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What is true is what we believe; when we no longer believe in anything, nothing! What remains is sensation, but sensation analysed is diamond dust!
Remy de Gourmont, Sixtine, Roman de la vie cérébrale, 1890
MUSIC AS THE STRUCTURE OF THE NUMERAL ESSENCE OF THE WORLD ─ We have seen that the problem of musical composition, if we attempt to develop it from a materialist and Darwinian perspective, comes up against two main obstacles: the problem of the rule on the one hand, i.e. the organisation of music in a normed system (which cannot be reduced to pure matter, consequently), and the problem of signification on the other, which we have linked to the theme of creativity. We now turn to the proposition that music develops with reference to a normed system, that is, that it is, according to the theory we developed in Book I, the product of a certain form of truth.
The musical work, conceived not as a random manifestation (as might be the sound of the wind, for example, playing notes through the crack of a window) but as a voluntary and meaningful act, always develops from an idea, the abstract (or concrete) representation of a melody. It presents signifying regularities that end up drawing a system of rules (harmonic and legal to begin with) and as such express a certain form of legality. But doesn't disharmonic or atonal music, which we mentioned in the previous chapter, run counter to this legalistic vision of music? First of all, music is said to be disharmonic when it does not respect the traditional rules of harmony. Disharmony can take the form of the use of unstable, dissonant or unresolved chords, chord progressions that do not follow classical harmonic relationships (with no clear functional logic) or a sound balance disturbed by sharp contrasts or discordant combinations of sounds. A disharmonic work may be tonal, but it plays on the extreme tension or lack of resolution of the chords (certain passages in Stravinsky's Rite of Spring, for example, are disharmonic but remain partly "tonal"). Music is atonal when it is not based on any specific tonality, i.e. there is no central tone towards which the notes and chords gravitate. Atonal music is marked by the absence of hierarchy between notes (no dominant or tonic), by a dissolution of functional harmonic cadences (no classical tension or resolution) or by an exploration of new structural logics, such as dodecaphonic series (Schoenberg, Webern, Berg). Atonal music may be highly organised and structurally coherent, but it avoids any reference to a traditional tonal system (Schoenberg's Pierrot Lunaire is an atonal work that does not follow any conventional tonal system). Can we really say, however, that atonal and disharmonic music escape all normative criteria?
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On closer examination, Arnold Schoenberg's Pierrot Lunaire and Pierre Boulez's Le Marteau sans Maître, although not part of the conceptual framework of traditional harmonic music, are not purely arbitrary. Each of these works is based on its own structures of legality, whether it be the serial principle in Schoenberg's work or the rigorously organised formal models and permutations in Boulez's. In this way, their musical coherence is no longer based on the concept of the harmonic. In this way, their musical coherence no longer resides in classical functional harmony, but in the internal systems of relationships and constraints that give these works their logic and intelligibility. In Pierrot Lunaire, Schoenberg does not rely on any dominant tonality but organises his musical discourse through recurring motifs and melodic cells, developed and transformed throughout the work. Although these motifs are not linked to any tonal system, they nevertheless establish an internal coherence, guaranteeing the unity of the musical discourse. Similarly, Boulez's Le Marteau sans Maître is based on an integral serialism, in which each sound parameter ─ pitches, durations, dynamics, timbres ─ is subject to a rigorous organisation based on predetermined series. Here again, the absence of classical harmonic markers is not equivalent to an absence of structure (on the contrary, the structure remains present and establishes a form of immanent legality). These works illustrate the idea that even outside the tonal framework, music retains its principles of internal organisation, which ensure its intelligibility and coherence. With Le Marteau sans Maître, Pierre Boulez, while also claiming intertextuality with René Char's poems (of the same title), places himself squarely within the problematic of meaning and correspondence (the apparent anarchy of the subject does not imply the anarchy of its expressive support).
But what about anarchic or random works? Do they have an internal coherence, a meaningful intentionality? In John Cage's 4'33, the performer does not play a note for four minutes and thirty-three seconds, leaving silence and ambient noise to fill the sound space. John Cage, influenced by Zen Buddhist culture, encourages the audience to practise attentive listening, becoming aware of each sound, regardless of its source or nature. Cage pioneered the use of indeterminacy and chance in music. 4'33 is one of the most representative examples of this approach, each performance of the work being, by definition, unique (since the ambient sounds are, of course, never the same). With 4'33, Cage challenges the boundaries of what we call "music" and encourages the audience to consider all sounds, even the most ordinary, as potentially musical. In short, Cage is here at the limit of the criterion of musical intentionality. The ambient hubbub certainly does not fall within this intentional criterion (like the wind that whistles as it rushes through a window opening), but it is nevertheless intended by the "composer" who designates it as "worthy of interest". The listener (who, in this case, is also an actor in the piece, undoubtedly participating in the hubbub with his own commentary on the work) chooses to accept or refuse the
composer's proposal. If he accepts the proposal, it is because he too finds it worthy of interest. He thus chooses to give it a meaning, a significance, entering at the same time into the dialectic of intentionality. In this acceptance, there is also assent to an implicit rule, that of the absence of musical rules, which is based (all the same) on a tacit contract between the composer and the listener. Now, as soon as the listener accepts this tacit contract, he agrees to enter a signifying and regulated world in which the absence of rules is in fact defined in relation to pre-existing rules (those, for example, which consist of having the orchestra play rather than the audience).
In our world of meaning, the absence of normativity is a fantasy, and randomness is always defined in relation to regularity. This relationship explains the difficulties inherent in the intentional production of a truly random series. In fact, so-called random numbers can only be generated from physical phenomena that are intrinsically unpredictable ─ although we would still have to specify what 'intrinsically random' means in a deterministic world. Processes such as Brownian motion, thermal noise, electrical circuit fluctuations or radioactive decay are often used to provide a source of randomness. In the absence of these physical phenomena, any attempt to create randomness results in pseudo-random sequences, which are merely mathematical simulations of the properties of randomness. So, the universe of meaning, which is also the universe of intentionality, is in essence inseparable from a form of organisation. In the case of Cage's work, if the content of the work is random (although regularities could undoubtedly be identified from one 'performance' to another), this is not the case with the work itself, which is clearly the product of an artistic or intellectual intention. In a sense, 4'33 is reminiscent of the empty picture frames we sometimes find in front of a tourist monument or a landscape. The interest of the work lies not so much in its content per se (the landscape or the hubbub are not the main object of our attention here) as in the artist's intention, which invites us to take a fresh look at an element that he has not directly shaped. In this sense, the artist is not just creating a work of art; he is inviting us to adopt a posture of active observation, making us attentive spectators of the world. In other words, the meaning of the work is layered, with the artist's intention taking precedence over the content of the work itself.
If we set aside atonal or disharmonic works, which we regard as borderline cases of musical theory (and which nonetheless fall within the criterion of legality, as we have attempted to demonstrate), we note that most musical works develop from a system of harmonic, tonal and rhythmic rules, and as such express a certain form of legality. Jean-Pierre Changeux, for example, rightly points out that "octave, fifth and fourth intervals are expressed in terms of simple numerical ratios, 2/1, 3/2 and 4/315." He adds, however, that "if intervals are perceived as consonant or dissonant, it is always in relation to a given grammar and not in itself16", an idea with which we agree. Consonance and dissonance are not absolute (what is dissonant in a given...
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