thickness that is an admission of vagueness, I pick out a texture, a certain organization of the mass, as, for example, in a bell sound. I can compare metal sheet and bass piano, saying that the texture that characterizes these two sounds, which are otherwise different (in tessitura, thickness, etc.), is formed of a thick underlay, surmounted by a bright fringe . . . (whereas in the bell I perceive various nodes I can more or less situate): it is possible to perceive relationships such as these between sounds belonging to the same genre.

30.8. SPECIES OF MASS

We saw in section 30.3 that depending on the listening conditions, the pitch field was covered from one octave to another across repeated harmonic intervals—which is the case with traditional music—or else in a continuous fashion, in a calibration where the degrees are melodic (calibration in mels). We suggest that if the tonic notes are far enough apart to be perceived in the traditional way, this is precisely because of the presence of harmonics (not perceived in isolation, although contributing to the timbre) that put a sort of grid in the pitch field and thus give a defined context for perception; but as soon as adjacent notes are piled on top of each other, these notes and their respective spectra occupy the pitch field in too confused a manner to impose any sort of order on the ear, and then we find ourselves in the perceptual conditions for the calibration in mels. Even if it does not explain the criterion of mass, this property of the field, explored by physicists with pure sounds, at least demonstrates why in certain cases the notion of thickness replaces the notion of interval. Between these two extreme examples, each one coming under one of the two reference points in the perceptual pitch field, are sounds of ambiguous pitch: depending on context or conditioning, in these cases we hesitate between describing them as colored mass or breaking them down into a number of tonic sounds.

Thus, when contemporary musicians accumulate tonic sounds, happily mingling them with nodal sounds (gongs, cymbals, bells) while still notating everything in discrete pitches, it is a safe bet that this notation lets them down in the way it indicates harmonic intervals. They are no longer dealing with traditional reference points in the pitch field. The other mode of perception intervenes, which only has thicknesses and colors in indeterminate relationship with the reference degrees or intervals.

The experience of electronic music leads to the same thoughts. Slices of white noise of perfectly homogeneous mass are calibrated into distinct intervals: now, the accuracy of the cutting produces nothing remarkable as far as perception is concerned; it is even impossible usually for a listener to calibrate such sounds on listening to them and to situate them any more than approximately in the tessitura unless he retrains his ear, a notion that, it seems, has not even entered the heads of the electronic school. The experience of concrete music, which uses all sorts of sounds, has brought to light numerous ambiguous examples where perception functions in two distinct registers, depending on whether the sounds appear tonic or thick. Generally speaking, suitably grouped tonic notes give not a chord but a mass satisfying a criterion of thickness (which we can attempt to calibrate, but with no great accuracy) and that is situated more or less clearly in the tessitura (which we can train ourselves to locate, not in degrees but in register).

This double evaluation, in the general run of things where sounds cannot be reduced to tonics, can be defined as a particular species of mass—in register and in thickness. Here we are not dealing with the extreme precision of a cardinal scale but the subtleties of an ordinal series. In ambivalent cases, depending on context, only one of the two reference modes will appear appropriate, either degrees and intervals or color and register. It should be noted that we have no specialist vocabulary to describe the perceptions belonging to the second mode; this is why here we use an exclusively analogical vocabulary to talk about species of mass.

30.9. THE TWO PITCH FIELDS

So what made us think there are two sorts of field, two ways of calibrating and evaluating pitch? Were it not for the presence of various masses—either tonic or thick—such an idea could not command attention since it runs counter to any simple generalization. Similarly, physicists only had this idea when, instead of pure sounds in a harmonic context, they presented a series of long, drawn-out melodic sounds. But where they saw only two calibrations, they should, in fact, have seen two sorts of object-structure relationships: one discontinuous, fitting in with the idea of harmonic context, the other continuous, fitting in with the idea of melodic texture. These two markers then lead to two sorts of relationships called value-to-characteristic relationships: one is the degree-tonic relationship, the other the color-thickness relationship. From the point of view of the objects (thick or thin), the question is to go further into characteristics; where the field and perceptual markers are concerned, it is to define calibrations. In the first case we encounter the problem of pitch calibrations, which are cardinal, in the other color calibrations, which are ordinal.

We do not intend to go any further into the former. Is there anything that has not been said, written, thought, dreamed up about pitch calibrations and all their baggage: tonality, modality! We will leave it to an abundant and scholarly body of literature to develop the associated questions; as for ourselves, we will concentrate on establishing their place in perceptual reality. In fact, this raises a fundamental question, one that is often tackled in musicologists’ manuals: is the scale natural or artificial? Is it the product of historical usage, linked to a tradition (and how then can the origin of such a tradition be explained), or is it determined by the sound structure of objects, where the individual person and nature, physiology, and acoustics come together?

30.10. PITCH CALIBRATIONS

When a harmonic sound is perceived, we must imagine that it occupies the ear, not just with one degree but also with all the degrees of its partials, a structure that is precisely that type of perception where synthesis is carried out spontaneously. Should another sound present itself, we easily imagine that it enters all the better into the previous grid because it occupies one of those degrees itself or, more precisely, that its spectrum leads to a perception that relies in part on the structure perceived previously. Here we are referring to the so-called phenomenon of consonance, as well as the physical-acoustic correlation between the different sounds in the scales. We will take the risk of sticking our own little oar into everything that has been said and said again on this subject.

Physicists, we have seen, attempt to explain consonance by the absence of irritating beats. This is a very flimsy explanation because it is in the area of consonance—when, for example, two tuning forks are very near to being in tune—that beats are most clearly heard; now, in music there is never absolutely precise consonance in the physical sense of the term; moreover, if this were the case, temperament would be impossible. This apparent paradox has led many musicians to consider temperament as a dreadful compromise, indispensable but regrettable, a sort of original sin. These two attitudes seem neither realistic nor genuine. Consonance is explained intuitively by the partial superimposition of the spectra of the different sounds in a chord. And for this to be done statistically in the best possible way, a tempered scale has to be found—not sin, at all, but the salvation of the system!

In reality, if we run quickly through the famous names still associated if not with the invention at least with the defining of scales, we can see the same musical intention: to find, unsuccessfully as it happens in the case of Pythagoras and Zarlino, the square of the circle: temperament!

30.11. TEMPERAMENT

Convinced, intuitively and not without reason, that there is of necessity a relationship between the degrees of the scale and the successive partials, these ancestors of experimental music, as we know, are confronting a very simple but very insoluble arithmetical problem.4 Pythagoras starts from the sequence of fifths and at the twelfth jump, after F, C, G, D, A, E, B, then the series of sharps, the last fifth (E-sharp) does not fall accurately as the seventh octave of the initial F: the scale does not resolve. Zarlino also starts from fifths and shrewdly places them at the two ends of the perfect chord (the third being obtained by lowering two octaves of the fifth harmonic, thus in the relationship 5/4 with the tonic). Two perfect chords attached in this way to C, E, G, one lower with C as the dominant, the other higher with G as the tonic, give seven notes, which are:

	F	A	C	E	G	B	D
in relationship with C taken as a unit as follows:	2/3	5/6	1	5/4	3/2	15/8	9/4

arising from the same proportions (1, 5/4, 3/2) applied to the two other perfect chords; hence Zarlino’s scale:

	C	D	E	F	G	A	B
corresponding to the relationships:	1	9/8	5/4	4/3	3/2	5/3	15/8.

We need to find the middle way. Is the A obtained in this way the same as the A in the fifth of D? The latter would be 3/2 of D (i.e., 27/16). Now compare this fraction with the 5/3 that establishes the A in Zarlino’s scale; the fractions 27/16 and 5/3 are as 81/48 and 80/48, and this is the notorious comma of difference between the two As 1/81 away from each other. The only rational solution required a so-called irrational number, unknown to the Ancients: the twelfth root of 2—that is, the number that multiplied twelve times by itself gives 2—enables the octave to be restored.

If we compare this now practicable scale with Zarlino’s, we can see that the tempered fifth is moved nearer by 1 savart (i.e., 1/300 of an octave or 1/25 of a semitone); the fourth is accurate; the third and the sixth are moved nearer by about 3 savarts (roughly 1/8 of a semitone).

We can easily understand that marking out the harmonic field does not follow a superstition, a myth of simple relationships. An approximation is just as good for this purpose, the twelfth root of 2, the generator of a system that is approximate but remarkably well-suited to instruments, as well as to the human ear.

An instrument tuned in this way has every chance of making its entire string system resonate, as does the piano, because of the latitude of sympathetic phenomena. For its part, the ear doubtless adapts perfectly well to the fact that from the very first fifth everything is approximate, provided that the other sounds fit comfortably into the same grid. This is doubtless what explains both the necessity of temperament and its success since Bach. We can also see how far other musics get it wrong in terms of excess or default—some through being too scrupulous with a too precisely harmonic system, which unsurprisingly deprives them of harmony (India), others through a lack of instrumental rigor that only achieves approximate and limited degrees in calibrations of pitch (Africa).

30.12. CRITERION OF HARMONIC TIMBRE: CLASSES AND CHARACTERISTICS

Because of the mutual interdependence of perceptions of mass and timbre we will find classes for harmonic timbres that complement classes of mass. For masses in class 1 and 7 (pure frequencies or bands of frequency): a nonexistent timbre. For tonic masses in class 2: a “tonic” timbre. For nodes (classes 6 and 5), the timbre, as we have said, constitutes the “rest” of the sound, what is not described in the mass, and is often the subject of a later analysis (complex timbre): it can thus conceal practically unperceived channelings, unless the node, perfectly fused together as in a cymbal, is inseparable from it: we could say that then the timbre is merged or “continuous.” A sound that is itself channeled will be heard as timbre for the halo, which is not analyzed: this halo will present further channelings or a continuous timbre, depending on how far the analysis is taken or whether the masses are more or less well fused together. Finally, a group of tonic sounds can present a continuous, even harmonic, timbre depending on the texture of the chord and its instruments.

But in certain cases and within certain limits timbre remains independent of mass. If a violin plays a note, then two or three notes close together, it is the mass of the sound that will become thicker, without the timbre appearing to change, nor does the timbre appear to change if the violin plays with double stopping. Conversely, we only have to refer to the interplay of harmonics and unisons in stringed instruments to highlight all sorts of refined and clearly apparent interactions of timbres. Also, when we refer to differences in timbre between an open string, a vibrato, and a harmonic, we are clearly talking about the different characteristics of a violin’s timbre. Here we need only quote those who have witnessed this.

Can we take the study of characteristics further by using acoustic correlations? Could we take up some work done by physicists for this? Certainly, at this precise point in our discussion, we can discuss the characterology of objects. The findings of some physicists might help to smooth over problems with the instrumentarium, but often too many variables are involved, it seems, for us ultimately not to prefer the judgment of the ear, which is so spontaneous, to laborious syntheses. Characterology dealing only with well-established timbres is only of secondary interest to music: it concerns phonetic, vocalic, or consonantal objects and, furthermore, the aim of the analysis and synthesis of their formants, which, we now understand, is to identify consonants and vowels, not to describe them. These have much more to do with the distinctive features of phonetic sounds than sonority or diction. They are only marginally relevant to musicality.

30.13. SPECIES OF TIMBRE

We defined the method for evaluating different species of mass above. Can we do the same for timbres, given the reciprocal link between these two aspects of perception? This is very unlikely. Timbres, in traditional music, do not have the fundamental structural role given to pitch; moreover, the perception of timbre has practically always been referred back to its causal origin and even studied as such, doubtless in order to explain polyphonies more clearly. If it happens that we can assign a fundamental role to it in contemporary music, this is because it seems possible to go against the tide in two ways: one against nature, by greatly refining our perceptions, the other against society, by renouncing our customs.

In any case, there is no classified index for perceptions of harmonic timbre. We could suggest using terms such as the fullness or narrowness of timbre, its richness or poorness, brilliance or dullness—all terms intended precisely to make up for what the specification of the corresponding masses lacks in terms of the perception of the matter under study. But, as with nontonic species of mass, in practice this vocabulary can only really be used if it drops vague analogies. We will give two examples of what might be an aural exercise to lead to a better appreciation of timbre and the choice of an appropriate qualifier.

Here is the first: the higher a sound, the clearer, generally speaking, it appears. We should have no difficulty in getting listeners who have had no specific training to agree on the fact that a high piano note appears clearer than a low note. Now, suppose we give these listeners a few lessons in musicianship with the tape recorder, giving them the benefit of our experiments on the piano and our comparisons between accelerated and slowed-down sounds. We already know that a low note contains high harmonics: it is both rich and brilliant; a high note, on the contrary, has hardly any harmonics: it is poor and dull. Our listeners, after these comparisons, will have to agree to revise their terminology: the low note is relatively clearer than the high note. This is because they have learned to separate the perception of the tonic, dark or light, from the harmonic halo, light or dark. A few weeks of training would lead our listeners on that offensive against both the natural and the cultural. Perhaps tomorrow’s musical education will include such training.

A second example is highly traditional: a nonmusician will perceive a piano chord as a single sound object. He knows very well it is a chord, and he will recognize a certain texture of mass in it, but he will be incapable of analyzing it, which a beginner from his first years of theory classes will do very well: C, E, G, he will say. Now play him the same chord with its notes divided among various instruments, and his musical training will soon prove to be inadequate: perhaps he will be able to identify the notes, but he will not manage to recognize the timbres. Perhaps an excellent musician would not manage to do this either if the timbres have fused together, which, in any case, is desirable: so we will have to refer to the timbre of the chord. Such, as we can see, are the different levels of training at the very heart of traditional musical society. So we will be very careful about describing harmonic timbre in the pitch field. We could in fact suggest two characteristic pairs, for the thickness of the timbre, on the one hand, and its site, on the other. The fullness or narrowness of the timbre would reveal its extent in the tessitura, while we could deduce its color, dark or light, from its site. These terms can only be clarified after much research. We can also hope for some help from correlations between spectra and perceptions; we should at least see if these analogical terms are appropriate for both the physical phenomenon and the musical perception, which would shed light on the whole process.

We can finally turn to timbre in the field of intensities; here we would be dealing with the brilliance or the richness of the timbre relative to the intensity of the tonic. But we know that sounds without harmonics also have secondary qualities of volume and density: should we include these with mass, or say that they are a timbre—that is, the “rest of the perception”—even when there is no spectrum? So the complementary pair volume and density would then be the hostile pair of what is perceived in color and degree? We lose ourselves in speculation.

30.14. IMPORTANCE OF THE CRITERION OF MASS

To round off this chapter, we would like to highlight the particularly important role of the perception of mass and its criteria in experimental music. First of all, mass is remarkably permanent in music, the permanence of the matter of homogeneous sounds, and therefore lends itself to close and detailed study. But as we have seen, the concept of mass contains perceptions deriving from two modes of apprehending the pitch field—one traditional and codified, the other new and, until now, explored more or less in the dark. Finally, the concept of mass is a crossroads where ancient and modern musics can meet—the tonic and the thick sound, the chord and the “stuff” of sound (or “species of chords,” in the words of Messiaen, who often sees music in color). We should note that the logic of our experiments leads us to generalize the notion of timbre and on the perceptual level make it into a complement of the mass of every musical object. We must go beyond the ancient method of referring timbre back to instruments. We can return to this when appropriate, the other way round: for analyzing genres of timbres, and for synthesizing instruments.