13

Temporal Anamorphoses II

Timbre and Instrument

13.1. TIMBRE OF AN INSTRUMENT AND OF AN OBJECT

Until now we have been maintaining a truism, the concept of “instrumental timbre,” in keeping with the quite empirical definition in chapter 2: the sum of the characteristics that refer the sound to a given instrument.

In the last chapter, however, we alluded on several occasions to the timbre of a sound without clearly referring it to a specific instrument but rather considering it as a characteristic belonging to the sound, perceived in itself. It is high time to point out that, when the musician keeps on saying “a very rich note,” “a good, or bad, timbre,” and so on, it is because he does not confuse two concepts of timbre: one relative to the instrument, an indication of source in ordinary listening, which we spoke about in chapter 2, and the other relating to every object produced by the instrument, an appreciation of the musical effects contained in the objects themselves, effects that are desired by both musical listening and musicianly activity. We even went further, attaching the word timbre to a part of the object: the timbre of attack, as opposed to its steepness.

But, defined in this way, the timbre of an object is nothing other than its sound form and matter, a complete description of it, within the limits of the sounds that a given instrument can produce, when all the variations in facture it may have are taken into account. The word timbre with reference to the object is therefore of no further help to us in the description of the object in itself, since it merely involves us in a reanalysis of the most subtle of the informed perceptions we have of it. If we happen to mention the timbre of an object, it will therefore be by virtue of musical habit and for the sake of using an expression familiar to musicians who understand by implication that it belongs to a well-defined collection of objects. We still need, however, to reach a better understanding of this latter use of the term, by shedding light on the paradox that makes out that instruments have a timbre and, at the same time, that every sound object obtained from them still has its own particular timbre.

13.2. TIMBRE OF PIANO NOTES

If we strike various notes on the piano and examine both their dynamics (fig. 13) and their harmonic content, we discover several things:

FIGURE 13. Bathygrams of piano notes going from bass to high register (arpeggio C, E, G-sharp, C), over seven octaves, twenty-two notes.

1. A general law of dynamics: they are steeper and steeper as we move higher in the tessitura. The bathygrams of the six open strings of a guitar would show a similar progression.

2. More precisely, dynamic registers, shown in regular lines in the bass, and fluctuating lines in the mid- and high registers (these fluctuations can be revealed by cutting: in fact, if a cut is made in a dynamically steeper or less steep place, the ear immediately senses a harder, or softer, and even, if the cut is in a fairly pronounced dip, a progressive, attack).

3. Harmonic developments in the course of the resonance, also revealed by cuts, which reproduce sounds of various timbres, and can go as far as resembling a flute.

What conclusions can be drawn from these experiments on the timbre of piano notes? Since this instrument (like all other instruments, we may suppose) seems to produce notes with physical characteristics that vary according to the register, how can we explain the fact that it nevertheless possesses a characteristic overall sonority, in short, a timbre that is so clearly identifiable?

Is it the cultural conditioning of the ear to specific instruments? Or are there objective reasons, “laws of the piano,” which adequately account for the perception of a consistent instrumental timbre, or at least explain and justify such effective cultural conditioning?

13.3. CONCEPT OF A MUSICAL INSTRUMENT: LAW OF THE PIANO

Looking simultaneously at the harmonic content and the dynamic profile of each note puts us on the right track. In fact, the higher the tessitura, the steeper the dynamic; and the lower the tessitura, the richer the harmonic complexity. We can illustrate these contrasting variations in the following way: a melody played in the midregister of the piano is recorded on magnetic tape, then transposed two octaves higher by speeding it up, and two octaves lower by slowing it down. In doing so, the natural dynamic steepness is changed by a constant factor (here equal to 4 or 1/4), while the relative harmonic composition of each note remains unaltered (since the entire spectrum is transposed with the fundamental).

Now we obtain a sound that is completely different from the sound of the natural piano at the same pitches: a melody played on the piano two octaves higher or two octaves lower; yet it is a completely unrecognizable sound, as if in some way it were coming from a new instrument, which is simply the “transposed piano.” If we compare the “transposed piano” with the natural piano, we observe, on the one hand, that the natural bass is both dynamically steeper and harmonically richer than the bass obtained by slowing down; on the other hand, the natural high register is both softer and poorer than the high register obtained by speeding up. Finally, we notice that the transposed piano, which keeps the properties of the notes constant, is unbearable and “random.” Its registers seem to clash, whereas in the natural piano they balance and complement each other. We can therefore say that an instrument such as the piano, which generates a whole family of musical objects that are different but undeniably belong to the same type, comes, as an instrument, from a characteristic correlation between the following factors:

• the dynamics (therefore the steepness of attack) vary in direct ratio to the tessitura;

• the harmonic complexity varies in inverse ratio to the tessitura. We could therefore write, entirely in symbols (since no quantitative law can express perceptions such as these):

Dynamic steepness × Harmonic richness = a constant, a formula that represents the “law of the piano” we were looking for to explain the “musical suitability” characteristic of the objects this instrument presents to the ear.

13.4. EXPERIMENTS ON THE TIMBRE OF THE PIANO: TRANSMUTATIONS AND FILTERING

We can verify these findings in a rather amusing way:

(a) Transmutations:

Imagine that we can obtain a sound from the midregister of the piano that is both richer and steeper than the usual attack: if it is transposed by slowing down into the bass register, its harmonic richness may then be exactly the same as the richness of the bass register, and its dynamic, similarly flattened out by the transposition, may also be the same as the dynamic of the bass notes. A sound like this can actually be obtained by striking a medium piano string with a plectrum, which of course gives a different musical object from the usual object when the string is played. But when totally transposed into the bass register, it is very close to a note played on the keyboard in this register. This plectrum piano resembles a guitar as well. When a slowed-down guitar sound is used, it also is like the bass register of the piano.

(b) Filtering:

1. If we take a bass piano sound (A1, 55 Hz) and, with the aid of a low-pass filter, eliminate the high register zone, the sound rapidly becomes strange or even unrecognizable: the ear is therefore sensitive to the slightest reduction in the high register.1 More precisely, if we filter above 400 Hz, the piano, mutilated in this way, cannot be recognized. It is only recognizable if it is left intact up to about 1,000 Hz.

If we carry out the reverse manipulation, and this time without touching the high notes, eliminate part of the bass, we observe that we can remove much more than we might have supposed a priori, without the ear’s having any trouble recognizing the sound; in practice, eliminating bass frequencies up to 200 Hz (which amounts to removing the fundamental and the first two harmonics) leaves the perception of both the instrumental origin and the initial pitch intact (see fig. 14).

FIGURE 14. Filtering a bass note (55 Hz).

2. If, on the one hand, we take a very high note (C7, 2,092 Hz), we observe that the ear is hardly disturbed by filtering in the frequencies above the note, on condition, however, that it does not descend into the frequency of the fundamental; on the other hand, filtering in the bass (just below the frequency of the fundamental) profoundly impairs the perception of timbre; in practice we observe that a zone of about three octaves must be left below the sound if we want to avoid changing it (see fig. 15).

FIGURE 15. Filtering a high note (2,092 Hz).

What conclusions can we draw from these experiments on filtering? We have mentioned the harmonic content of natural or transposed piano notes. Here we discover that there is, in fact, much more to this content than a simple harmonic coloring added on to the fundamental. In effect, sounds with bass fundamentals have their energy in the high register more than at the pitch of the fundamental, and the opposite is also true: the high notes on the piano make use of bass resonances much lower than the frequency of the fundamental; perhaps it is the muffled thump of the hammer that is eliminated in this case by the high-pass filter: the note, deprived of its “punch,” reduced to its harmonic vibration, would become unrecognizable through this alone.

Whatever the case may be, we can see that in reality every piano note has a whole range of pitches extending into the high and bass registers, where resonances that do not seem to be connected to the frequency of the fundamental, and a harmonic cluster belonging to the string or strings that are struck, operate simultaneously. The timbre of the piano is therefore based on a second correlation, a second law, a second invariant, which could be formulated symbolically, and with the same reservations as above: Localization in degree × situation of the energy in the tessitura = constant or: nominal pitch × “timbre” of the corresponding note = constant.

13.5. TIMBRES AND CAUSALITIES

It may be surprising that justifying the perception of an instrumental timbre—that is, an apparently simply caused permanent feature, as we were saying in the last chapter—should occasion such detailed discussions. In effect, the ordinary ear, accustomed to discern and describe the energetic history of sounds, will never confuse an organ with a piano sound, or a kettledrum with an oboe. So what more is there to the concept of instrumental timbre? The question, as we have already suggested, is not in simply distinguishing a pipe from a string or a membrane; indeed, we should not lose sight of the fact that we are talking about musical instruments and that, consequently, it is ultimately the musical ear that is involved. Moreover, this of course is what has guided instrument makers throughout their long history. Returning to our earlier experiments and reflections, we notice, in fact, that even if the perception of an instrumental timbre is based on a causal permanence (a series of metallic strings, all made to vibrate by one percussive procedure), it owes its description as specifically musical to a certain relationship between the objects given by the various strings that is by nature musical and allows us not only to recognize, but also to evaluate and describe, one or other particular timbre. To the causal permanence (struck string) is added a certain variation of musical effects, desired by the instrument maker, proportionate to artistic requirements, and obtained mechanically in a variety of ways: doubling or tripling the strings in the high register, winding the strings in the bass register, coupling and resonance from the soundboard, different thicknesses of felt on the hammers, and so forth. The high notes, in particular, are certainly the hardest to “get hold of,” and we could say that with these there is a sort of “wheeling and dealing”: the impact is there to attract attention and make the note in question stand out dynamically, while its pitch value is weak, barely adequate.

So through the piano we gain a general idea of the concept of instrumental timbre: a musical variation “counterbalancing” a causal permanence and making it more flexible. From these findings we can now shed light on the discussion we started in chapter 2 on the timbres of electronic and concrete sounds. We had come to the conclusion that these timbres are situated on both sides of the balance that traditional instruments achieve. In fact, electronic sounds, calibrated in acoustic parameters, present registers that have no connection with ancestral contiguities: what irritates us the most about them? That we cannot understand how they are made? On the contrary. We soon get used to this: the ear is quite happy to classify and name them as “electronic sounds.” But what it cannot cope with is failing to find the interplay of balance between causal permanence and musical variation, safeguarded by a law of compensation across the register, which traditional instrument makers had so much difficulty in achieving, and which modern instrument makers could no doubt manage to rediscover if they paid more attention to it. Meanwhile, electronic sounds announce their presence by an, as it were, “nonexistent” instrumental timbre. Thus the permanence-variation theory proposed in a very general way in chapter 2 finds a more precise explanation here.

In relation to the concept of instrumental timbre, concrete sounds, for their part, have the two characteristics of coming mainly from disparate causes and of not having qualities as familiar to the musical ear as, for example, a piano note: dynamic form and harmonic content. It therefore seems difficult at first to find a point where a musical element could possibly “counterbalance” the causal element and, consequently, to define clearly identifiable registers of concrete sounds; we come back to the same difficulty as for electronic sounds: the timbre eludes us.

In both cases there is nothing but timbres of objects, strung together in the electronic world but disparate in the real world.

Now, the reflections in this and the last chapter, dealing mostly with the piano, help us to identify two factors in the perception of instrumental timbre: the dynamic form, which is recognized in ordinary listening and sensitive to causations (the energetic anecdote of the sound), and the harmonic content and development, which are more specifically musical perceptions. This would lead us to a method for “discovering” timbres, especially in concrete sounds. We will illustrate this natural distinction between causalities and structures by means of an experiment to see how, by removing causalities that are too intrusive and specific to each object, it is possible to get nearer to the perception of musical structures.

13.6. CAUSALITIES AND HARMONIC STRUCTURES: FUNCTIONAL ANAMORPHOSES

If we play a sound heavily loaded with harmonics, such as a metal rod played with a bow, then a piano chord that endeavors, as far as it can, to give an imitation of the complex harmonies of the rod, it is most unlikely that a traditional musician would hear in the latter sound anything but a crude subterfuge, a “putting into music” of the former.

But what happens if we get rid of the perception of causality, eliminating the attack by cutting? Clean cuts in objects, and the new relationships that develop because of these cuts, cannot be understood in the context of the localization anamorphoses examined in the last chapter. These are not anatomical cuts, at the level of an individual component, but macroscopic cuts, which separate “articulations of sound.” But in both of these cases, by cutting objects out of time, we create other objects, and their content, as well as their relationship to each other, may be fundamentally changed. Thus we can compare a piano chord and a rod rubbed with a bow and find certain relationships between them, and then we can compare fragments of these same objects and discover surprising relationships between these also: it is this phenomenon that we call functional anamorphosis. In the example we chose, the sound of the rod is what we will call a complex “large note,” the causal unity of which is indisputable, whereas its reduction to the piano is a little piece of music: we cannot compare a raw object and a fragment of language without bias. But by cutting, and retaining only the final resonance of the “piano piece,” we will see not only that the functional relationships of objects fragmented like this are changed but that a real similarity of structure is revealed in the place of the earlier crude, anecdotal imitation.

Let us call the rod-object A and its piano “reduction” a. To avoid being satisfied with one single experiment, we will also compare a bow striking a piece of sheet metal, sound B and its piano reduction b. Let us cut these sounds into two pieces: A = A₁ + A₂ and a = a₁ + a₂, etc. (fig. 16).

FIGURE 16. Functional anamorphoses.

It is of course understood that the experiment in question should take place acousmatically, with listeners who are more or less musical but less informed than the reader may be.

First experiment; final portions: structural relationships; sound A₂ will be played followed by a₂, then sound B₂ followed by b₂. We observe what follows:

1. Causality (anecdotal listening): the ear senses that A₂ and B₂ definitely come from analogous acoustic (and sound) phenomena but is not able to tell which and, in the same way, that sounds a₂ and b₂ also come from one instrument (which is quickly identified by the practiced ear as a piano).

2. Musical character: but we also observe that the ear can detect another similarity between these sounds, which is musically more interesting than the quest for causes, that is to say, a certain likeness of harmonic character. This is only a very crude comparison, where we need simply to observe that the listener clearly perceives the intention we had to compare A₂ with a₂, and B₂ with b₂: musically there is a greater resemblance between sounds a₂ and A₂, and sounds b₂ and B₂ (although their origins are different), than there is between sounds A₂ and B₂ or sounds a₂ and b₂ (with the same origin but with different harmonic characteristics).

Second experiment; initial portions: masking of structures by causality; the above observations are corroborated by what follows. Now we will play the initial portion of these four sounds, which clearly indicate their instrumental origins, and we will have to agree that here there can be no possible musical comparison between the harmonic contents. All the musical attention is now absorbed by the phenomenon of causality: the difference between the causal origins is so intrusive (a rod being rubbed and the percussion of a piano hammer) that the ear ignores any relationship between the harmonic characteristics. Here we must emphasize the psychological nature of the “masking” that causality imposes on the ear. We could say that when instrumental causalities are very dissimilar, the musical ear is blinded and becomes incapable of musical analysis.

Third experiment; illustration of functional anamorphosis: musical attraction and continuity; insofar as all the musical effort is directed toward a type of listening that is to some extent purified of causality, where the ear is placed in the best possible conditions to establish relationships not between events but structures, the importance of the following exercise will be understood, despite its crudeness. We will use the opportunity afforded by the tape recorder to play sounds “backward” and then listen to:

A₂ played backward, followed by a₂ the right way round

a₂ played backward, followed by A₂ the right way round

then

B₂ played backward, followed by b₂ the right way round

b₂ played backward followed by B₂ the right way round.

We observe that these permutations amount to varieties or variations in the musical meaning of the term. They are all musically interesting and different, which shows that ordering the components, reversing them, and comparing them provide new musical information, through a sort of attraction that demonstrates that the observed structural similarity is effective.

What can we conclude from these experiments? What we see is that the perception of a functional relationship is not necessarily linked to a causal factor: we establish musical correlations between sounds simply on the basis of their harmonic content, by giving them the same “neutral” attack (cutting with scissors).

Once the anecdotal attack is masked or eliminated, a new type of musical relationships appears, dependent only on the qualities of the contents, so that we can hope to find similarities between sounds with disparate origins and so establish registers of concrete sound objects. Is this enough to restore a timbre? Surely this is going back to electronic fusion? Not anymore. To find a timbre, we will have to establish a new balance involving an invariant suggesting a “likeness.” Concrete materials, because of their disparity and the number of their characteristic sources, allow us, better than electronic sounds, to shape this type of timbre and thus to create a “pseudo-instrument,” from which collections of objects appear to come.

13.7. CAUSALITY AND MUSIC

So, having drawn out the idea of the timbre of a series of objects from the idea of instrumental timbre, we are now in a position to make a few remarks about the perception of causalities in music.

Inasmuch as the perception of causality is directed toward the perception of an instrumental timbre, and is consequently at the basis of the structures perceived among musical objects, we can see that it is impossible to overemphasize its fundamental role in traditional music. Even if we think the composer uses sounds that are abstract enough to remove any anecdotal element, the fact remains that the mode of sustainment, for example, imposes its logical, predictable, functional nature on the ear. We fly in the face of the evidence if we believe that pure music exempts the ear from its most essential function: to inform the individual about events that are taking place. We are talking here about classical sounds—that is, clearly defined causalities, with an aural understanding (a particular type of instrument conditions a particular musical civilization) and occurring in registers characterized by specific instrumental timbres.

But the concept of the timbre of a series of sounds allows us to extend these conditions to any type of sound (concrete, in particular): to ensure that his work is well structured, the experimental composer will, in fact, use cleverly unusual sounds, such that the newly conditioned ear will no longer insist on knowing their instrumental cause but will persist in seeking out their logical nature.