to Alain Neveux

The Challenge of Tristan Murail's Work

Éric Humbertclaude

translated from the French by Jacqueline Rose

----- Opening Paragraphs -----

What is the specificity of Murail's works? It is to have invented a sort of musical time, that while being irreversible and nostalgic, exists before the score is composed; a time without beginning, in the process of being constructed. Murail's music : an aeolian harp?

This innovation, originating in France between 1975 and 1985, will perhaps create a snarl in musical history. Here is why.

What is the specificity of Murail's works? It is to have invented a sort of musical time, that while being irreversible and nostalgic, exists before the score is composed; a time without beginning, in the process of being constructed. Murail's music : an aeolian harp?

This innovation, originating in France between 1975 and 1985, will perhaps create a snarl in musical history. Here is why.

The Work of Tristan Murail from 1975 to 1985: "Trans-scrire"

Between 1975 and 1985, Tristan Murail (1947 - ) laid the foundations for a style of musical notation no longer derived from the symbolization of instrumental figures, which had, under Boulez's influence, reached spectacular heights.

During a conference held at IRCAM in April 1985, Murail distributed the following summary-program:

A Brief Personal Itinerary Concerning Spectral Composition

    Initial experiences with spectra (1973-1977)
    • The harmonic spectrum as a point of departure (Grisey: Périodes, Partiels , Murail: Sables)
    • Analogies between standard electronic techniques and the spectral sphere: ring modulation, initial frequency calculation (Grisey: Partiels, Modulations , Murail: Territoires de l'Oubli, Ethers )
    • The era of the pocket calculator
    Systematization of spectral calculations (1978-1980)
    • The systematic application of ring modulation for an entire work (Les Courants de l'Espace )
    • The use of frequency modulation as a spectral model (Gondwana )
    • The era of the pocket computer and the PDP-10
    Formalization and computerization (1980- 1984)
    • Generalization of the spectral idea; the use of functions to define note values and frequencies
    • Non-linear spectra
    • The era of the graphic screen and the personal computer
    Toward a true workstation for the composer (1985 - )
    • Orchestral simulation
    • Toward a treatise on computerized orchestration?
    • The era of home synthesis

Once he began writing music, Murail, much like György Ligeti, endorsed a way of listening that was global but which avoided being "probabilistic". He designated composers Olivier Messiaen and Giacinto Scelsi as sources of inspiration. However, his pursuit of a "role model" disappeared with his first significant work Mémoire/Erosion(1975-1976), in favor of the "trans-scription" of dynamic acoustic phenomena.

"Trans-scription", by all means! Henceforth, composition would consist of simulating the psychoacoustic properties of timbre, such as fusion and fission, through the use of suitable algorithms, and then making them audible by choosing the instrument best corresponding to this or that psychoacoustic characteristic. By grasping easily identifiable procedures exposed during a work, (such as the delay and treatment process in Mémoire/Erosion or the bell sounds in Gondwana ), the listener identifies a group of acoustic forms and comprehends their internal dynamic and evolution as the singularity of style.

These forms will be called perception models. A model implies the notion of analogy and must satisfy criteria whose choice depends on the intended result. The ensuing object does not render all of the model's possibilities and responds to only a limited number of correlations, otherwise, both model and object would be identical. On the one hand, using a model allows noticeable data from a given object to be formalized inductively, and on the other hand, grants it a prospective quality which incites bringing apparently different models together.

Murail's works, from the decade being considered, contain perception models falling into two general categories: models using simulation, and models using flexion. Since the composer's use of flexion models is limited ( see part IX of Désintégrations , or pages 42-43 of Time and Again ), this article will concentrate on only simulation models, and more precisely, with archetypes of this sort.

Models that simulate electronic music processes

The following works are based on the imitation of procedures analogically exported from electronic music technology.(1)

Mémoire/Erosion (1975-1976), for horn and nine instruments, simulates the delay and treatment process:

"The solo horn produces sounds which will be 'recorded' by a purely imaginary setup. As in the case of electronic sampling, each phrase played by the horn will be heard again, repeated after a certain period of time. The other instruments obviously provide the replay. However, the original phrase or sound will never be repeated as is. With each repetition, the erosion process enters into action, so while the original structures derived from the horn solo are being destroyed, new structures are progressively being constructed. These will then also be subjected to the erosion process, and so forth. Many types of erosion are at work in Mémoire/Erosion : timbral erosion, smoothing or rounding of edges, proliferation, interference. (...) Each of the horn's interventions can be compared to a planted seed that germinates and develops, but is overcome by entropy. By the end of the score, all that remains is white noise, complete disorder, and total lack of differentiation."(2)

Territoires de l'oubli (1975-1976), for piano, thoroughly exploits the echo process:

"Take the phenomenon of echo. Considering that a normal echo repeats steadily and identically - which is not of great interest - it is possible to imagine a type of echo, which, for example, slows down through each consecutive repetition, and at the same time modifies the repeated object according to certain rules. The following example shows a sound (the note C) which is subjected to this type of imaginary echo. In this case, the harmonics of C appear progressively and are lowered an octave with each repetition, to produce increasingly complex timbre-chords (this is the opposite of a natural echo, which tends on the contrary, to filter)."(3)

Ethers (1978), for six instruments and ad libitum electronic setup, develops various techniques of filtering that follow the phasing process.

"A person can also be inspired by the process called 'phasing', which produces a sort of shifting filter. Translated into instrumental writing, this process generates internal movements in the harmonic mass; a manner of sweeping through all of the frequencies. I used it particularly in Ethers." (4)

Treize couleurs du Soleil Couchant (1978), for five instruments and electronics, owes its whole harmonic structure to the ring modulation process.

" This type of process can be put into general use to organize a passage, or even an entire score with a system that creates successive pitches. Formulated in this way, the laws of harmonic progression will easily encompass all categories of complex, intermediary or unstable sounds, etc. ... obliging theses sounds to be used. The total structural form of Treize couleurs du Soleil Couchant and certain passages of Partiels by Gérard Grisey are based on diagrams of this type.
The sound generator (a) creates its own harmonics (by passing through an intermediate stage (a') where the timbre breaks down), harmonic 1 creates its own harmonic (c). The sounds (c) and (d) react on each other as in a ring modulator, making difference (1) or sum tones (2) audible; (2) then serves as a sound generator, etc. ..."(5)

Models based on spectral simulation

Spectral simulation first appears with Gondwana (1980), for large orchestra. It consists of reproducing specific aspects of a "natural" spectrum (derived from the acoustic analysis of instrumental timbres) or an "artificial" spectrum (derived from frequency algorithms). The spectrum's internal make-up is based on theories of differential fields and the superimposition of multiple components interacting between themselves, which force the composer to write for a sizable orchestra and to use specific instruments.

Two examples reveal how the "mysteries of the sound spectrum" are simulated:

  • Gondwana , in which Murail simulates natural spectra (the sounds of bells and trumpets) which link together or are derived from each other,
  • Time and Again (1985), in which a "machine" (the DX7 synthesizer) triggers the creation of a set of artificial spectra played by the orchestra.

Simulating natural spectra

In the Eighties, many composers were fascinated by the sound of bells; this being the first non periodical complex timbre to be precisely reproduced (cf. Mortuos plango, Vivos voco (1980), for tape composed by Jonathan Harvey).

A bell's tone, even though perceived in time as a distinct and unmistakable timbre, is very difficult to hear with regards to a specific pitch; it causes a large number of partials to vibrate, which are not whole multiples of the reference frequency. Such a sound is called an "inharmonic", as opposed to a "harmonic" sound where all the partials are whole multiples of the fundamental. These sounds are unstable at a fixed and defined pitch, because the perceived pitches vary greatly from one hearing to the next. It is however possible to "experience" an impression of pitch due to what the ear assigns as a "mean pitch" (this not necessarily being the lowest frequency).

The timbre of a bell is determined by the shape of its spectral sound envelope, the model being: a short attack followed by an exponential decay. The envelope controls frequency durations and the amplitude ratios imposed on the partials. The ear detects and easily recognizes the shape of an envelope; if the outline changes in the course of time, the timbre will be perceived differently. Since bell sounds are non periodical, the acoustic cycles of each partial will not coincide in time, and their respective periods will be constantly out of phase. Murail used this psychoacoustic fact to compose Gondwana : joining two inharmonics makes perception unpredictable, and moreover, uncontrollable.

The first section of Gondwana is based on the transmutation of an inharmonic (simulated bell spectrum) into a harmonic (simulated trumpet spectrum), while the strings successively play twelve different types of envelopes that have been enhanced with subtle accelerandi and ritardandi. With each hearing, the ear attributes a different pitch sensation to this passage, just as for a bell, always choosing a unique trajectory irreducible with the previous one. This remained to be proven!

Simulating artificial spectra

During the Eighties, the DX7 was the most famous of all numerical synthesizers. It had the advantage of being able to create a multitude of complex harmonic or inharmonic sounds, impossible to produce with an analog synthesizer. Each user could elaborate a "personal" sound with a finely controlled level of inharmonicity. Murail, like so many other composers, discovered that this instrument enriched spectral material. He could "interpolate" timbres without resorting to manipulating technology that was difficult to access (such as the IRCAM computers).

In Time and again , the DX7 is used for specifically structural purposes, treating the orchestra with a dual function: "amplifier" and "prism".

Section C of the work begins with an amplification relationship. The DX7 plays the partials contained in the timbre of its own spectrum (inharmonic) while the piano and the other orchestral instruments enrich this spectrum with approximate partials belonging either to this spectrum, or to the potential fundamentals which would be composed by the DX7. Each note on the DX7 keyboard is orchestrated with a specific instrumental color.

At the end of section C, the DX7 produces spectral supports, while the orchestra diffracts the partials of the resulting spectra by using a filtering process or a defective doubling process. Like a prism, the orchestra deviates and breaks down the partials of each spectrum created by the DX7. The effect is particularly striking.

Models that simulate a pulsation process

Simulating a pulsation process, implies looking for immediate emotional stimulation. This simulation, which is present in almost all of Murail's works, is produced when numerous qualifying factors converge, and only one resultant emerges, which itself is the result of temporal relationships between sound events and the energy that produces them. Two aspects of this sort of simulation will be explored: simulating accelerando/ritardando and the simulation of a spectral collision in Désintégrations (1982-1983) for tape and ensemble.

Simulating "accelerando/ritardando"

When Murail writes an accelerando or a ritardando, he does not organize the sound events according to an arithmetical progression. His only concern is the representation of a logarithmic system that translates durations into real time perception. In this way, he transforms this information's usual function. See, for example, the three pieces in the cycle Artisanat furieux from Boulez's Marteau sans Maître , which present every conceivable manner of fluctuating tempo:

  • Avant l'Artisanat is written with a fixed metronome marking that is constantly being inflected by the indications poco ritardando and presser.
  • L'Artisanat furieux is based on three tempi with irrational arithmetical relationships. Their organization creates a quasi-permanent mobility of the time flow, even though the change from one tempo to another is abrupt.
  • Après l'Artisanat , combines the techniques from the two preceding pieces.

In this cycle, Boulez composes "tempo dynamics". Oscillating between metronomic but wonderfully flexible speeds (the rhythm supervises the tempo), durations are perceived with reference to the relationships found between short and long note values. Conversely, Murail lets us hear the relationships between impulses so clearly, that duration is actually perceived as a continuum of events (one reference, among others: the ritardando at letter E in Gondwana ).

When Murail superimposes an accelerando and a ritardando by making dynamic contours confront each other (see letter I in Ethers, for flute and five instruments), the listener perceives an auditory illusion dear to Jean-Claude Risset: the "paradoxical rhythm" of an overall pulsation becoming increasingly rapid while at the same time slowing down.

Simulating a spectral collision

In the first section of Désintégrations , a spectral collision is simulated when two spectra, whose fundamentals are a minor third apart, fuse to obtain a resultant spectrum that sounds like a bell. Murail makes them pass from one to another, like an irregular pendulum, in non-linear time ratios.(6) The spectra are filtered differently each time.(7) The listener, captivated by the swing between spectra, is caught constantly waiting for the fusion, while at the same time sensing that it is imminent. The tension reaches its peak when Murail perturbs the perception of organized durations with a logarithmic ratio used to simulate accelerando/ritardando.

Tablature, readapted


Pieces composed by Murail between 1975 (Mémoire/Erosion ) and 1985 (Time and Again ) result from the work of sampling orchestrated spectra. They do not contain a referential spectrum, and in addition, are written with numerous models that are occasionally combined. From time to time, Murail lets fragmented models be heard during the same piece, but in any case, a single model never suffices.

"All procedures have direction and meaning, or even significance, that allow the listener to sense that he is being taken somewhere, and that there is someone in the driver's seat. Vectoring the musical discourse inevitably creates sensations of tension and release, of advancement or of stagnation, and plays on the comfort of the expected and the pleasure of surprise, on the phenomena of thresholds, or, on the reversal of insidious trends, which creates the dynamism of discourse; in a nutshell, that which, beyond writing styles and styles in general, and beyond superficial revolutions and sterile arguments, directly summons the mental schemata of the occidental listener."(8)
How does perception find its way through Murail's music? Since the composer has defined a dialectic system of tension/release, or rather "inhalation/exhalation", each piece wavers constantly between groups of one-to-one relationships of the sort: sound/noise, harmonic/inharmonic, recurring/non recurring, static/dynamic, that are analog to the natural evolution and vicissitudes of a sound's life. Through these relationships (real two-dimensional references for the listener) it is possible to situate the perception models' development at any moment. When defined within the immediacy of hearing, these relationships enable a more or less rudimentary syntax to be established for the works, based on the fact that:

a) The composer uses sound to define a typology for perception:

    This sound, through spectral sensitivity, can easily be detected and controlled directly by the ear; the algorithms (most of which come from techniques of sound synthesis) enable frequency units to self-generate with both a global (constitution of harmonics and inharmonics) and local perspective (formants, sum tones, difference tones, and folding frequencies in the case of frequency modulation)(9). This explains why it is not necessary to resort to other types of formalization, since each instrument is chosen only for a particular specificity, with regards to what the perception model must render audible.

b) Tablature stores the transcription of sound:

    Tablature is a notational system midway between a program, which records a list of mechanical operations to be accomplished, and an actual score, which uses a group of symbols to permit a sound event to be represented by various signs. Tablature is characterized by the practical spirit of the instructions it contains, these being resumed by concrete indications of manipulation, most often directly accessible to the instrumentalist; which is why tablature does not possess the universal character of symbolic notation.(10)When compared to a score, tablature does not embody the composer's actual intention. Thus, it is impossible when reading a score by Murail, to imagine what will actually be heard. As an intermediate process between the composer's intuition and what the interpreter produces, tablature is a set of instructions which has the advantage of immediacy, while at the same time superbly ignoring certain concepts. (Founding an aesthetic on sound matter comes down to conceiving musical time as the object of what the timbre's internal nature carries within as latent duration.)


The "trans-scription" of a model, is an immutable writing process; that is to say, the choice of a simulation and the description of its psychoacoustic characteristics which can be formalized as:

    a) finding a "logic of expression" which lets the expected simulation develop while actually integrating a series of imposed constraints,

    b) creating a model in which we recognize the initial data system.

"To trans-scribe" means writing a "program" or set of instructions that allows a given series of operations to be carried out. Once the material has been chosen, the composer creates a network of transformations on the "interior and exterior" of each model, making its structure vary by rules specific to that model. Most of these rules are based on elementary acoustic laws which instruments put into practice.

A model consists of an outline (produced by the interaction between envelopes and temporal functions) and of dynamic spectral components. This polymorphous property will be, in many respects, illustrated by the comparative study of all the ritardandi in Murail's works - from the ritardando in Tellur (1977), for guitar, to the ritardandi in Time and again (1985), for large orchestra. The same is true for the delay-transformation process in Mémoire/Erosion : Changing the material and/or the instrumentation will not significantly alter the work. A model represents the result of a correlation, in which the outline's autonomy can be noted in relation to the sound material.

During his first ten years of composition, Murail was looking for just this: the form of a type of perception drawing its resources from only the "enthusiasm to create".


How does innovation suddenly appear in musical composition?(11) It is no doubt related to a perception code dating from a specific period, allowing an inspired creator to understand how to define a particular function when confronted by something unprecedented. Though radical innovation is impossible, it is not necessary to appropriate the nostalgia for a work or tradition from which the creator cannot be detached. Who has not one day desired to be the genius author of a previously written score?

By reconsidering the relationship systems between sound events in a work, through organizing sound material in a way that overthrows commonly held compositional ideas, and by putting aside the concept of thematic figures when writing a work, Murail proposed a new relationship to musical time based on the association of technological gestures with spectral sensitivity, which integrates each instrument into a work's genesis, because the choice of instruments is based not only on acoustic pleasure (in contrast to Boulez who wrote only for the instruments that he was fond of), but also on submission to the particularities of writing with perception models (for example: the orchestration of a spectral formant will require a trumpet or a flute, depending on the instrument's level of harmonicity or inharmonicity).

A final evaluation will of course be made someday, but that is not the question. With absolute specificity, Murail has, through the processes belonging to his first decade of creation, dared to relentlessly "trans-scribe" the spectrum while only slightly evading traditional rules of composition. But, that is not all. According to Prigogine, "time has neither beginning nor end", "it precedes even the birth of our universe".(12) Is it not here that we find the fundamental intuition which drastically differentiates the propositions made by Murail from those of Boulez? Irreversible and nostalgic, time exists before a work's composition, and is not consubstantial to it, due to the anteriority of the perception models. In a work by Murail, an instrument's timbre is the "trans-scription" of the sound material, and the absolute of notation which, for the interpreter and the author, becomes THE finality of a work.

This is the challenge of tablature, because here, the future is not given, it becomes.

What lies Ahead

After Time and again (1985), Murail composed Les sept paroles du Christ en croix (1986-1989), Vues aériennes (1988), and Allégories (1989); as many works dedicated to different instrumental ensembles, as responding to singular aesthetic stakes, but all the while maintaining the specificity of instrumental timbre and tablature as compositional absolutes.

"And Serendib (1991-1992)?And L'esprit des dunes (1993-1994)? Will you smirch them as well with a new quest?", retorted someone to me, while winking an eye. "Hasn't Murail, with Time and again , taken the decisive step toward an opening of his musical language, which takes him away from his former writing techniques?"

In 1996, twenty years after composing Mémoire/Erosion , Murail explains his work in this way:

"What are your principal compositional preoccupations at present?"

"I am interested in what I call complex musical objects. This study began with Allegories (1989), in which everything is derived from the structure of a musical gesture exposed at the opening of the work: its spectral envelope, and actual rhythmical implications and textures were expanded, compressed and contorted in various ways throughout the piece. Serendib (1991-1992), which was constructed from a sequence of five waves with variable lengths, is another example. I looked for a means of stretching and contorting these waves, while still maintaining a coherent relationship between the transformations and the initial forms. I even tried to reproduce this process to construct the overall form, but that idea proved to be only partially feasible, since time obeys its own rules, which are not geometric. In L'esprit des Dunes (1993-1994), I applied this method to real instrumental sounds, among others "khöömi" singing from Mongolia, and the sound of a Mongolian jew's harp, and I thus obtained motives which helped to elaborate the microforms as well as the spectral content of the piece and all of the melodic outlines. Next, I asked the computer to analyze spectra with various degrees of similarity or dissimilarity, and to invent ways of connecting the different parameters within the successive spectra. The computer proposed many possible solutions to obtain these types of transformation, among which I selected those which seemed most easily exploitable.

"I took this idea even further in Le Partage des eaux (1995-1996), a piece for large orchestra which I have recently finished, that I based on the sound analysis of a wave breaking against the shore. Thanks to the program 'Audioscript', (made at IRCAM for Macintosh) which I have at my home, I analyzed the minutest details of the first seconds of the wave's sound, and broke this sound down into some forty or fifty successive segments. The first step then consisted of eliminating all of the weakest components that did not play a fundamental role in the sound, and then selecting those of the fifty samples which seemed most interesting to me; in this case, the first eight. Their assemblage constitutes a very unusual musical object, which places itself beyond any notion of harmonicity or inharmonicity: the structure, extremely rich and dense, is truly chaotic. Next, I orchestrated this object in the most direct manner possible, principally using the fluidity of the flute and the clarinets to reconstruct the core of the analyzed sound, which I colored with the orchestra's highest instruments (piccolos, violin harmonics, piano, etc.), before gradually contorting it, while still remaining faithful to the initial orchestration, and introducing increasingly varied orchestrations as the distortion augmented. I particularly used certain polyphonic functions from 'Patchwork', employing functions that I had myself programmed, to conceive and develop several simultaneous levels of transformation and distortion carried out at different speeds. I also used a technique of virtual vocoding, which enabled me to obtain a hybrid timbre by applying the wave's chaotic sound structure to various types of inharmonic or harmonic spectra.

"This way of working has the advantage of teaching a person to think of the sounds from a different point of view than that of a composer: from now on, we will no longer be confronted by lists of simple static frequencies, as was the case about ten years ago. We work with completely structured objects, truly multidimensional, which consequently make the work of composition much more stimulating, more passionate."(13)

Thus, Murail goes further, but subtly, without renewing his original intuition; for these "complex musical objects", developed through advances in the computer realm, are the technological prolongation of the spectrum principle. On the other hand, they make a clean cut with the past in their way of implementing the capacity to dictate the manner in which the composer must describe them and the terms of their intelligibility. More radical than the spectrum, this sort of object permits composition, that no longer flirts with a creative context having a deterministic connotation ("we will no longer be confronted by lists of simple static frequencies, as was the case about ten years ago"). Here, creative activity is resolutely probabilistic in construction; the model generates sound material that is not more definite, but is however feasible and irreversible (an illustration: Le partage des eaux ). It remains to be seen, whether in the next pieces by Murail, these objects will be capable of providing the expected "behavior" and results, according to the situations in which the composer stages them. In any case, Murail remains optimistic; he has given up nothing and yet continues to evolve. In addition, his work is inspired by of one of the most promising theories of physics belonging to this fin du siècle, that of Prigogine. (In the simplest terms, processes of unbalance create dissipative self-organization, from which a fundamentally oriented, but not essentially phenomenological time emerges).(14)

Prigogine: "macroscopic irreversibility is the expression of aleatory characteristics on the microscopic level".(15)

In fact, the only thing that matters to me in Murail's music, is the singularity that, because the work as a whole does not create its own time, it never ceases conversing with the global time that enables it to be heard.

Murail's, is a music with indistinct boundaries. Does a work actually begin (see the introduction to Ethers )? When does the work end, if at the last audible note one has the impression that an almost infinite number of possible extensions still exist (see the end of Désintégrations )? In fact, Murail's music makes me think of an aeolian harp in action. The aeolian harp is the only "instrument" whose "music" is totally implicated in the present.(16) Wind, ever changing and dependent on aleatory phenomena, is the unstable and irreversible source, that passing through the harp, makes it sound by causing its cord's (or tube's) harmonics and partials to resonate. The same wind passing through the same harp at a later time or passing through different harp placed in another location, will sound otherwise. The wind, is what I consider musical time in Murail's music (the time being independent from the piece's form), and the harp, the musical composition.(17)

As a result, isn't the performer left feeling condemned to fulfill his role in a reductive manner, having only "to refine his sound" (though such an operation can prove itself to be difficult, as in Ethers for example)? In Murail's music, the periods of pulsation are large, and blend into the model's overall movement without allowing the performer to intervene, and even if the performer shifted some element of the dialog slightly, nothing fundamental would change for the listener. It is not that Murail's music repudiates the use of rubato, it makes rubato rather permanent, and this is what irritates the performer: having the rubato taken out of his competence, and escaping him!(18) In fact, the specific characteristic of rubato, in its traditional usage, is that of not being written, because its strength is precisely to permit constant osmosis between a piece's notation and the performer's fleeting gesture.

The moment is approaching when it will basically no longer be possible to compose as has been done for so long.


  1. (Back to text) After working on spectral simulation, Murail abandoned this type of imitation, probably as being too basic despite the discovery of extraordinary sounds and shimmering forms.

  2. (Back to text) Tristan Murail, La Révolution des Sons Complexes , "Darmstädter Beiträge" (Mainz: Schott,1980), pp. 81-82.

  3. (Back to text) Ibid., pp. 82-83.

  4. (Back to text) Ibid., p. 84.

  5. (Back to text) Ibid.; p. 85.

  6. (Back to text) For the time curve, see Spectres et Lutins, "Därmstädter Beiträge", (Mainz:Schott,1982).

  7. (Back to text) Elliot Carter had already used this collision phenomenon in the introduction to the Double Concerto (1961), for harpsichord and piano, but with radically different material than that used in Désintégrations.

  8. (Back to text) Tristan Murail, "Questions de Cible", Entretemps, (Paris, 1989) No. 8, p. 157.

  9. (Back to text) Concerning the origins of folding frequencies, see: Murail, Spectres et Lutins.

  10. (Back to text) Thus, when tablature appeared in history, during the XVI century with the birth of instrumental music, its notational system permitted musicians to use instruments without knowing how to read notes.

  11. (Back to text) I wrote the bulk of this work in an earlier version. see Eric Humbertclaude, "Le reflet d'une oreille", Images du XXème siècle (Paris: Papiers/Sacem, 1986), pp. 62-69.

  12. (Back to text) See Ilya Prigogine, La fin des certitudes, (Paris: Odile Jacob, 1996), pp. 193-215.

  13. (Back to text) Tristan Murail (an excerpt from an interview with Julian Anderson, for CD linernotes, ADES, Paris, #205 212, 1996, pp. 41-45).

  14. (Back to text) As a matter of interest concerning the transfer of scientific concepts into the human sciences, see the well known example of Kant's application of Newton's laws in the development of his philosophy (Kant, Essai pour introduire en philosophie le concept de grandeur négative, Paris: Vrin).

  15. (Back to text) Prigogine, La fin des certitudes, p. 69.

  16. (Back to text) I will take the risk of saying: in the science fiction atmosphere so revered by Murail. Will Murail's detractors still feel the need to interpret these ideas in a derogatory fashion? Throughout the centuries, and even before the appearance of science fiction, the evocative powers of the aeolian harp did not escape poets and writers.

  17. (Back to text) Here as well, if I were sure that the following suggestion would not be perceived as preposterous and fantastical, I would dare to make a comment on the esoteric quality of Murail's music, based on the composer's analysis of the spectrum's immateriality as made in his articles, and secondly, I would underline the singularity of certain titles chosen for his works which do not seem to be the result of chance or of "poetic necessity", when taking their origins into account (see C'est un jardin secret... , Gondwana, Les sept paroles du Christ en croix). There is a line of thought, existing, since the time of Pythagoras, which presents as an elementary principle of life, the adequation and interdependence of the microcosm and the macrocosm through sound. Because vibration is born of number, thereby encompassing all vibratory phenomena, the universe sings, and man, as a part of the universe, becomes a resonant note in the cosmic harmony. The resonance of a body (microcosm) can be compared to work on the spectrum, while the "music" of the spheres (macrocosm), is the resulting composition (meta-spectrum). - This is the ancestral quest for spectral identity, whose best known description is found in verse two of this text from hermetic literature: The Emerald Table (Tabula Smaragdina). This is only a very brief indication of my research (as a justification), but I see no other way to interpret Murail's obsession with the valorization Nature through certain titles of his works (Treize couleurs du Soleil couchant). (The idea of Messiaen's influence does not hold up, because in Murail's music, there is no simulation of animal cries.) Finally, it must also be noted, that in the few articles written by Murail (all concerned with the explanation of his compositional techniques), the most important is entitled Spectres et Lutins (Specters and Sprites)! This of course explains itself by an amusing formula (the lutin in its computer definition, is a graphic entity, while the spectrum is calculated by the computer), but...

  18. (Back to text) Boulez's music also placed the performer in an uncomfortable position by avoiding rubato (1. creating rhythm from the smallest note value. 2. dressing the whole thing up to bend the construction according to the composer's will).