Boulez and the Concept of Chance

 

 

 

David Walters

 

Structure 1a (1952) constitutes the culmination of Boulez’s obsession with the principle of necessity in music. However, a major aesthetic problem arose during this experiment: that the rigorous application of the principle of necessity inevitably led to the appearance of an unnecessary element. Through an attempt to create a new consistent musical language in which every element was brought within a rationalized system, he lost control over the musical material and arrived at ‘total absurdity’.[1] The sonic results of his total serialist work sounded quite random. It was clear that the attempt to eliminate the unnecessary from the musical work was impossible. He responded by attempting to find a way to control and ‘absorb’[2] this random element into his approach to music itself. His conceptualization of this problem – the issue of chance - is the subject of this essay.

 

In this paper, I shall begin by analyzing the concept of chance itself, and then explore Boulez’s views on musical automatism[3] and chance procedures that preoccupied his thinking during the years leading up to the composition of his Third Piano Sonata in 1957. I examine his proposal for a new conception of musical form – ‘mobile form’ – and investigate several terms which Boulez has employed to articulate his ideas on chance in the musical work, including ‘mobility’, ‘improvisation’ and ‘parentheses’. Throughout, I attempt to clarify the specific terms he employs and locate them within their historical contexts.

 

Boulez’s reflections on chance primarily date from 1952 to 1957 and were influenced by several factors. The most fundamental influence on his conception of chance is the writer and poet Stéphane Mallarmé. Mallarmé’s obsession with the idea of chance can also be seen in several surrealist texts to have shaped Boulez’s thinking, most strikingly in the experiments in ‘automatic writing’ and also in the thematic content of works such as Breton’s novel Nadja.[4] Similarly, one should recognize the importance of the nouveau roman writers of the 1950s and 1960s such as Alain Robbe-Grillet and Michel Butor on Boulez’s aesthetics. All these influences are considered throughout this essay. Undoubtedly, Boulez’s thoughts on chance were very much shaped by developments in music in the 1950s. Most obviously, the Darmstadt School’s investigation into ‘complete’ control over all musical elements, which reached its culmination in total serialism, shaped Boulez’s conception of chance in the musical work. The most obvious examples are Boulez’s own compositions, Polyphonie X (1951) and the first book of Structures (1952). The apparently opposite explorations into complete chance, exemplified by Cage’s 4’33” (1952), and Cage’s theoretical writings in general, also contributed towards Boulez’s reflections upon chance, as Jameux correctly notes.[5] However, I would argue that Cage’s role in this respect was chiefly in provoking Boulez to confront the problem of chance in music rather than in helping him conceptualize chance itself.[6] I shall examine Boulez’s conceptualization of these two extremes of control and chance in his important article ‘Aléa’ (1957), a text that provides much of the material of this essay.

 

 

The Concept of Chance

 

            Of all the terms he uses, none is more important to understand in context than the concept of chance [‘le hasard’] itself. It is a main source of misunderstanding of Boulez’s aesthetics and draws on a tradition of thought and set of assumptions concerning the concept of the art work and the aims of art itself.

 

Despite the popular image of Boulez as a composer unconcerned with ‘expression’, his preoccupation with technical issues of the musical language is fundamentally rooted in the need for musical expression. Indeed, the inherited means of expression – the musical language – is regarded by Boulez as a problem in itself. The means of expression, transformed and expanded by various composers throughout Western music history, is considered by Boulez as contingent insofar as it could have developed differently. Its tendency to become reified restricts the composer’s possibilities for expression. Nevertheless, the composer cannot create music outside of the inherited forms of expression. The task of the composer is to overcome this inheritance through rationalization of the means of expression in order to free himself/herself of its limitations.

 

 

It is vital to view Boulez’s thoughts on chance from this perspective: the issue of chance concerns the wider problem of musical expression. One can see, therefore, that his use of this term does not merely correspond to the English word ‘chance’. It is not only a synonym for the fortuitous meeting of different elements or an event that cannot be predicted with certainty before it occurs, i.e. the unforeseen. These connotations are, nevertheless, part of the meaning of this term but do not constitute its complete definition. I would propose that one begins to approach the concept of chance by understanding it as something exterior to the composer’s own thought. If an element of a given artwork is not under the artist’s control, i.e. it is not necessary and functional, that element does not have a meaning. This undermines the notion of art as the expression of the free autonomous subject, which Boulez assumes as the raison d’être of artistic endeavor. He seems to understand chance in this way when he describes it in ‘Aléa’ (1957) as that which ‘does not ‘compose’’.[7] For a more accurate description of chance, it is helpful to consider the source from which Mallarmé drew the term, at least via other writers – the writings of Hegel. Hegel provides a definition of what is usually translated in English as the ‘Contingent’ and is the same concept as chance:

 

[T]he Contingent is something that is not self-possessed and is alien.[8]

 

The ‘Contingent’ is that which is alien - i.e. exterior - to the subject and does not belong to, or has not been ‘consumed’ by, the subject. It is because chance is not ‘self-possessed’ that makes it an unnecessary element in the musical work. Boulez’s aversion to the passive acceptance of inherited musical material is based on this idea. The inherited idea is not ‘possessed’ by the composer, as it is drawn from the works of previous composers. When the composer possesses his own material, i.e. he has complete mastery of the technical means at his disposal, he arrives at the utopia of the ‘pure work’ I shall discuss later.[9] However, as I shall consider, Boulez arrives at the recognition that chance is contained not only in the non-self-possessed inherited material but also in the composer himself. In an article from 1963, he expands upon this by arguing chance arises through ‘the chronology of the various encounters in your life and even the chronology of that chronology’.[10] This affects the musical work through a composer’s distinctive musical taste and compositional mannerisms.

 

The claim that chance is something unnecessary is suggested by McCalla in the following statement, written on literature rather than music:

 

The elimination of le hasard is the exclusion of the arbitrary, and the exploration of language as its own agent, rather than as that of an ultra-linguistic reality.[11]

 

In other words, the attempt to eliminate chance is part of the attempt to eliminate that which is exterior to the medium of expression itself.

 

            Having begun to consider the way in which Boulez conceives chance, I would like to analyze the most comprehensive account of his thoughts on this subject which appears in ‘Aléa’ (1957).

 

 

Chance: by Inadvertence or Automatism

 

            The term ‘aléa’, presented both as the title of Boulez’s article and within the text itself, was employed by Boulez to refer to chance elements within music, and this constitutes its first usage in a musical context.[12] Etymologically, it is derived from the Latin word ‘alea’ meaning ‘throw of the dice’. This clearly signals his debt to Mallarmé’s poem ‘Un coup de dés’ (1897) in the conception and formulation of this term and in his thoughts on chance in general.

 

In the article ‘Aléa’, Boulez identifies the two different ways in which chance is introduced into musical composition. The first is identified as ‘chance by inadvertence’, the second as ‘chance by automatism’.[13] He presents these two different types of chance as if they are the two extremes of chance and total control respectively. This can be confusing, as it becomes clearer later in the same article that they are really two different means of confronting chance.

 

First, Boulez is highly critical of experiments he rather misleadingly calls ‘chance by inadvertence’.[14] This refers to the deliberate use of chance techniques to create music, such as throwing dice or the employment of vague notation. Most of his criticisms center on the lack of involvement of the composer’s invention. He describes the results as an ‘artificial paradise [¼]: a narcotic which protects against the needle prick of invention.’[15] His most damning criticism is that, despite its attempt to avoid the composer’s subjectivity, it always returns in the decisions involving the way chance is introduced, e.g. decisions concerning performance such as the time frame or the venue.[16] That is to say, the composer always tends to reintroduce traditional notions of the musical work. Boulez suggests that, if one wants to arrive at ‘chance by inadvertence’ in every respect, ‘my vote goes, without question, to natural chance, which needs no instruments to reveal itself.’[17] This type of chance is only consistent if one is never involved in the process of making sounds at any stage. This is clearly impossible, as even if one follows Boulez’s suggestion above, the listener inevitably implants his own conceptions of music into the listening experience. Implicitly, Boulez attacks chance techniques because, whilst they purport to eliminate the composer’s subjectivity, they exist because of a subjective desire to eliminate that subjectivity. Even vague notation does not avoid this; rather the performer makes the choices instead of the composer.[18]

 

One reference in ‘Aléa’, in particular, reveals the main target of this criticism. He argues that these experiments into ‘chance by inadvertence’ draw on ‘a quasi-oriental philosophy in order to conceal a fundamental weakness in compositional technique’.[19] This reference to ‘oriental philosophy’ is also a feature of Boulez’s entry for the Encyclopédie Fasquelle on Cage in the following year (1958).[20] As Nattiez notes, these criticisms are primarily targeted at Cage’s experiments into chance procedures.[21] The attack on Cage’s approach which appears in ‘Aléa’ was not the first criticism to appear in Boulez’s writings. In a letter to Cage dating from December 1951, a time when Boulez was composing his first book of Structures, he already expresses his reservations about the American composer’s chance procedures in his work Music of Changes (1951):

 

The only thing, forgive me, which I am not happy with, is the method of absolute chance (by tossing the coins). On the contrary, I believe that chance must be extremely controlled.[22]

 

 

Throughout the 1950s, the writings of Boulez and Cage become more hostile to each other. This hostility culminated with Boulez’s ‘Aléa’ (1957) and Cage’s sarcastic response in his lectures at the Darmstadt Summer School in 1958.[23] To this day, much of the confusion concerning Boulez’s and Cage’s ideas on chance derive from the failure to acknowledge the vastly different assumptions both held regarding art. Boulez approached chance from the tradition of French thought  which assumes that the role of art is to reveal the world in some way. Chance, the contingent aspect of expression, impedes this goal. The artist is forced to find a way of overcoming chance in order to retain control of his work. Consequently, the artist attempts to eliminate, as far as possible, all alien elements such as his own unconscious use of inherited ideas. Opposed to this conception of art is Cage’s attempt to obliterate the artist’s expression entirely. The first premise in Boulez’s approach – the need for expression – is completely rejected by Cage. In short, although both Boulez and Cage appear to reject the ‘composer’, they view this task from different traditions and with different conceptions of what exactly they wish to reject.

 

Returning to ‘Aléa’, the second way in which chance is introduced into musical composition is identified by Boulez as ‘chance by automatism’. This refers to the manipulation of sound components through the use of serial grids and numbers in total serialism. Like his attitude towards ‘chance by inadvertence’, he is highly critical of this approach that he describes as ‘mechanistic, automatic, fetishistic’.[24] However, he does not reject out of hand number grids, or the automatic generation of musical structures generally, indeed he claims they are necessary to help organize the sound world of the work. On this point, his argument can be tracked back as early as 1951 to the following passage, also notable for the first mention of the term ‘automatism’ in his writings:

 

We may therefore conceive of musical structure from a dual viewpoint – on the one hand the activities of serial combination where the structures are generated by automatism of the numerical relations. On the other, directed and interchangeable combinations where the arbitrary plays a much larger role.[25]

 

In this passage, Boulez adopts a favorable attitude towards the generation of numerical relations by automatism. It is only when this automatism is used fetishistically and reduces the imagination of the composer to a minimum that it becomes problematical.[26] By 1954, he begins to state this worry with greater concern: ‘technique is becoming a screen, a much-needed shelter from more awkward questions.’[27]

 

Returning to ‘Aléa’ in 1957, Boulez writes:

 

Composition aspires to the most perfect, polished, irreproachable objectivity. [¼] Schematisation simply takes the place of invention; imagination, a mere servant, limits itself to giving birth to a complex mechanism, which in turn takes in the task of generating microscopic and macroscopic structures until the exhaustion of all possible combinations marks the end of

the work.[28]

This criticism of the aspiration towards aesthetic ‘objectivity’ would continue into the 1960s in his Darmstadt lectures and Penser la musique aujourd’hui (1963). In his Darmstadt lecture entitled ‘Forme’ (1960), Boulez argues that musical compositions displaying a ‘fetishistic’ preoccupation with numbers and the principle of permutation do not achieve ‘form’ but a ‘mere sampling of local structures’.[29] In other words, when the composer simply generates musical structures through automatism, the result is merely the sound of musical patterns in time. Again, he reiterates this in another lecture at Darmstadt in 1961 when he argues that ‘no form is justified by the mere logic of its unfolding’.[30] When the composer loses mastery over his material by succumbing completely to a type of musical logic, i.e. a type of consistency, the resulting work is meaningless and consequently loses its raison d’être of expression.[31]

 

 

Of course, all of these criticisms concerning ‘chance by automatism’ can very easily be directed at Boulez’s Structure 1a. (1952) Boulez acknowledges this in a letter to Henri Pousseur dating from shortly after Aléa was first presented at Darmstadt in which he reveals that the criticisms in ‘Aléa’ are primarily targeted at himself.[32]

 

The term ‘automatism’ itself is of particular interest, as it is a key term in Breton’s definition of Surrealism:

 

SURREALISM, n.m. – Pure psychic automatism by which one intends to express verbally, by writing or by any other way, the real function of thought. Dictated by thought, in the absence of all control exercised by reason, and outside all aesthetic or moral preoccupations.[33]

 

 

Through ‘automatism’, Breton argues, the artist can escape the sedimented ideas of the rational mind and consequently achieve a new form of expression. This notion of automatism led to the surrealist experiments in ‘automatic writing’ which, influenced by Freud’s ideas on ‘free association’, avoided rationalization by dictating the poet’s ‘stream of consciousness’. Stacey makes a parallel between this idea of automatism, specifically concerning Artaud’s automatic writing, and Boulez’s exploration of automatism in Structures.[34] There is unquestionably a strong connection between the automatism of surrealism and Boulez; indeed, it is probable that Boulez deliberately uses this term with surrealism in mind. Both approaches aim to achieve a new concept of expression unlimited by sedimented ideas through the annihilation of chance. However, whereas surrealism attempted to achieve this through an abandonment of rationality, Boulez opted for the Mallarméan solution of complete rationality (i.e. complete necessity). Similarly, whereas surrealism avoided inherited grammatical rules in the belief that one could arrive at this new form of expression immediately (i.e. ‘automatically’), Boulez avoids inherited grammatical rules but then replaces them with his own. One can see that the surrealist’s abandonment of rationality in ‘automatic writing’ is much closer to Boulez’s category of ‘chance by inadvertence’ than ‘chance by automatism’. In an interview in 1993, he makes it clear that he understands the surrealist experiments in ‘automatic writing’ in this way. He describes Cage’s method of ‘coin tossing[35] as the equivalent of automatic writing in literature, not his own method of generating musical structures by automatism. He continues by arguing that the problem with automatic writing in both literature and music is that it ‘does not engender any grammar, and a vocabulary does not exist without grammar’: consequently, it does not express anything.[36] One notes that it is the necessity of achieving an adequate means of expression which serves to provide music with its justification.

 

In summary, both chance by inadvertence and chance by automatism are criticized by Boulez. The former is rejected completely whilst the latter is rejected in its extreme cases. Both approaches are different means of removing the composer from making choices and both inevitably lead towards chance in some way. However, even if the composer actively intervenes in the process of composition, chance is introduced into the work from the chance encounters of the composer’s life and musical taste. Boulez summarizes this inevitability of chance:

 

the less one chooses, the more the single possibility depends on the pure chance encounter of the [sound] objects; the more one chooses, the more what happens depends on the coefficient of chance implied by the subjectivity of the composer.[37]

 

Having established that Boulez recognizes chance is inevitable, it is also clear, for reasons concerning his desire for a new form of expression, that his attitude towards it is hostile. This hostility is based on two aesthetic concepts intrinsic to Boulez’s aesthetics: ‘renewal’ and ‘necessity’.

 

First, he criticizes chance on the grounds that it cannot ‘renew’ itself. Writing specifically on ‘chance by inadvertence’ (although this argument can be applied to chance in general) he writes that ‘[i]nadvertence is fun to begin with, but one soon wearies of it, all the more quickly for its being condemned never to renew itself.’[38] This refers to the acknowledgment that chance always remains itself, as it cannot change. Chance in one musical situation constitutes the same as chance in another situation. He makes this point succinctly in the following: ‘[i]n its All-Objectivity, the work represents a fragment of chance which [¼] is as justifiable (or unjustifiable) as any other fragment.’[39]

 

 

The second criticism, which follows on from the first, is that chance is an ‘unnecessary’ element within a musical work and therefore it does not express anything (i.e. it is meaningless).  Once the work cannot express anything, Boulez argues, it loses its self-justification. I would argue that this is his most fundamental criticism of chance. However, as I have already established, he discovered with Structure 1a that chance is always present in the musical work and it is impossible to annihilate it completely.

 

Having established that Boulez recognized the inevitability of chance in the musical work, I would now like to examine his solution to this problem.

 

 

Boulez’s Solution to the Problem of Chance

 

 

In the following passage, Boulez describes his ‘desperate’ struggle with chance:

 

Desperately, one tries to dominate one’s material by an arduous, sustained and vigilant effort, and desperately chance persists, sneaking in through a thousand unfillable cracks.[40]

This quotation is a good starting point to examine his response to this problem. It is very similar to a sentence buried in Bonniot’s preface to Mallarmé’s Igitur (1869) which describes Mallarmé’s development from Igitur to ‘Un coup de dés’ (1897):

 

After having completely exhausted himself in an effort to dominate himself increasingly completely and arduously, [Mallarmé] arrives at this conclusion, desperately, that Chance persists[.][41]

 

Several identical words appear in both statements by Boulez and Bonniot, such as ‘dominate’, ‘arduous’ and ‘chance persists’. The two quotations are so strikingly alike that Boulez would appear to be drawing on Bonniot’s description. The following sentence in Bonniot’s preface reveals Mallarmé’s solution to this problem:

 

this existence of Chance is tempered by the creation of a Constellation [42]

 

 

The creation of a ‘Constellation’ was Mallarmé’s attempt to ‘absorb’ (i.e. to integrate) chance into the work of art.[43] This idea can most readily be seen in his poem ‘Un coup de dés’[44] which utilizes the typographical disposition of the words on the page to enable the eye to follow different routes through the text. Indeed, the concept of the ‘Constellation’ and the aesthetic development that led Mallarmé towards this idea is literally threaded throughout this poem. Distinguished from the rest of the text by large capitalized letters, two main lines run throughout Mallarmé’s work:

 

A THROW OF THE DICE WILL NEVER ABOLISH CHANCE

NOTHING WILL HAVE TAKEN PLACE BUT THE PLACE EXCEPT PERHAPS A CONSTELLATION[45]

 

The first line articulates the problem of the inevitability of chance within the work of art. Note the apparent contradiction of this sentence: a throw of the dice is usually considered to be a synonym for chance. However, the ‘chance’ to which Mallarmé refers is the contingent aspect of the historical material which cannot be overcome through chance procedures such as throwing dice. The last line, which is not as straightforward as the first, signals Mallarmé’s solution of the ‘Constellation’.

 

The capitalization of the term ‘Constellation’ that appears in the preface by Bonniot, who was a close student of Mallarmé, suggests it may originally have been drawn from German literature, possibly the writings of Hegel. However, this term, or its equivalent in German, does not appear in Hegel’s writings. It occurs, however, more than half a century after Mallarmé in the writings of Adorno. Paddison writes that in his espousal of his ideas, Adorno favored:

 

the idea of the ‘constellation’ of fragments, each equidistant from an unstated centre, marking the place of the object of enquiry, whose presence is conjured up and at the same time negated by a text which constantly denies identity with its object.[46]

 

This is the essence of Mallarmé’s conception of the ‘Constellation’. It is the introduction of elements of ‘mobility’[47] into the form of the work which prevent any singular conception of meaning to dominate. For Mallarmé, this involved placing the words on the page in a way that enables them to be read in more than one order. This introduction of mobility is a means of acknowledging and ‘absorbing’, to use Mallarmé’s term, chance. Paddison’s description of Adorno’s approach is very similar to Rosen’s description of Mallarmé’s ‘Un coup de dés’:

 

Mallarmé’s poem [Un coup de dés] concerns the play of chance which remains implicit in any creative ordering, the freedom of meaning essential to a form both defined and closed. He affirms as a delusion the classical idea of the work of art that attempts to ignore chance and contains at its centre a definitive nucleus of meaning. Un coup de dés neither abolishes chance nor yields to the probabilities, but contains them by an essay in transcendence.[48]

 

 

For Boulez, Mallarmé’s image of the ‘constellation’ was the solution to the parallel problem in music. This can be seen most clearly in Boulez’s Third Piano Sonata (1957-). He describes the form of the five movements, or ‘formants’, of his Sonata as a ‘constellation’. As if to reiterate this point the pivotal third formant is entitled Constellation-Miroir. The five formants, of which only three have been published, can be played in one of eight orders, to be chosen by the performer. Writing on this formal mobility, Boulez notes that ‘the idea of the form is circular: each autonomous development may serve as beginning or end’.[49] There are also multiple pathways within each formant that a performer can choose. For example, the first formant Antiphonie is written on separate sheets which can be arranged in four different orders.

 

The Third Piano Sonata is Boulez’s first work to incorporate ‘mobility’ of form in order to grant the performer elements of choice. This introduction of mobility, i.e. a ‘controlled chance’ would become known as ‘mobile form’, a term I shall examine shortly.[50] After the pinnacle of total serialism of Structure 1a (1952) in which his compositional choices were limited as far as possible (i.e. automatism), he set about permitting himself elements of choice on a local level. This can be seen in his next major work, Le marteau sans maître (1955). In this intermediate work between Structure 1a and the Third Piano Sonata, the composer’s choice is not entirely subjugated to the automatism of serial relations. His Third Piano Sonata can be understood, therefore, as the continuation of this idea of introducing mobility into the work, from the local structural level to the larger-scale form. Boulez himself acknowledges this in an interview dating from 1990, arguing that his primary preoccupation from 1952 onwards was the following problem:

 

Since I have allowed for choices on the local level, why not extend such choices to the form itself?[51]

 

In other words, Boulez seeks to be consistent in his introduction of ‘mobility’. Before continuing, I would like to clarify the terms of ‘mobility’ and ‘mobile form’.

 

 

 

Mobile Form and Mobility

 

 

The concepts of ‘mobility’ and ‘mobile form’ (or ‘the mobile’) in Boulez’s writings are difficult to define. ‘Mobility’ appears in Boulez’s writings twelve years before the term ‘mobile form’, and whereas the idea of mobile form was widespread in the 1950s and early 1960s, Boulez’s specific principle of ‘mobility’ was not. Having acknowledged that these two concepts have their own separate ‘histories’, I would like to stress that he conceives them as being essentially the same: ‘mobility’ is the aesthetic principle and ‘mobile form’ is the introduction of ‘mobility’ into the form itself. I would first like to consider the notion of ‘mobility’.

 

Primarily, one should understand ‘mobility’ as the possibilities at any given moment of musical creation (i.e. in performance or composition) within a particular field of choice. My reasons for this definition will become clearer during my examination of this term. This concept appears in Boulez’s first ever publication ‘Propositions’ (1948) in which he defines mobility as ‘[e]ach time a note occurs it will be in a different register’. He opposes this idea to ‘fixity’, defined as when ‘each of the twelve notes has a fixed location’.[52] Due to this definition, Nattiez claims that:

 

[Boulez’s concept of mobility] has nothing to do with the introduction of chance into the compositional process; it is concerned with the freedom that the composer gives himself regarding the registral disposition of each note in the series.[53]

 

Besides the fact that Boulez’s definition describes a rather crude musical idea to be understood as part of his embryonic musical theory, Nattiez’s argument is rather simplistic. First, I would suggest Boulez’s narrow definition presents a concrete example (indeed, a particularly narrow example) of the general principle of mobility (and fixity). Second, even taken at face value, this definition does not necessarily exclude other possible meanings for this term. In light of later developments, it would be inconceivable that Boulez had retained this very narrow definition throughout his writing career. I would suggest this early definition provides an insight into his early attempts to rationalize his own musical technique. However, a much more informative view into this term is provided by Cage.

 

 

According to an article by Henry Cowell dating from January 1952, Cage reveals that ‘Boulez influenced me with his concept of mobility’.[54] Consequently, when, in an article published later in the same year, Cage provides his own definition of ‘mobility’, one can consider its implications for understanding Boulez’s conception of this term. Cage distinguishes between the two opposing poles of ‘mobile’ and ‘immobile’. Writing with number charts in mind, he states that ‘mobile means an element passes into history once used giving place to a new one; immobile means an element, though used, remains to be used again’.[55] This definition of ‘mobile’ is very similar to Boulez’s important concept of ‘renewal’. The concept of renewal manifests itself both in the aesthetic position that constantly revitalizes, or ‘renews’, all inherited concepts, and also in the compositional approach itself which aspires to vary constantly all aspects of the musical work. The concept of mobility must, therefore, be understood as being closely linked to the principle of renewal, as it aesthetically revitalizes one’s conception of the work and compositionally enables greater variation and ‘mobility’. This is stated clearly in ‘Aléa’ at the point which Boulez first introduces the idea of mobile form into his essay. He argues that the development of mobile form is based, in part, on ‘the desire to create a self-renewing kind of mobile complexity’.[56] He continues:

 

[I]n a musical world where all notion of symmetry is tending to disappear, and a concept of variable density is assuming a more and more basic role on every level of composition – from the material up to the structure – it is logical to look for a form which is not fixed, an evolving form which rebels against its own repetition; in short, a relative formal virtuality.[57]

 

One can easily see in this quotation the concepts of renewal and variation underpinning Boulez’s thoughts on mobile form.[58] As mobility is associated with renewal, it clearly constitutes something different from chance which, as I showed earlier, Boulez describes as being ‘condemned never to renew itself’.[59] Therefore, when I defined mobility (above) as ‘the pssibilities at any given moment of musical creation [¼] within a particular field of choice’ it is essential to avoid confusing these possibilities with the multiple possibilities of chance.[60] However, these two concepts of mobility and chance are, nevertheless, associated, as they both are concerned with possibilities, some of which will become ‘fixed’ or ‘realized’. Nevertheless, whereas chance involves events which remain exterior to one’s thought, mobility is concerned with choice, i.e. the freedom of the autonomous subject.

 

 

The idea of ‘mobile form’, prevalent in the 1950s and early 1960s in various art-forms, has its precedents in the ‘mobile’ of the visual arts, particularly the mobiles of Alexander Calder (1898-1976). The ‘mobile’ or ‘mobile form’ consequently has its own history which is different to that of Boulez’s concept of mobility which dates from the 1940s. However, the idea of mobile form is certainly part of his conception of the general principle of mobility. The term ‘mobile form’ first appears in his writings in the article ‘Form’ (1960). He provides an alternative name - ‘material form’[61] suggesting that the score, which he describes as a ‘possible score’,[62] can serve as a basis, i.e. ‘material’, for ‘one or more ‘fixed’ scores chosen from the multiple ‘possibilities’.[63] This last point is highly illuminating. It reveals the link between Boulez’s concepts of ‘mobility’ and ‘fixity’ dating back to 1948 and the idea of mobile form. This statement confirms he conceives ‘mobility’ as the possibilities available to the composer which, with respect to mobile form, are either chosen (i.e. ‘fixed’) or remain unrealized possibilities.

 

So far, I have established that Boulez’s introduction of mobility into musical form in his Third Piano Sonata was provoked primarily by the impasse of Structure 1a. I would now like to consider two key literary ideas influential on Boulez before I return to the details of his proposal of musical mobile form. Although it must be recognized that there were musical factors that precipitated Boulez’s development towards mobile form,[64] I would argue that the substance of Boulez’s aesthetic conception is particularly influenced by literature. The first literary idea I shall examine is Mallarmé’s concept of the ‘pure work’. The second idea is that of the ‘labyrinth’.

 

 

 

Mallarmé and the ‘Pure Work’

 

 

Boulez has acknowledged that he was ‘very attracted’ to Mallarmé around 1950.[65] At that time, he read two of three key works by Mallarmé that confront chance and which point towards the ‘pure work’. In the chronological order in which they were written these are Igitur (1869), ‘Un coup de dés’ (1897) and Le Livre (posthumous), all of which should be kept in mind when considering the Third Piano Sonata.

 

 

Of these three works, I would argue that the earliest, Igitur, is by far the most influential on Boulez’s aesthetic theory, not only with respect to the concept of chance but also in consideration of Mallarmé’s aesthetic position generally.[66]

 

Boulez notes that around 1950 he read ‘Un coup de dés’.[67] This is probably correct, as he mentions in a letter to Cage dated June 1950 that he is working on a composition entitled ‘Un coup de dés’.[68] Although this work was subsequently aborted, Boulez would later return to Mallarmé’s poem as the basis of his Third Piano Sonata. The first reference to Mallarmé in his published articles appears the following year in ‘Moment à Jean-Sébastien Bach’ (1951) in which he quotes the last line of ‘Un coup de dés’: ‘Tout pensée émet un coup de dés’.[69] ‘Un coup de dés’ would provide Boulez with his inspiration for his Third Piano Sonata[70] and, as I shall consider shortly, led to his introduction of mobility into musical form. However, his Third Piano Sonata is distinctively different from Mallarmé’s poem because the former allows mobility in the order of the musical sections whereas the overall form of the latter is fixed and only permits different pathways through the text. In this respect, Boulez’s aesthetic conception in this work anticipated one of Mallarmé’s final works called, quite simply, Le Livre.

 

Le Livre (posthumous) is an unfinished book consisting of loose pages which can be read in different orders or isolated from the rest of the book. Edited and introduced by Jacques Scherer, it was first published, in its incomplete form, on 13 March 1957 at a time when Boulez had already established the mobility of form in his Third Piano Sonata. Boulez read it shortly after it had been published, later in 1957. In an interview from 1990, he maintains he found in Le Livre:

 

 a kind of confirmation: in fact, when I had thought of open form, I had in mind the typographical arrangement of “coup de dés” that allowed the reading of phrases diagonally, in such a way that, depending on whether one chose one bifurcation or another, several meanings were mingled.[71]

 

 

For Mallarmé, the formal mobility of Le Livre was a means of ‘absorbing’ chance to enable a new form of expression. His sought to annihilate chance contained within the writer, i.e. the contingent aspects of his writing such as his individual mannerisms. By enabling more than one pathway through Le Livre, that is to say by avoiding the pathway of the author, Mallarmé hoped he would arrive at what he called the ‘pure work’.[72] The ‘pure work’ is a work in which the chance of the particular writer’s voice is absorbed by the structure and mobility of the work and consequently disappears. Mallarmé describes this aspiration in his important critical essay ‘Crise de vers’:

 

The pure work implies the disappearance of the poet’s delivery, which concedes the initiative to the words, by the collision of their mobilised inequality; they are lit up by reciprocal reflections as a virtual trail of fire on gems, replacing the perceptible breathing in the ancient lyrical breath or the enthusiastic personal direction of the phrase.[73]

 

 

Scherer articulates this aspiration in his study of Mallarmé’s Livre:

Ordinary books are personal: Le Livre will be objective. Ordinary books are circumstantial: Le Livre will not attach itself to any particular object and will treat the totality of existing things. Ordinary books are only albums: Le Livre will be ordered according to a structure.[74]

 

 

Several references to Mallarmé’s Livre appear in Boulez’s writings dating from around the early 1960s. One of the first references is a mention of Mallarmé’s idea of ‘l’opérateur’ that Scherer highlights in his essay on Le Livre.[75] Boulez uses this term to refer to the ‘network of proposed possibilities’ which are the ‘material for l’opérateur’.[76] Mallarmé envisaged public recitals of parts of Le Livre which would be read by the ‘opérateur’, after which discussions could be held. Regarded in this light, the role of the ‘opérateur’ would be similar to that of the priest, as he would select passages to be read and contemplated. Boulez clearly understands this process of selection as comparable to the composer’s selection from the multiple possibilities generated by automatism at the outset of composition. The idea of the opérateur is particularly interesting as in Bonniot’s preface to Igitur (1869),[77] Bonniot helps to clarify this term. Whilst writing on Mallarmé’s projections for Le Livre, Bonniot claims that at the end of this process:

 

[Mallarmé] becomes surgeon and removes himself completely from existence by that which he calls “the operation” – a book full of probable treats and that would absolutely not be lacking in signification for everyone.[78]

 

Mallarmé’s idea of the ‘opérateur’ is connected with the notion of performing an operation that removes oneself from existence – i.e. from the contingency of existence. For Boulez, the performer would, more or less, adopt the role of l’opérateur with regard to the Third Piano Sonata.

 

 

 

The Labyrinth

 

Boulez frequently employs the image of the ‘labyrinth’, sometimes described as the ‘maze’ or ‘town map’,[79] to depict the mobile form of his Third Piano Sonata. These images articulate his new conception of musical form as consisting of particular landmarks to be visited via several pathways. Whereas in ‘Aléa’ (1957) he uses the term ‘constellation’,[80] by the time of ‘Sonate, que me veux-tu?’ in 1960 he appears to favor the image of the labyrinth. I would propose that this is due to two reasons.

 

First, Boulez’s switch might be due to the connotations of the term ‘labyrinth’, which suggests movement in time and the choice of pathways, which is closer to the experience of musical mobile form than the more static image of the ‘constellation’. This is suggested by Boulez’s first discussion of the idea of the ‘labyrinth’ that appears in ‘Sonate, que me veux-tu?’ (1960):

 

the work must keep a certain number of pathways open by means of precise dispositions in which chance represents the ‘points’, which can be switched at the last moment.[81]

 

Second, the metaphor of the ‘labyrinth’ was prevalent in French literature at the end of the 1950s and early 1960s, particularly in the authors of the nouveau roman. One such writer, Michel Butor, was a friend of Boulez at that time and whose novel L’Emploi du temps’ (1956) is cited by Boulez as an example of a labyrinth structure. Moreover, a novel by Alain Robbe-Grillet (1922-), arguably the leading figure of the nouveau roman, entitled Dans le labyrinthe (1959),[82] was published at around the time of Boulez’s switch from the idea of the ‘constellation’ to that of the ‘labyrinth’.

 

There are clear parallels between the constant re-evaluation of events in Butor’s ‘textual labyrinth’ and Boulez’s approach in his Third Piano Sonata. Both provide, through labyrinth structures, a means of replacing the fixed point of view of the author with a relative and multi-layered artwork which, as Boulez writes, allows ‘different levels of reading’.[83] This was a key aspiration of the nouveau roman writers in general, whose impersonal description of objects and events and rejection of the narrative speaker shares a marked similarity to Boulez’s approach at this time. Most importantly for Boulez, the introduction of pathways into the musical work enables the chance of the composer’s voice to become ‘absorbed’ into the form. Boulez refers to this absorption of the author’s voice when he claims that ‘the work must be like a labyrinth, one must be able to lose oneself in it.’[84]

 

 

                        The notion of being ‘able to lose oneself’ in the work is typically described by Boulez as the search for ‘anonymity’. Writing in 1960 he reveals that ‘[i]f I had to find a profound mobility [for the Third Piano Sonata], it would be the research of such ‘anonymity’.[85] This term, I would argue, has contributed enormously to the misconception that Boulez rejects any form of musical expression. It refers to the desire to concentrate upon the demands of the work-in-hand in order to arrive at the ideal of the ‘pure work’. Through ‘annihilating’ the contingency of the existing material in every aspect the work becomes necessary.[86] Nevertheless, this anonymity does not mean that the resulting work is not ‘expressive’ in some way - it merely describes the rejection of all inherited forms of expression. Similarly, this anonymity does not imply that the composer expresses an objective (i.e. anonymous) account of history. Anonymity enables the possibility of a form of expression in which every aspect becomes a necessary and expressive part of the resulting work: the musical means and the composer’s thought become identical.[87] Indeed, Boulez regularly celebrates the uniqueness of the resulting work, claiming that ‘composition is such an individualistic act!’[88]

 

Returning once more to ‘Aléa’, the latter half of this article considers the practical problems of integrating chance into the musical composition. Although it is perhaps not clear, he divides this discussion into the introduction of chance on the local level of composition, i.e. from moment to moment, and the introduction of chance on the global level, i.e. form. I would briefly like to consider some of the examples and issues discussed: first, on a local level.

 

 

 

The Introduction of Chance on a Local Level: Improvisation

 

As an example of the introduction of chance into the most ‘elementary level’,[89] i.e. on a local level,[90] Boulez cites the introduction of ‘rubato’ by the performer into the work. By the term rubato he refers not merely to small deviations in tempo but to a more general principle of ‘mobility’ in other sound components such as dynamics and register which he calls ‘articulative suppleness’.[91] He insists, however, that this introduction of chance should be written into the score and not left to the performer’s taste. He writes:

 

 

If the player can modify the text at will, such modification must be implied by the text, and not merely supplementary to it. The score must contain this interpretative ‘chance’ like a watermark. [¼] In this way I introduce via the score the necessity for chance in the performance: a directed chance.[92]

 

His avoidance of leaving these elements of choice to the performer is due to his distrust of merely reproducing inherited musical ideas unconsciously. This distrust of everyday spontaneity is a particular feature of Boulez’s symbolist influences and was reinforced by the failure of the surrealist experiments in ‘automatism’ that I considered earlier.[93] With specific reference to this aspect of performer choice or spontaneity he writes that this freedom needs to be guided and projected, as ‘instant’ imagination is more susceptible to weaknesses than illuminations’.[94] He repeats this point in 1968 when he writes that performers usually respond to vague notations with ‘contemporary clichés’.[95]

 

 

It is important to mention Boulez’s concept of ‘improvisation’ during this discussion of chance on a local level. Whilst his attitude to ‘improvisation’ understood in its usual sense (i.e. performer ‘spontaneously’ playing without a score) is typically hostile,[96] the particular usage here refers to a specific aesthetic idea. It makes its first appearance in Boulez’s writings in ‘Aléa’[97] and should be understood, therefore, as deriving from his consideration of the integration of chance within the musical work. He expands upon this idea in the article ‘Construire une improvisation’ (1961) in which he defines improvisation as the ‘forcible insertion (Einbruch) into the music of a free dimension.’[98] One can see that his definition of the term is used in a much more narrow sense than its common usages elsewhere e.g. cadenzas, jazz improvisation etc. However, it is very similar to the definition provided by Stockhausen in a letter to Boulez at the end of 1953.[99] Judging from his response, Boulez was unfamiliar with the term used in this narrow sense, as he queries its meaning.[100] Stockhausen replies that it refers to the selection of a particular duration, frequency or intensity within a defined ‘space’.[101] This is, in essence, the way in which Boulez conceives the concept of improvisation. It not only refers to the performer’s moment by moment selection of musical components within a defined ‘space’, but also that of the composer during composition. It is important to appreciate this usage of the term ‘improvisation’, as by 1993, he argues that ‘improvisation is a kind of writing, even though immaterial’.[102] Elsewhere, he makes the same point that improvisation operates within existing ‘formal frames’ transmitted ‘orally’ which remain unwritten.[103] Therefore, Boulez’s idea of ‘improvisation’ is, quite specifically, the ‘forcible insertion into the music of a free dimension’, whether this is unwritten and ‘orally’ transmitted, as in jazz improvisation for example, or written, as in the avant-garde explorations in the late 1950s and early 1960s into performer choice.

 

 

The Introduction of Chance on a Global Level: Parentheses

 

 

Up to this point in ‘Aléa’, Boulez has considered the introduction of chance into what he calls the ‘elementary level’, in other words on a local, moment to moment, level. He continues by considering the introduction of chance into the form of the musical work itself. He describes this, rather obscurely, as the integration of chance within an ‘orientated whole’,[104] i.e. within the global musical form. This description seeks to distinguish the introduction of chance into the global musical form from the moment-to-moment ‘non-orientated’ chance at the ‘elementary level’. The following is Boulez’s aesthetic summary of his new conception of musical form which, in effect, is a description of his Third Piano Sonata (1957-):

 

In a form of this kind, therefore, one could imagine junction points, or platforms of bifurcation, mobile elements capable of adapting (with certain modifications which would possibly be written in) to fixed structures which could themselves be selected arbitrarily but with the restriction that, in the ‘course’ of the development, a given event could only happen once.[105]          

 

This describes the various pathways through a musical work available to the performer. By granting the choice of the order of the musical sections (each of which cannot be repeated) within certain limits, one arrives at ‘a new concept of development which is discontinuous in a way that is foreseeable and foreseen.’[106] This description presents an idea that can be traced back to an article published three years earlier in which he employs for the means of explication the notion of ‘parentheses’. The term ‘parentheses’ in his texts has attracted the attention of several commentators. Writing in 1954, Boulez declares:

 

Let us claim for music the right to parentheses and italics¼; a concept of discontinuous time made up of structures which interlock instead of remaining in airtight compartments; and finally a sort of development where the closed circuit is not the only possible solution.[107]

 

 

Deliège suggests a possible link between Boulez’s term ‘parentheses’ and Mallarmé’s device of inserting clauses into the main sentence, which ‘disguise the main clause’.[108] As Scherer observes in his 1947 study of Mallarmé’s writings, Mallarmé frequently uses parentheses, the content of which is typically just as equal in importance as the main clause. Scherer also notes that Mallarmé’s parentheses can introduce a new register of speech, often more subjective, into the text.[109]

 

Boulez, himself, expands upon what he means by the term ‘parentheses’ in an article published in 1958, only one year after ‘Aléa’ (1957). He appears to conceive parentheses in its traditional sense: a clause which comments upon the main clause that may be omitted without destroying the overall form and meaning. Understood in this way, parentheses can be considered as one particular aspect of mobile form. Boulez writes that:

 

This intrusion of ‘chance’ into the form of a work may manifest itself [¼]by means of commented structures – effervescences – from which one can subtract these commentaries without altering their general physiognomy – the necessity of parenthesis.[110]

 

The use of the metaphor of ‘parentheses’ to refer to musical sections that can be reordered or removed encapsulates Boulez’s conception of form and constitutes, therefore, something completely different from the idea of musical quotation which concerns the deliberate reference to past works and an aesthetic ‘rupture’ with the work being composed. Consequently, the apparent contradiction Decroupet notes between, on the one hand, Boulez’s championing of parentheses and, on the other hand, his rejection of quotation is fictitious.[111]

 

 

Although Boulez appears to advocate ‘parentheses’ as the introduction of mobility into musical form, he is wary of the crude compositional method that is content with merely ‘juxtaposing self-contained sections’.[112] This is an issue because the different sections become static blocks of musical material that do not impact on each other. He seems particularly sensitive to this problem, perhaps due to his reservations concerning Messiaen’s (and Stravinsky’s) use of juxtaposition.[113] Boulez first discusses this issue in 1954, in the passage I quoted on the previous page concerning ‘interlocking structures’. In a much later text he presented at the Collège de France in 1989, he rather complicates this issue concerning parentheses. He criticizes the aesthetic approach that places ‘history in parentheses’, particularly postmodernism.[114] This is a rejection of the compartmentalization[115] of the musical material into historical styles that is characteristic of postmodernism and similar to the juxtapositional techniques of Messiaen and Stravinsky.

 

Despite the fact that the idea of ‘parentheses’ is a particularly complicated and not very well articulated term to describe his conception of formal mobility, it should be recognized that it helped to shape his conception of mobile form.[116] Indeed, this idea is a clear indicator of the importance of Mallarmé’s influence on Boulez’s concepts of chance and mobility.

 

 

Conclusion

 

Towards the end of ‘Aléa’ (1957), Boulez quotes from Mallarmé’s Igitur (1869):

 

In short where chance is involved in an action, it is always chance that fulfils its own Idea in affirming or negating itself. In the face of its existence, negation and affirmation both fail. It contains the Absurd – implies it, but in a latent state and preventing it from existence: which permits the Infinite to be.[117]

 

 

The first line in this typically highly dense passage by Mallarmé establishes that chance constitutes something different from one’s own Idea: i.e. it always ‘fulfils its own Idea’ rather than the Idea of the artist. I considered this problem at the beginning of this section in light of Hegel’s definition of the Contingent as ‘something that is not self-possessed and is alien’.[118] The second line points to the impossibility of avoiding chance by embracing it wholeheartedly (as in Cage’s approach) or ignoring it altogether. The final line is the most cryptic and refers to the ‘multiple possibilities’, to borrow Boulez’s terminology, ‘latently’ suggested but only a limited number can be chosen. The sheer vastness of the multiple possibilities is what constitutes the ‘Absurd’.

 

After quoting this passage, Boulez continues by claiming that his solution to the problem of chance, the deliberate introduction of mobility into the musical form, is perhaps the ‘only means of fixing the Infinite?’[119] This is a reference to the same part of Igitur from which the passage above is drawn. Mallarmé writes that a consequence of throwing the dice is that ‘the Infinite is finally fixed.’[120] This means that one of the multiple possibilities has been realized and ‘fixed’, an idea that foreshadows much of Existential thought. The usage of the term ‘fixed’ in this passage is particularly interesting, as it recalls Boulez’s distinction of ‘mobility’ and ‘fixity’ that appears in 1948. Although there is no reason to question his claim that he first encountered Mallarmé’s writing a little later than this (around 1950), perhaps Mallarmé’s terminology of ‘fixity’ confirmed and helped Boulez to formulate this idea further.

 

Boulez’s approach towards the introduction of chance into the musical work, particularly with respect to his use of images such as the Constellation and the labyrinth, points to something more than an experiment in compositional technique. Like many of his ideas concerning musical technique, it reflects a fundamental shift towards a new conception of musical practice on a wide-reaching theoretical level. The deliberate introduction of relativism into the musical form and the conscious attempt to integrate mobility in music are mirrored in his theoretical approach. This new conception of his musical practice led Boulez towards what would become his mature aesthetic approach: a consciously dialectical approach.

 

 

 



[1] [‘l’absurdité totale’] Boulez, P. Penser la musique aujourd’hui (Paris: Éditions Gonthier, 1963) p. 22 (in French) and published as Boulez on Music Today translated by Susan Bradshaw and Richard Rodney Bennett (London: Faber & Faber, 1971) p. 25 (in English).

    2 I refer to Mallarmé’s notion of ‘hasard absorbé’. See p. 16.

[3] Musical automatism refers to the manipulation of sound components through the use of serial grids and numbers in total serialism. See p.5.

[4] See: Breton, Andre Nadja (Paris: Gallimard, 1949). I consider this Surrealist factor later. See p. 7.

[5] See: Jameux, D. Pierre Boulez translated by Susan Bradshaw (London: Faber and Faber Ltd., 1991) pp. 89-90 (in English).

[6] I would disagree, therefore, with the claim that Boulez’s exploration of chance drew heavily from Cage but was disguised under the name of Mallarmé. This suggestion is implied by Cage himself, who is quoted by Peyser as saying: ‘With me the principle [of chance] had to be rejected outright; with Mallarmé it suddenly became acceptible to him. Now Boulez was promoting chance, only it had to be his kind of chance.’ Cage quoted in Peyser, J. Boulez: composer, conductor, enigma (London: Schirmer, 1976) p. 129 (in English).

[7] Boulez refers to ‘chance which does not ‘compose’’. [‘ce hasard qui ne “compose” pas’.] (My translation.) Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 419 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 37 (in English).

[8] [‘das Zufällige ist das Unbesonnene und Fremde’.] Hegel Phänomenologie des Geistes introduced by Johannes Hoffmeiste (Berlin: Fritzsche & Ludwig KG) p. 498 (in German) and Phenomenology of Spirit translated by A. V. Miller (Oxford: Clarendon Press, 1977) p. 431 (in English). In the remaining part of this sentence that includes this definition, Hegel provides an example of the contingent: ‘a throw of the dice’ [‘wie durch ein Würfeln’]. This is particularly interestesting in consideration of Mallarmé’s famous poem ‘Un Coup de dés’ (1897).

[9] See p. 16

[10] [‘la chronologie de vos rencontres, et la chronologie même de votre chronologie.’] Boulez, P. ‘Nécessité d’une orientation esthétique’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 536 (in French) and Orientations (London: Faber and Faber, 1986) p. 69 (in English).

[11] McCalla, J. Between Its Human Accessories: The Art of Stéphane Mallarmé and Pierre Boulez (Ph.D. University of California, Berkeley, 1976)  p. 57.

[12] Note that Boulez uses the term ‘aleatory’ not Cage’s concept of ‘indeterminacy’.

[13] [‘le hasard par inadvertance’, ‘un hasard par automatisme’.] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 410 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 29 (in English).

[14] One could argue that ‘automatism’ more readily fits the description of ‘accidental chance’ as this chance is accidentally created.

[15] [‘paradis artificiel [¼]: ce genre de narcotique protège, en effet, de l’aiguillon que vous inflige toute invention’.] Ibid., p. 408 (in French) and p. 26 (in English).

[16] See: ibid., p. 408 (in French) and p. 27 (in English).

[17] [‘Alors nos préférences vont, sans conteste, à l’inadvertance naturelle qui n’a pas besoin d’instruments pour se manifester.’] (My slight modification.) Ibid., p. 408 (in French) and p. 27 (in English).

[18] See: ibid., p. 409 (in French) and p. 28 (in English).

[19] [‘l’adoption d’une philosophie teintée d’orientalisme qui masquerait une faiblesse fondamentale dans la technique de la composition’.] Ibid., p. 407 (in French) and p. 26 (in English). Also in: Boulez and Cage (1993) pp. 18-19.

[20] Boulez notes that the American composer is influenced by ‘oriental ideas in the thinking and form of his early works’. Boulez, P. ‘Cage’ article for the Encyclopédie Fasquelle reprinted in Boulez-Cage Correspondence collected, edited, introduced by Jean-Jacques Nattiez,  translated by Robert Samuels (Cambridge: Cambridge University Press, 1993) p. 152 (in English).

[21] Nattiez, J-J, Introduction to Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) pp. 18-19 (in English).

[22] Boulez, P. Letter from Boulez to John Cage 12. 1951 in Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) p. 112 (in English).

[23] Cage mentions Boulez in another text from Cage’s 1958 Darmstadt Summer School course: ‘Who’s interested in Satie nowadays anyway? Not Pierre Boulez: he has the twelve tones, governs La Domaine Musical’. Cage, J. ‘Erik Satie’ in Silence (London: Calder and Boyers, Ltd., 1968) p. 65 (in English). After Boulez’s mention of Cage in ‘Aléa’ in 1957, Boulez very rarely mentions him again in his writings. For example, Boulez only refers once to Cage in Jalons (1989) in order to provide an example of a composer who refused to distinguish between different types of musical material. See: Boulez, P. Jalons (pour une décennie) collected and edited by Jean-Jacques Nattiez, with foreword by Michel Foucault (Paris: Christian Bourgois Éditeur, 1989) p. 408 (in French). An earlier reference to Cage, in 1967, appears to be Boulez’s final word on their disagreement and merely reads: ‘Take John Cage, who is a particularly interesting case. Before he became infatuated with Zen and employed a technique of rhythmic sequences borrowed from the raga, he wrote interesting works.’ Boulez, P. ‘Oriental Music: A Lost Paradise’ in Orientations (London: Faber and Faber, 1986) p. 422 (in English).

[24] [‘mécaniste, automatique, fétichiste’.] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 409 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 28 (in English).

[25] [‘On peut donc concevoir la structure musicale sous un double point de vue: d’un côté les activités de combinaison sérielle, avec engendrement des structures par automatisme des relations numeriques; d’autre part, les combinaisons dirigées et interchangeables, où l’arbitraire joue un rôle beaucoup plus considérable.’] Boulez, p. in ‘Le Système mis à nu’ in Points de repère collected and edited by Jean-Jacques Nattiez (Paris: Éditions du Seuil, 1981) and published in English as Boulez (1986a) p. 139 (in French) and published in English as ‘The System Exposed’ in Orientations (London: Faber and Faber, 1986) p. 141.

[26] See: Boulez, P. ‘Nécessité d’une orientation esthétique II’ in  Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995)  p. 573 (in French).

[27] [‘la “technique” devient paravent, abri souhaité pour se protéger de questions plus délicates à envisager’.] Boulez, P. ‘Recherches maintenant’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995)  Boulez (1995) p. 331 (in French) and published in English as ‘Current Investigations’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 15. The reference to the ‘commentary’ concerns the analyses provided by composers to describe their own works.

[28] [‘La composition veut tendre à la plus parfaite, à la plus lisse, à la plus intouchable objectivité. [¼] La schématisation, simplement, prend la place de l’invention; l’imagination – ancillaire – se borne à donner naissance à un mécanisme complexe qui, lui, se charge d’engendrer les structures microscopiques et macroscopiques jusqu’à ce que l’épuisement des combinaisons possibles ait signalé la fin de l’œuvre.’] (My modified translation.) Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 408 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 27 (in English).

[29] [‘un simple échantillonnage de structures locales’.] Boulez, P. ‘Forme’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 364 (in French) and published in English as ‘Form’ in Orientations (London: Faber and Faber, 1986) p. 95. In Penser la musique aujourd’hui (1963), Boulez refers to this problem as the ‘permutations of samples’. [‘permutations d’échantillons’.] See: Boulez, P. Penser la musique aujourd’hui (Paris: Éditions Gonthier, 1963) p. 43 (in French) and published in English as Boulez on Music Today translated by Susan Bradshaw and Richard Rodney Bennett (London: Faber & Faber, 1971) p. 42. The earliest mention of this idea appears at the end of ‘Auprès et au loin’ (1954). He argues that ‘A work is thus limited to being one fragment of probability among many’. [‘l’œuvre se borne donc à une espèce de lambeau probable parmi tant d’autres lambeaux’.] Boulez, P. ‘¼Auprès et au loin’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 314 (in French) and published in English as ‘¼Near and Far’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 157.

[30] [‘aucune forme n’est justifiée par une simple logique de déroulement’.] Boulez, P. ‘Le goût et la fonction’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 523 (in French) and published in English as ‘Taste: “The Spectacles Worn by Reason”?’ in Orientations (London: Faber and Faber, 1986) p. 58.

[31] Writing in 1989, Boulez describes the problem of automatism in precise terms: ‘what is most striking is the absence of delimitation, I would say the absence of necessity. The most curious result of this schematic intervention is precisely the absence of direction, the absence of intention.’ [‘ce qui frappe le plus, c’est l’absence de délimitation, je dirais même l’absence de nécessité. Le résultat le plus curieux de ce dirigisme schématique est précisément l’absence de direction, l’absence d’intention.’] (My translation.) Boulez, P. Jalons (pour une décennie) (Paris: Christian Bourgois Éditeur, 1989) p. 80.

[32] See: Decroupet, P. Developments et ramifications de la pensée sérialle: Pierre Boulez, Henri Pousseur, Karlheinz Stockhausen 1951-1958 Doctoral thesis: Université de Tours, Paris 1994 p. 155. I draw from Decroupet’s extract of a letter from Boulez to Poussuer written late July 1957, shortly after Boulez’s ‘Aléa’ had been presented (in German) by Heinz-Klaus Metzger at Darmstadt 1957.

[33] [‘SURRÉALISME, n. m. Automatisme psychique pur par lequel on se propose d’exprimer, soit verbalement, soit par écrit, soit de tout autre manière, le fonctionnement réel de la pensée. Dictée de la pensée, en l’absence de tout contrôle exercé par la raison, en dehors de toute préoccupation esthétique ou morale.’] (My translation.) Breton, A. ‘Manifeste du Surréalisme’ in Manifestes du surréalisme (Paris: Jean-Jacques Pauvert, 1972) p. 35 (in French).

[34] Stacey, P. Boulez and the Modern Concept (England: Scolar Press, 1987) p. 22 (in English).

[35] (In English.) Boulez in: Boulez, P. and Szendy, P. ‘Le texte et son pré-texte’ in Genesis 4: Manuscrits. Recherche. Invention. 4/93 Revue internationale de critique génètique, Paris, published by IRCAM, p. 139 (article in French).

[36] [‘elle n’engendre aucune grammaire, et un vocabulaire n’existe pas sans grammaire.’] (My translation.) Ibid., p. 139.

[37] [‘moins on choisit, plus la chance unique dépend du pur hasard de la rencontre des objets; plus on choisit, plus l’événement dépend du coefficient de hasard impliqué par la subjectivité du compositeur.’] (My slight modification.) Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 414 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 33 (in English). Note the similarity between what Boulez calls the ‘coefficient of hasard’ to Sartre’s ‘coefficient of adversity’. An example of this in Sartre’s writings appears in L’Étre et le néant (1943) translated into English as Being and Nothingness translated by Hazel E. Barnes and introduced by Mary Warnock (London: Routledge, 1958) p. 481.

[38] [‘L’inadvertance est drôle, pour commencer, mais on s’en lasse très vite, d’autant plus vite qu’elle est condamnée à ne jamais se renouveler.’] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 408 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 27 (in English).

[39] [‘Dans sa Toute-Objectivité, l’œuvre représente [¼] un fragment de hasard justifiable autant (ou aussi peu) que n’importe quel fragment.’] Ibid., p. 408 (in French) and p. 27 (in English).

[40] [‘Désespérément, on cherche à dominer un matériau par un effort ardu, soutenu, vigilant, et désespérément le hasard subsiste, s’introduit par mille issues impossibles à calfater¼’] (My slight alteration to the translation.) Ibid., p. 411 (in French) and p. 30 (in English).

[41] [‘Après avoir usé toute une vie dans un effort de domination de soi-même de plus en plus complet et ardu, il arrive à cette conclusion, désespérément, que le Hasard subsiste’.] (My translation.) Bonniot, E. Preface to Igitur in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 430.

[42] [‘cette existence du Hasard est tempérée par la création d’une Constellation’.] (My translation) Ibid., p. 430.

[43] This is noted by Breatnach, McCalla and Stacey. See: Breatnach, M. Boulez and Mallarmé (Aldershot, England: Scolar Press, 1996) p. 65; McCalla, J. Between Its Human Accessories: The Art of Stéphane Mallarmé and Pierre Boulez (Ph.D. University of California, Berkeley, 1976) p. 46; Stacey, P. Boulez and the Modern Concept (England: Scolar Press, 1987) p. 81 respectively.

[44] Although this poem is referred to in most literature and throughout this article in its most usual form of ‘Un coup de dés’, strictly speaking its full title is ‘Un coup de dés jamais n’abolira le hasard’.

[45] [‘UN COUP DE DÉS JAMAIS N’ABOLIRA LE HASARD / RIEN N’AURA EU LIEU QUE LE LIEU EXCEPTÉ  PEUT-ÊTRE  UNE CONSTELLATION’.] Mallarmé, S. ‘Un coup de dès’ in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) and Collected Poems translated and with commentary by Henry Weinfield (Berkeley: University of California, 1994) pp. 124-145 (in English).

[46] Paddison, M. Adorno’s Aesthetics of Music (Cambridge: Cambridge University Press, 1993) p. 19 (in English).

[47] I shall examine the concept of ‘mobility’ shortly. See  p. 12.

[48] Rosen, C. ‘The Piano Music’ in Glock, W. (editor) Pierre Boulez: A Symposium (London: Eulenburg Books, 1986) p. 95 (in English).

[49] [‘la forme est conçue circulairement: chaque développement autonome peut servir de commencement ou de fin’.] Boulez, P. ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 439 (in French) and Orientations (London: Faber and Faber, 1986) p. 150 (in English).

[50] See p. 12.

[51] Boulez in: Boulez, P. and Menger, P-M ‘From the Domain Musical to IRCAM: Pierre Boulez in conversation with Pierre-Michel Menger’ Perspectives of New Music, vol. 28 no.1 (Winter 1990) p. 11 (in English). He makes the same point in an article dating from 1960, claiming that the urgent task is to restore ‘the parity between the formal powers of music and its morphology and syntax. Fluidity of form must be integrated with fluidity of vocabulary.’ [‘mettre les pouvoirs formels de la musique en parité avec la morphologie et la syntaxe; la fluidité de la forme doit intégrer la fluidité du vocabulaire.’] Boulez, P. ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 433 and Orientations (London: Faber and Faber, 1986) p. 144 (in English).

[52] [‘chaque fois qu’une note se présentera, ce sera à des registres divers’ [¼] ‘les douze sons auront chacun leur place bien déterminée’.] Boulez, P. ‘Propositions’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) and published in English as ‘Proposals’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 50.

`[53] Nattiez, J-J Introduction to Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) p. 16 (in English).

[54] Cage, J. in Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) p. 98 footnote 1. This quotation originally appeared in Cowell’s account of New York musical life that was published in the Musical Quarterly 38 1 (January 1952) pp. 123-136.

[55] Cage, J. in: Boulez, P.; Cage, J.; Feldman, M.; Wolff, C. ‘4 musicians at work’ Transformations Vol. 1 No. 3 (1952) p. 171 (in English).

[56] [‘le désir de créer une complexité mouvante, renouvelée’.] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 410 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 29 (in English).

[57] [‘dans un univers musical d’où toute notion de symétrie tend à disparaître, où une idée de densité variable prend une place de plus en plus primordiale à tous les échelons de la construction – depuis le matériau jusqu’à la structure -, il est logique de rechercher une forme qui ne se fixe pas, une forme évoluante qui se refusera, rebelle, à sa propre répétition; en bref, une virtualité.’] Ibid., p. 410 (in French) and p. 29 (in English).

[58] The final line which describes ‘a relative formal virtuality’ is a reference to Mallarmé’s concept of ‘virtuality’. The concept of virtuality constitutes Mallarmé’s depiction of the idea of the multiple possibilities that the work opens: in Mallarmé’s case the virtuality of words.

[59] [‘elle est condamnée à ne jamais se renouveler’.] Ibid., p. 408 (in French) and p. 27 (in English). For my earlier citation of this passage see p. 9.

[60] Understood in this sense, Nattiez’s statement that ‘[Boulez’s concept of mobility] has nothing to do with the introduction of chance into the compositional process’ is correct. Nattiez, J-J Introduction to Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) p. 16 (in English).

[61] [‘forme matérielle’.] Boulez, p. ‘Forme’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 365 (in French) and published in English as ‘Form’ in Orientations (London: Faber and Faber, 1986) p. 95.

[62] [‘une partition possible’.] Ibid., p. 365 (in French) and p. 95 (in English).

[63] [‘on tirera une ou des partitions fixes, parmi les multiples qu’elle permet.’] (My slight modification.) Ibid., p. 365 (in French) and pp. 95-96 (in English).

[64] Breatnach correctly notes that before Boulez’s Third Piano Sonata, Stockhausen and Pousseur had already written works focusing on similar experiments in form. See: Breatnach, M. Boulez and Mallarmé (Aldershot, England: Scolar Press, 1996) p. 81 (in English). Jameux also observes that Stockhausen’s Klavierstück XI (1956), which features 19 structures that can be played in any order with any number of structures omitted, was premiered two months before Boulez’s Third Piano Sonata. See: Jameux, D. Pierre Boulez (London: Faber and Faber Ltd., 1991) pp. 87-88 (in English).

[65] In an interview with Deliège, Boulez claims that his first encounter with Mallarmé was around 1948-49. See Boulez in: Boulez, P. and Deliège, C. Par volonté et par hasard: Entretiens avec Célestin Deliège (Paris: Éditions du Seuil, 1975)  pp. 63-64 (in French). In an interview with Szendy, he argues that it was around 1950-51. See Boulez in: Boulez, P. and Szendy, P. ‘Le texte et son pré-texte’ in Genesis 4: Manuscrits. Recherche. Invention. 4/93 Revue internationale de critique génètique, Paris, published by IRCAM, p. 145 (in French).

[66] For an examination of Mallarmé’s Igitur, see Walters, D. ‘The Aesthetics of Pierre Boulez’ Ph.D. dissertation University of Durham 2003 pp. 222-225.

[67] See Boulez in: See Boulez in: Boulez, P. and Szendy, P. ‘Le texte et son pré-texte’ in Genesis 4: Manuscrits. Recherche. Invention. 4/93 Revue internationale de critique génètique, Paris, published by IRCAM, p. 145 (in French).

[68] Boulez, in: Boulez-Cage Correspondence (Cambridge: Cambridge University Press, 1993) p. 62 footnote 1 (in English).

[69] Boulez, P. ‘Moment de Jean-Sébastien Bach’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 79 (in French) and published in English as‘Bach’s Moment’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 14.

[70] In an interview dating from 1993, Boulez recalls that he ‘began [his] Third Sonata inspired by the Coup de dés [sic]’. [‘j’ai commencé ma Troisième Sonate en m’inspirant du Coup de dés’.] (My translation.) Boulez in: Boulez, P. and Szendy, P. ‘Le texte et son pré-texte’ in Genesis 4: Manuscrits. Recherche. Invention. 4/93 Revue internationale de critique génètique, Paris, published by IRCAM, p. 145.

[71] Boulez in: Boulez, P. and Menger, P-M ‘From the Domain Musical to IRCAM: Pierre Boulez in conversation with Pierre-Michel Menger’ Perspectives of New Music, vol. 28 no.1 (Winter 1990) p. 11 (in English).

[72] [‘œuvre pure’.] (My translation.) Mallarmé, S. ‘Crise de vers’ in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 366 (in French).

[73] [‘L’œuvre pure implique la disparition élocutoire de poète, qui cède l’initiative aux mots, par le heurt de leur inégalité mobilisés; ils s’allument de reflets réciproques comme une virtuelle traînée de feux sue des pierreries, remplaçant la respiration perceptible en l’ancien souffle lyrique ou la direction personnelle enthousiaste de la phrase.’] (My translation.) Mallarmé, S. ‘Crise de vers’ in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 366 (in French)..

[74] [‘Les livres ordinaires sont personnels: le Livre sera objectif. Les livres ordinaires sont circonstanciels: le Livre ne s'attachera à aucun objet particulier et traitera de la totalité des choses existantes. Les livres ordinaires ne sont que des albums: le Livre sera ordonné selon une structure.’] (My translation). Scherer, J. Le Livre de Mallarmé (Paris: Librairie Gallimard, 1957) (1957) pp. 21-22 (in French).

[75] See: ibid., pp. 68-74.

[76] [‘des réseaux de possibles proposées’ ‘au travail de “l’opérateur”’.] (My slight alteration of the original.) Boulez, P. ‘Forme’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 359 (in French) and published in English as ‘Form’ in Orientations (London: Faber and Faber, 1986) p. 90 (in English). Boulez also mentions this idea in ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 436 (in French) and published in English with the same title in Orientations (London: Faber and Faber, 1986) p. 148. Immediately before this later reference to Mallarmé’s idea of ‘l’opérateur’, Boulez quotes from Le Livre, without providing a specific page reference: ‘a book neither begins nor ends: at the very most it pretends to do so’. [‘Un livre ne commence ni ne finit: tout au plus fait-il semblant’.] Ibid., p. 436 (in French) and p. 148 (in English). For the original see: Scherer (1957) leaf 181 (in French) (it is the only text on this page). In his essay preceding Le Livre, Scherer draws attention to this phrase by quoting it at the end of his first chapter. See: Scherer, J. Le Livre de Mallarmé (Paris: Librairie Gallimard, 1957) p. 24 (in French).

[77] I have already established that Boulez has probably read this preface. See p. 9.

[78] [‘devient chirurgien et lui supprime tout à coup l’existence par ce qu’il appelle “l’opération” - livre plein de régals probables et qu’il voudrait non dénué absolument du signification pour tout le monde.’] (My translation.) Bonniot, E. Preface to Igitur in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 427.

[79] See: Boulez, P. ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 441 (in French) and published in English in Orientations (London: Faber and Faber, 1986) p. 151. In a 1984 discussion with Jameux, Boulez acknowledges that ‘the image of the town has always seduced me’ and admits that it aided his conception of Répons (1981-): ‘The town is [¼] the more or less conscious model of the geography of Répons.’ [‘[L’image d’une ville m’a toujours séduit’ [¼] ‘La ville est [¼] le modèle plus ou moins conscient de la géographie de Répons.’] (My translation.) Boulez in: Boulez, P. and Jameux, D. ‘Repons de Pierre Boulez: genese d’une œuvre’ CNAC magazine, no. 23, (10. 1984) pp. 16-17.

[80] Note also that Boulez uses the term ‘Constellation’ as the title of the central movement of the Third Piano Sonata.

[81] [‘l’œuvre doit assurer un certain nombre de parcours possibles, grâce à des dispositifs très précis, le hasard y jouant un rôle d’aiguillage qui se déclenche au dernier moment.’] (My slight modification.) Boulez, P. ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 434 (in French) and published in English in Orientations (London: Faber and Faber, 1986) p. 146.

[82] Dans le labyrinth (1959) is written impersonally except for the first and last word – ‘I’ and ‘me’ respectively. It is the story of a soldier ordered to deliver a package whose contents he does not know in an unfamiliar city which he comes to know gradually. See: Robbe-Grillet, A. In the Labyrinth translated by Richard Howard (New York: Grove Press, Inc., 1960) (in English).

[83] [‘polyvalence des niveaux de lecture’.] (My translation.) Boulez in: Boulez, P. and Deliège, C. Par volonté et par hasard: Entretiens avec Célestin Deliège (Paris: Éditions du Seuil, 1975) p. 28 (in French).

[84] [‘l’œuvre doit être comme un labyrinthe, on doit pouvoir s’y perdre.’] (My translation.) Ibid., p. 27.

[85] [‘S’il fallait trouver un mobile profond à l’œuvre que j’ai tâché de décrire, ce serait la recherche d’un tel “anonymat”.’] (My translation.) Boulez, P. ‘Sonate – “que me veux-tu”’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 443 (in French) and published in English in Orientations (London: Faber and Faber, 1986) p. 154. Boulez continues to use the term of ‘anonymity’ today. Speaking of Structures (1952), he states that ‘the important thing was to achieve anonymity’. Boulez in: Boulez and Walters (2002) p. 409 (in English).

[86] In this respect, one recalls Boulez’s statement that ‘there is only creation in the unforeseeable becoming necessity.’ [‘il n’y a de création que dans l’imprévisible devenant nécessité.’] (My translation.) Boulez, P. ‘Éventuellement’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 288 (in French) and published in English as ‘Possibly¼’ in in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 133.

[87] One recalls Boulez’s claim that the composer arrives at an ‘original instrument’ when the language ‘is totally adapted to [one’s] own thought.’ Boulez in: Boulez and Walters (2002) p. 402 (in English).

[88] [‘la composition est un acte tellement individuel!’] (My translation.) Boulez in: Boulez, P. and Grange, H-L ‘Qui en veut à Pierre Boulez?’ in Diapason Harmonie, 359 (1990) April,  p. 46 (in French).

[89] [‘Niveau le plus élémentaire’.] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 412 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 30 (in English).

[90] Although Boulez uses the term ‘elementary level’ in ‘Aléa’, I use the much more accurate term of ‘local level’ or ‘local form’ which Boulez employs in his later writings dating from the 1960s. Both terms refer to the moment by moment unfolding of music.

[91] [‘la souplesse d’articulation’.] Ibid., p. 412 (in French) and p. 31 (in English).

[92] [‘Si l’interprète peut modifier à sa guise le texte, il faut que cette modification soit impliquée par ce dernier et non qu’elle soit seulement en surcharge. Le texte musical doit porter en filigrane cette “chance” de l’interprète. [¼] J’introduis ainsi par le texte une nécessité de hasard dans l’interprétation: un hasard dirigé’.] (My slight alteration of the translation.) Ibid., p. 412 (in French) and p. 31 (in English).

[93] See p. 7

[94] [‘l’imagination “instantanée” est plus susceptible de défaillances que d’illuminations’.] (My translation.) Ibid., p. 413 (in French) and p. 32 (in English).

[95] [‘clichés’ ‘contemporains’.] Boulez, P. ‘Où est-on?’ in Points de repère (Paris: Éditions du Seuil, 1981) p. 505 (in French) and published in English as as ‘Where Are We Now?’ in Orientations (London: Faber and Faber, 1986) p. 461.

 

 

[96] One is reminded of the statement I cited on the previous page that ‘‘instant’ imagination is more susceptible to weaknesses than illuminations’. For an example in Boulez’s writings concerning ‘improvisation’ specifically, he describes the usual type of ‘improvisation’ as ‘psychodramas [¼] [having] only a primary interest for their authors’. [‘psychodrames’ ‘Ils n’ont prioritairement d’intérêt que pour leurs auteurs’.] (My translation.) Boulez in: Boulez, P. and Billaz, A. ‘Entretien avec Pierre Boulez’ Revue des Sciences Humaines vol. LX No. 189 Jan-Mar 1983 p. 115 (in French).

[97] [‘improvisation’.] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 411 and p. 415 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 30 and p. 33 (in English).

[98] [‘irruption (Einbruch) dans la musique d’une dimension libre.’] Boulez, P. ‘Construire une improvisation’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 445 (in French) and published in English as ‘Constructing and Improvisation’ in Orientations (London: Faber and Faber, 1986) p. 155. Despite this short definition of ‘improvisation’ that appears at the beginning at this essay, the term ‘improvisation’ in the title of this text primarily refers to Boulez’s description of his recent composition Deuxième improvisation sur Mallarmé (1958).

[99] Stockhausen writes ‘I find myself increasingly in statistical composition: serial ‘improvisation’ between limits of serial spaces of time, pitch and intensity.’ [‘Je me trouve il plus en plus dans la composition statistique: “improvisation” sérielle entre limits des espaces serielles du temps, d’hauteur, de l’intensité.’] (My translation.) Stockhausen, K. Letter to Boulez dated in November before 20. 11. 53  (no page numbers). I am grateful to the Paul Sacher Archive in Basel, Switzerland for granting me access to this unpublished correspondence.

[100] Boulez asks ‘What do you mean by ‘improvisation’ between different limits?’. [‘Qu’est-ce que vous entendez [¼] pour “improvisation” entre les différentes limites?’] (My translation.) Boulez, P. Letter to Stockhausen dated in November before 20. 11. 53.

[101] Stockhausen essentially reiterates his first definition of ‘improvisation’ as ‘respecting the limits of durations, frequency bands and superior intensities’. [‘en respectant les limites des durées, bandes des fréquences et intensités supérieurs’.] (My translation.) Stockhausen, K. Letter to Boulez dated 20. 11. 53 (1953b) (no page numbers).

[102] [‘L’improvisation est une écriture, bien qu’immatérielle.’] (My translation.) Boulez in: Boulez, P. and Szendy, P. ‘Le texte et son pré-texte’ in Genesis 4: Manuscrits. Recherche. Invention. 4/93 Revue internationale de critique génètique, Paris, published by IRCAM,) p. 139 (in French).

[103] [‘des cadres formels’ ‘“oralement”’.] (My translation.) Boulez in: Boulez, P. and Billaz, A. ‘Entretien avec Pierre Boulez’ Revue des Sciences Humaines vol. LX No. 189 Jan-Mar 1983 p. 115 (in French).

[104] [‘ensemble orienté’.] (My translation.) Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 414 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 33 (in English).

[105] [‘On concevrait donc, dans une telle forme, des points de jonction, des plates-formes de bifurcation, sortes d’éléments mobiles susceptibles de s’adapter (avec certaines modifications qui y seraient inscrites dans l’éventuel) à des structures fixes éligibles de façon arbitraire, avec cette restriction que, sur le “parcours” du développement, un événement donné ne saurait arriver qu’une seule fois.’] (My slight modification.) Ibid., p. 415 (in French) and pp. 33-34 (in English).

[106] [‘une nouvelle notion du développement qui serait essentiellement discontinu, mais d’une discontinuité prévisible et prévue’.] Ibid., p. 415 (in French) and p. 33 (in English).

[107] [‘Réclamons pour la musique le droit à la parenthèse et à l’italique¼; une notion de temps discontinu grâce à des structures qui s’enchevêtrent au lieu de rester cloisonnées et étanches; enfin une sorte de développement où le circuit fermé ne soit pas la seule solution à envisager.’] (My slight alteration of the English translation.) Boulez, P. ‘Recherches maintenant’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 335 (in French) and published in English as ‘Current Investigations’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 19.

[108] Deliège, C. ‘The Convergence of Two Poetic Systems’ in Glock (editor) Pierre Boulez: A Symposium (London: Eulenburg Books, 1986) (pp. 102-103 (in English).

[109] See: Scherer, J. Expression littéraire dans l’œuvre de Mallarmé (Nizet, 1947) pp. 58-60 (in French).

[110] [‘Cette intrusion du “hasard” dans la forme peut se manifester [¼] soit à l’aide de structures commentées – effervescentes – d’où l’on peut soustraire ces commentaires sans altérer leur physionomie générale – nécessité de parenthèse.’] (My modified translation.) Boulez, P. ‘Son, verbe, synthèse’ in Points de repère (Paris: Éditions du Seuil, 1981) p. 166 (in French) and published in English as ‘Sound, Word, Synthesis’ in Orientations (London: Faber and Faber, 1986) p. 179 (in English).

[111] See: Decroupet, P. Developments et ramifications de la pensée sérialle: Pierre Boulez, Henri Pousseur, Karlheinz Stockhausen 1951-1958 Doctoral thesis: Université de Tours, Paris 1994 pp. 131-132 (in French).

[112] [‘la juxtaposition de “sections” centrées sur elles-mêmes?’] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 415 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 33 (in English).

[113] One is reminded of Boulez’s criticism of Messiaen that he ‘does not compose – he juxtaposes’. [‘il ne compose pas – il juxtapose’.] Boulez, P. ‘Propositions’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 256 (in French) and published in English as ‘Proposals’ in Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 49. I would like to add that this sensitivity to this problem is not unique to Boulez. For example, Adorno makes this criticism of Stravinsky’s Symphony in Three Movements (1945) which uses ‘the static juxtaposition of “blocks”’. Adorno. T. W. The Philosophy of Modern Music translated by Anne G. Mitchell and Wesley V. Blomster (London: Seabury Press, 1973)  (1949) p. 211 (in English)

[114] [‘l’histoire entre parenthèses’.] (My translation) Boulez, P. ‘Mémoire et création I’ 3. 2. 1989 – 3. 3. 1989 (9 lectures) (unpublished) p. 3. I am grateful to the Paul Sacher Archive in Basel, Switzerland for granting me access to this unpublished material.

[115] In a recent interview, Boulez states this avoidance of compartmentalisation clearly: He states that ‘I want to get rid of the idea of compartments in a work’. Boulez in: Boulez, P. and Di Pietro, R. Dialogues with Boulez (Lanham, Maryland: Scarecrow Press, 2001) p. 70 (in English).

[116] It is important to note that the idea of parentheses helped to stimulate Boulez’s musical practice not only on a global level of form but also on a more local level. An example that Boulez himself provides is in his later composition Cummings ist der Dichter (1970) in which he attempted to find an equivalence for the parentheses in the text by assigning a group of specific instruments which disappear in a manner similar to the parentheses. See Boulez in: Boulez, P.; Loselle, A.; Caws, M. A.; Perloff, N. (1992) ‘Poetry and Music: A Roundtable discussion’ Paroles gelées (1993) 9. p. 10 (in English). Deliège, writing on Le marteau sans maître (1955) although his point could be applied generally, claims that the idea of parentheses finds its best reflection in Boulez’s compositional practice. (See: Deliège, C. ‘Pierre Boulez entrevu’ in L’Avant Scene Opera’ Sept./Oct. 1981 no. 36, p. 170 (in French).) I would disagree and suggest that whilst it has helped to stimulate directly Boulez’s music through equivalences its main importance is that it has shaped his conception of mobile form.

[117] [‘Bref dans un acte où le hasard est en jeu, c’est toujours le hasard qui accomplit sa propre Idée en s’affirmant ou se niant. Devant son existence la négation et l’affirmation viennent échouer. Il contient l’Absurde – l’implique, mais à l’état latent et l’empêche d’exister: ce qui permet à l’Infini d’être’.] (My modified translation.) Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 419 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 38 (in English). This is identified by Walsh. For the original quotation from Mallarmé’s Igitur (1869) see: Mallarme, S. ‘Igitur’ in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 441 (in French).

[118] [‘das Zufällige ist das Unbesonnene und Fremde’.] Hegel, G. W. F. Phänomenologie des Geistes introduced by Johannes Hoffmeiste (Berlin: Fritzsche & Ludwig KG) p. 498 (in German) and published in English as Phenomenology of Spirit (Oxford: Clarendon Press, 1977)  p. 431 (in English).

[119] [‘le seul moyen pour essayer de fixer l’Infini?’] Boulez, P. ‘Aléa’ in Points de repère I: imaginer (Paris: Christian Bourgeois Editeur, 1995) p. 419 (in French) and Stocktakings of an Apprenticeship (Oxford: Clarendon Press, 1991) p. 38 (in English).

[120] [‘l’Infini est enfin fixé’.] (My translation (and identification).) Mallarme, S. ‘Igitur’ in Mallarmé Œuvres Complete (Paris: Gallimard, 1945) p. 442 (in French).