Introduction

A brief history

Premiered on 19 October 1997 in Donaueschingen by violinist Hae Sun Kang with electronics produced by Andrew Gerzso at Ircam (where the French premiere was performed two days later), Anthèmes 2, as is often the case with Pierre Boulez, developed out of an earlier work whose ramifications the composer wished to further explore. Anthèmes 1 is a short violin piece first composed in 1991 (then revised in 1992 and 1994) for the ninetieth birthday of Alfred Schlee, longstanding director of Boulez’s music publishing company, Universal Edition, and then revived the following year as a qualifying piece for the Yehudi Menuhin Violin Competition in Paris. The work comprises some nine minutes of music, which Boulez set about expanding into Anthèmes 2, a work expanded not only in terms of duration (it lasts more than twenty minutes) but especially through its new sonic breadth, achieved through technological means. Like Rituel and Mémoriale, Anthèmes 1 and 2 belong to the ...explosante-fixe... family of works, being derived from a seven-note fragment of the violin part of one of the several successive versions of ...explosante-fixe..., originally an open-ended compositional schema composed to mark the death of Igor Stravinsky and included in a tribute dossier published by Tempo magazine (UK) in 1971. In keeping with the requirements of a competition piece, Anthèmes 1 features a panoply of violinistic techniques, from the most classical to so-called extended techniques. Both Anthèmes revolve around the polar note D, a note that can be played in a variety of ways on the violin (as open string, artificial or natural harmonic, in varied voicings, etc.). The number seven plays a decisive role in the structure of Anthèmes (an artefact of the seven-note fragment of …explosante-fixe… from which it proliferated), which is notably reflected in the abundance of groups of seven notes (septuplets) and its form that follows an introduction with six sections. The work also testifies to Boulez’s renewed interest in thematic writing, the presence of recognizable musical figures being already suggested by the title, “anthèmes”, recalling by homophony the expression “en thème”, i.e., “in themes”. As Boulez explained in a public lecture at the French premiere of Anthèmes 2, on 21 October, 1997 at Ircam:

In my youth, I thought that music could be athematic, completely devoid of themes. In the end, however, I am now convinced that music must be based on recognizable musical objects. These are not ‘themes’ in the classical sense, but rather entities which, even though they constantly change their form, have certain characteristics which are so identifiable that they cannot be confused with any other entity. [Boulez in Goldman, 2001, p. 117]

The title word is also a neologism derived from the English “anthem”, thereby evoking the character of a hymn, that solemn idiom with a linear form, and indeed the overall character of Anthèmes is one of solemnity, but the peaceful ambiance is interrupted several times by fairly violent and sputtering eruptions.

Thematics and form

As already mentioned, the Anthèmes pieces proliferated from a short fragment of …explosante-fixe…, specifically the violin part of the version of the work from 1973, for solo flute, small ensemble and electronics. The opening of the violin part of the Originel movement of that work (played as the final movement of the work), features seven trilled notes that have the same pitches as the seven trills that begin Section I of Anthèmes 1 (in Anthèmes 2, this passage is extended to more than seven notes, the artefact from …explosante-fixe… is therefore even more obscured there). If one considers that the Introduction of Anthèmes (see form below) was seemingly composed at the end of the compositional process (since it appears at the end of Anthèmes 1’s manuscript [Boulez et al., 2009]), the openings of the two pieces/movements correspond strikingly [Figure 1].

Figure 1. Top: …explosante-fixe… (1973 version), Originel movement, violin part, b.1. Bottom: Anthèmes 1, section I, b.1-4 with 7 common notes circled [Score UE, 1992].

One observes that the D, polar note of Anthèmes, is also the middle note of the seven-note series. This genesis is significant and has consequences for Boulez’s subsequent invention, even if the composer himself considered the starting points of works to be of little importance. Speaking at the French premiere of Anthèmes 2 in 1997, he said :

This piece is, as is often the case with me, a reflection on something I’d already written, which wasn’t finished - which is a tiny nucleus of ...explosante-fixe... You showed it to me earlier, because I didn’t have the example to hand. But it’s exactly seven notes to start with, no more. So, I find that starting points are never very important. What’s important is the whole trajectory. And that trajectory, as you say, is between seven notes that last maybe five seconds, and a piece that lasts twenty minutes, so a lot of invention is still required. [Boulez in Goldman, 2001, p. 117-118]

The themes alluded to in the title refer to musical figures that undergo constant variation while nevertheless retaining their identifying characteristics (phrasing, tempo, rhythmic character, expression, playing technique, intensity, etc.), rendering them easily recognizable at each return. Each theme is imbued with its own straightforward performance instruction (for example, “calme, retenu” marked above a lazy and oft-repeated arpeggiated pizzicato chord, "brusque" above an impertinent rapid flourish, and “calme, régulier” inscribed over a languorous glissando that slides down the string). Each of its six relatively autonomous sections is separated by a characteristic figure: one or more long notes in harmonics, sometimes ending in a glissando that rises to indeterminate heights, constituting an aural signature which can be mistaken for no other sound in the rest of the piece; they are classic examples of what Boulez calls “signals”. Boulez associated these signals with the Hebrew letters that divided the Latin text of the Book of Lamentations, traditionally ascribed to Jeremiah, which he had recited in church during the Holy Week ceremonies of his childhood in the small town of Montbrison in France’s Loire Valley. Because of this reference to the Hebrew letters in the printed text of the Book of Lamentations, these signals are sometimes referred to as ‘letters’ in what follows (see §3.2). The six sections (or verses) of Anthèmes 2 are assigned roman numerals (I to VI), and the letters are indicated by the letter H (standing for harmonics) and their placement between verses indicated with roman numerals (H I, H I/II etc.). The long final sixth section is further divided into three subsections: the first one (VI.1) is thematically continuous with the rest of the piece; the middle section (VI.2) is autonomous, involving a play of recognition and surprise between four recognizable ‘characters’, and the third part (VI.3) is a conclusive coda in which the central note D is affirmed throughout. The chart in Figure 2 outlines the basic form of the different sections, including the bar numbers and the types of processing featured.

Figure 2. Sections of Anthèmes 1.

Though it might seem straightforwardly linear, the form of Anthèmes 2 is actually strikingly original: after its short introduction, five short sections are followed by a final one longer in duration than all that preceded it. While Boulez would sometimes write works with long final sections (for example, in Rituel), Anthèmes remains an extreme example of an end-loaded form. An analogous form is used in Gustav Mahler’s Das Lied von der Erde, Mahler’s lyric symphony having five movements followed by a sixth whose duration is as long as the first five put together. Mahler’s Song of the Earth was published, in 1912, by Universal Edition, who would become Boulez’s own publisher, and Anthèmes 1 was dedicated “en souvenir amical” to Alfred Schlee (1901-1999), the venerable director of Universal, on the occasion of his 90^th birthday. In this way, the form of Anthèmes might be considered a secret tribute to another illustrious Universal composer. This claim, while unverified, becomes less farfetched when one considers that Mahler’s Song of the Earth was, along with the Fourth Symphony, one of the two works by Mahler that Boulez had heard in concert in his youth [Boulez, 1995].

Compared to the earlier solo violin piece, Anthèmes 2 is much more ample, but Anthèmes 2 largely respects the proportions of the sections of its predecessor, each section being ‘stretched’ a comparable amount [Figure 3].

Figure 3. Comparison of relative durations of sections in Anthèmes 1 and 2 expressed as a proportion of the total duration (section durations include the durations of the ‘letters’ that follow them). Recordings used: Anthèmes 1 by Julie-Anne Derome [AR CD Atma, 1996] and Anthèmes  2 by Hae-Sun Kang [AR CD Deutsche Grammophon, 2000].

Technological setup

Score following

Around the time that Anthèmes 2 was being developed, researchers at IRCAM was trying to develop an audio-based technology for score following, that would trigger computer commands for audio processing (or patches) after comparing the sounds actually played by the violin against the score. However, the result was not dependable enough to be usable in performance when Anthèmes 2 was premiered and even in subsequent performances in the years that followed. Instead, audio commands were triggered manually in performance by the audio engineer who carefully followed along with the score in performance. Only in recent years has a new score-following computer application been used in performances of Anthèmes 2. Nevertheless, the fact remains that, like all of Boulez’s works produced at Ircam, Anthèmes 2 was conceived not only as a work of art, but also as the opportunity for the institute’s team to develop new technologies in the field of person-machine interface.

Spatialization

Anthèmes 2 can be performed in two configurations: in a “normal” concert hall with frontal stage or by placing the violin in the center of the performance space with the public surrounding the performer [Figure 4]. Boulez preferred the second configuration both for theatrical reasons but also because the work was frequently performed with Répons where the chamber orchestra was placed on a central stage in the performance space.

Figure 4. The two stage configurations for the performance of Anthèmes 2 [© Score UE, 1997b].

Pierre Boulez always used spatialization as a means to clarify the musical text. This is a specific example of a more general principle present in Boulez’s approach to composition in the latter part of his career where one type of musical writing is used to describe, accentuate or highlight the structure of another musical type of musical writing. Anthèmes 2 was the last work Boulez composed for electronics and as such it inherits many ideas related to spatialization already present in Répons, Dialogue de l’Ombre Double and …explosante-fixe…, and even harks back to Boulez’s early effort to combine orchestral and electronic sound, in Poésie pour pouvoir from 1958. Spatialization was also a major compositional parameter in many of Boulez’s works that do not use electronics, such as Figures, doubles, prismes (1963) and Domaines (1970). There is one important difference, however, between the approach to spatialization in Anthèmes 2 and the other works. In the works preceding Anthèmes 2, there was a direct relation between the physical position of a speaker and the perceived direction of the sound source. Anthèmes 2 was the first work to take advantage of the Spat software, a spatialization technology developed at Ircam in the 1990s which opened the way to virtual room acoustics and virtual sound sources [Jot and Warusfel, 1995; Carpentier et al., 2015]. Thus, the direct relationship between speaker position and the perception of a sound source was broken. As a result, the spatialization directives in Anthèmes 2 describe the desired perceptual position of sound sources, independently of the number of speakers (four, six or eight) used during a performance.

Spatialization in Anthèmes 2 gives rise to a novel notational system. A few examples of these spatialization instructions found in the score of Anthèmes 2 are provided in Figure 5. They instruct the programmer to, variously, “choose a path at random going up the left side or the right side of the hall”, “starting at the back-left position sweep through the front position to the back-right position then back to the starting point in 16 secs”, “make a clockwise rotation in 18 secs”, “starting at the front of the hall make a clockwise rotation in 18 secs”, and “choose at random a rotation in either a clockwise or anti-clockwise direction that takes 500 msec”.

Figure 5. Various spatialization instructions found in score of Anthèmes 2 [© Score UE, 1997a].

And yet, spatialization in Anthèmes 2 is always used in the service of the dramaturgy of the work rather than as some abstract compositional excursion into the “spatial parameter”. The violinist on stage is the focal point of all the spatial operations in the work: because of this physical presence, the electronic sounds are perceived as being either with the violinist or in opposition to her, either in a fixed position relative to the violin or moving around it, etc. This spatial game of hide-and-seek is more fundamental to the work than ensuring that any exact spatial placement within Cartesian space is observed.

Role of electronics

The electronic processing, developed at Ircam, performs real-time electronic transformations of the sound of the violin captured using a microphone, and sends this processed sound through a system of loudspeakers arranged around the room. A consequence of real-time electronics is that specific gestures and playing style of the violinist during a particular performance have a direct impact on the sound of the electronics. Boulez consciously chooses to restrict the role of electronics in this work to that of augmenting the sound of the violin, turning it into what he called a “hyper-instrument”. If the voice of the violin in this hymn is likened to that of an officiant, the multiple voices of the electronic score of Anthèmes 2 could be likened to that of a choir. In fact, in only one brief section (VI.1), does Boulez exploit the interplay between violin and electronics in a kind of call-and-response between the violin and the electronics. For the most part, Boulez uses electronics to create a homophonic texture within which the violin’s voice emerges.

Anthèmes 2 uses two very common types of audio processing to thicken the violin’s main line: frequency shifting and harmonizer. To a note played by an instrument, a harmonizer adds a number of other notes located at a fixed interval from it. In this way, a monody becomes a sequence of chords in parallel motion. After prolonged listening to a sound processed with a harmonizer, a phenomenon of fusion tends to occur, whereby we hear a single homogeneous sound imbued with a new timbre rather than a sequence of chords. In contrast to the harmonizer, frequency shifter adds one or more other sounds to the note played, separated from it by a fixed frequency (i.e., distinct by a certain number of hertz, not by a well-tempered interval). The resulting thickening of the line is less uniform than in the case of the harmonizer, since the logarithmic relationship between frequency and the notes of the scale means that the lower the note, the greater the gap between it and the sound emitted by the frequency translation. The opening of section I illustrates the difference, the first gesture (the grace-noted legato phrase) is augmented by four added notes via the harmonizer, while the ricochet-bowed septuplet is processed through frequence shifter whose output is sent around the hall [Figure 6].

Figure 6. Anthèmes 2, section I, b.1 [© Score UE, 1997a].

This figure also reveals how the score of Anthèmes 2 treats each of the electronic parts as individual “instruments” given its own stave in the score. This apparently trivial observation reveals a deeper truth about Boulez’s approach to electronics: the primacy of notated musical inscription, and, consequently, the pride of place this approach gives to processing that can be described in words or graphic symbols and thus which submit to a certain discursive logic. The notated electronics can also be seen as an attempt to transcend the ephemeral nature of computer equipment by describing processes through verbal formulas that could, in theory, suffice to convey his vision to musicians of the future. Clearly, this focus on notation precludes many electronic manipulations (ones less amenable to verbal or graphic representation), but what he loses on the one hand, he gains in transmission capacity. Moreover, Boulez’s approach to notating electronics (he adopts the same approach in other works with electronics, such as Répons and …explosante-fixe…) allows the person controlling the electronic part of the piece to interpret the music in the same way that an instrumentalist interprets a score. As Augustin Muller, who frequently performs the electronic part of Anthèmes 2, has observed, even though the electronic part is fully notated, he feels freer when performing the work than he does when performing other electronic works, the vast majority of which do not used a notated score, because he is at liberty to choose the precise sounds, colors, balance and spatial qualities of the sounds described in the notated score, much like a musician playing in a chamber ensemble.

Furthermore, through the use of delays, the electronics provide rhythmic extensions to the musical text. The use of “infinite” reverberation offers the possibility of extending the violin sound indefinitely. The generation of virtuoso computer “virtual” scores using violin sound samples opens the way for musical writing that transgresses the normal capacities of the violin – extending its ambitus and allowing for leaps, combinations of notes and speeds not attainable on an unprocessed violin. More specifically, the electronics are used for the creation of vertical structures of varying size constructed around single notes played by the violin. Sound spatialization is used—as in the other works of Boulez involving electronics – for describing and articulating the musical text.

Boulez’s approach to live electronics recalls the pedagogical sketches of Bauhaus artist Paul Klee, a parallel often made by the composer himself [Boulez, 1989; 2008]. Like Klee in many of his exercises, Boulez seeks to find ways to amplify a figure through thickening, extending, or otherwise altering its energy or flow [Figure 7].

Figure 7. Excerpt from Paul Klee, Pedagogical Sketches [Klee, 1953, p. 18-19].

Analysis

Introduction

This section “Libre” serves as kind of introduction to the work and contains several ideas found elsewhere in the composition. It affirms the importance of the number 7 and the polar note D, which appears in the form of a long trill – a favorite figure in Boulez (whose locus classicus is in Répons). The central D₄ plays a predominant role: it is the main note of the trill towards which the initial phrase converges; the note from which the dyads are built downwards; the initial note of all the short sequences; the reference note for the downward frequency shifting; the note which remains at the end of the infinite reverberation layers. A brief gesture of the col legno battuto played on the D natural at the end of bar 3 marks the end of the Introduction by suddenly cutting off the lingering reverberation. This same gesture will appear again at the end of the piece, thus indicating that the piece starts and ends with this central D₄. This initial gesture also metaphorically evokes the different stages of a sound’s evolution from an acoustic point of view, that is, attack–resonance–decay (the appoggiatura being the attack phase, the trill the resonance, and the short double stops with D being the decay). [Figure 8]

Figure 8. Anthèmes 2, section “Libre”, b.1-3 [© Score UE, 1997a].

Media 1a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 1b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

Certain general characteristics of the electronics can already be ascertained through this example. First of all, infinite reverberation serves to progressively create a static layer of sound. This works on two levels: 1) by taking the live sound of the violin during the first two bars of the introduction, followed by a slow fadeout starting at bar three; 2) by injecting a rapid sequence of violin samples (that are not heard directly) whose pitches are those found in the first bar. Thus, two layers of infinite reverb are created. Secondly, short sequences of violin samples intervene when the violin reaches the trill in bar one and also at each of the dyads in bar 2. In bar 3, a frequency shifter is used in order to transpose downwards the sound of the ricochet in order to enlarge the register of the instrument.

Letter sections

As has already been explained, these letters function as signposts that mark the transition between sections (HI, HI/II, HII/III, etc.), like the Hebrew letters that separate out the verses of the Book of Lamentations. Speaking about his concept of signals, Boulez explained that “signals are used to mark the points of articulation of a development, of a form. A signal can be considered above all as a mnemonic tool” [Boulez, 2019, p. 253]. If Anthèmes 2 can be viewed as alternating dynamic and static types of musical writing, the letters represent the static side of the pendulum. Several ideas are at work in all the “letter” sections [Figure 9].

Figure 9. Anthèmes 2, first “letter” H/I [© Score UE, 1997a].

Media 2a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 2b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

As one would expect, the sound of both the acoustic violin and the electronic transformations are placed in spatial positions that remain completely stationary, as befits these static events that mark a pause between the dynamic verses. Two harmonizers are used to transpose the sound of the violin respectively 11 and 23 semitones lower in order to expand the overall register downwards. The sound of the violin is further transformed via the use of two ring modulators that inject a complex spectrum into a comb filter tuned to a low notch frequency thus providing a rich static inharmonic spectrum. Lastly, infinite reverberation is used to sustain the harmonics played by the violin. Again, concerning spatialization, the acoustic violin, ring modulators plus comb filter and infinite reverberation are placed in the front of the performance space while the harmonizers are placed along the sides. Each letter section comprises a number of these bell-like sounds. Figure 10 lists the pitches of these notes that begin and end on the central D of the work.

Figure 10. Pitches of harmonic note “letters” in Anthèmes 2.

Section I

Overall, the writing for the violin in this section is characterized by a single expressive monodic line, adhering to the familiar Boulezian pattern of appogiatura (in this case, a seven-note run), followed by a sustained trill and ending with a number of short notes accented with grace notes. The electronics in this section serves to expand and articulate the violin part [Figure 11]. First, during all the expressive phrases, harmonizers are used to build chords downwards from the notes of the violin thus ‘thickening’ the instrumental melodic line in the sense of Klee’s pedagogical sketches. Then, dyads made from pizzicato violin samples are triggered each time the violin plays a trill. Thirdly, during each seven-note run, the effect is highlighted through the use of spatialization that projects the sound of the violin from the back of the hall to the front. Lastly, at the end of each run when the violin begins again its expressive melody, the first note of the line is “frozen” via the use of infinite reverberation thus heightening its impact and at the same time signaling the beginning of a new expressive phrase.

Figure 11. Anthèmes 2, section I, b.1-5 [© Score UE, 1997a].

Media 3a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 3b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

Section II

This section was inspired by the sculpture Compression “Ricard” (1962), a provocative work housed at the Centre Pompidou by the French artist known by his first name, César (1921-1998) [Figure 12].

Figure 12. César, Compression “Ricard” (1962) [© Centre Pompidou].

In it, César inserted various automobile parts of different colors into a hydraulic crushing machine, creating a tautly compressed block of multicolored metal. And indeed, section II is characterized by the musical equivalent of compression—in this case the absorption of multiple strands of a rhythmic canon into the single line of the violin. It has a ternary form (in Anthèmes 2 : A=II.1–61, B=II.62–72 A’=II.73–118). The three sections of this form are thrown into relief through the use of electronics, the outer sections employing a frequency shifter patch, the central passage using the harmonizer. The double starting points for this canon are a sequence of sixteen pitches and one of as many durations [Figure 13].

Figure 13. Pitch and duration sequences in rhythmic canon of section II of Anthèmes 2.

This sequence of pitches is performed in an unvarying loop, while the durations are twice transformed to form three distinct durational series. Each of the three distinct values of the durational series (I, II or III) is mapped onto another value to generate a new rhythmic series (for the first transformation, 3s are mapped onto 2s – i.e. a dotted eighth note becomes an eighth – 1s into 4s, 2s into 3s; in the second, 2s become 4s, 4 is mapped onto 3, and 3 onto 5) [Figure 14].

Figure 14. Transformations of durations (measured in sixteenth notes) of three-voiced rhythmic canon in second section of Anthèmes 2.

Each value of the three rhythmic sequences are then assigned the pitches of the unvarying note sequence in order, which is then compressed, César-style, into a single line (redrafted, for the sake of clarity in Figure 15). In the fourth, resultant, line, only the attacks of the short pizzicato sounds are taken into account, and the fifth line indicates the adjustments made in the score.

Figure 15. Beginning of the three-voiced canon in second section of Anthèmes 2 (pitches and rhythms only); divergences circled.

This resultant line need only be compared with the second measure of section II onwards to see how the rhythmic canon, a favorite technique of Boulez’s – as it was also of his one-time professor, Olivier Messiaen – is given concrete expression [Figure 16], even if it deviates from the plan on a few occasions (for example, to avoid having the violinist play awkward double-stopped perfect fifths).

Figure 16. Anthèmes 2, section II, b.1-6 [© Score UE, 1997a].

Media 4a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 4b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

The electronic part of this section offers a spatial counterpart to the canonical writing of the instrumental score: as the theme of the rhythmic canon is sent at variable speeds to the surrounding speakers, the sound alternates between a linear and a circular path. Boulez likened the spatial conception of this section to a ‘counterpoint in space’ that contrasts or complements the counterpoint in time of the violin’s line, creating a sonic texture that differs depending on the listener’s position in the concert hall. Moreover, the sound of the violin is superimposed with altered versions of itself, sent through frequency shifters (in order to enlarge the lower register). Delay is used to create patterns based on the rhythmic values of the original series of notes [Figure 17].

Figure 17. A page from Andrew Gerzso’s sketches for the delay patterns used in the processing of section 2 of Anthèmes 2.

In Figure 17, the attacks of the original rhythmic theme are translated into milliseconds, and the first delay sequence assigns the values of the first six attacks of the theme as their delay times. In nineteen successive passages (each of the rows of the figure), these delay values are gradually varied to correspond to other attacks of the theme, giving the impression of temporal expansion or contraction, the diagonal lines in Figure 17 illustrating the unequal total durations of each of the nineteen iterations. These compressed/expanded series of delays are superimposed over the violin part in order to extend the original idea but also to challenge the listener’s capacity to distinguish the violin and electronic parts. A further sonic layer is provided by what Gerzso termed the ‘cantus’ (the rightmost column in the sketch). These refer to three short rhythmic sequences generated from subsets of the violin’s rhythmic pattern that are sounded out by sampled pizzicato notes (the first cantus can be seen in the ‘Sampler’ stave in Figure 16).

Section III

In addition to the use of real-time sound processing, Boulez displayed an abiding interest in the virtuosic potential of the computer to transgress the possibilities of human instrumental performance. Here the idea is pushed farther by deliberately placing the violin and the electronics in confrontation with each other. The character of the musical writing for the violin is jumpy and erratic, a character confirmed by Boulez’s marking at the fourth measure of the section “Nerveux, irrégulier” and instructing the violinist to play very abrupt dynamic levels as well as to lengthen the loud notes and shorten the shorter ones. Indeed, listening to Hae-Sun Kang and Andrew Gerzso’s authoritative 2000 recording of the work [AR CD Deutsche Grammophon, 2000], one is struck by the way Kang manages to imbue each note of this section with a distinctive dynamic level and duration. The electronic part is created through the use of real-time composition algorithms that generate musical material similar in character to that of the violin. These two layers are then superimposed [Figure 18].

Figure 18. Anthèmes 2, section III, b.1-9 [© Score UE, 1997a].

Media 5a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 5b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

Speaking about this section at the French premiere, Boulez emphasized the aleatoric environment that the electronics produced:

You also have a random environment, where the violin plays a certain number of figures that are very directed, and the machine takes the same notes practically but does [something else] as if you were moving something very quickly but in a random order: only the field is fixed, but the order is not. Whereas here, the field is fixed, but the order is also fixed. Here too, we can see an opposition—not coordination this time—between a gesture that is highly voluntary and gestures that are completely involuntary. [...] And there’s always a contrast between very loud sounds and very piano sounds. There’s a contrast in tempo, I wrote ‘extremely irregular’ on purpose: it has to be as if it were ataxic, so that you get the impression [that the violinist] is no longer in control of her movements. It’s a kind of ataxia, but achieved through numerical values. [Boulez, in Goldman, 2001, p. 130]

As a result, listeners are unable to discern if they are hearing the acoustic or the electronic violin, an ambiguous situation of uncertain perception that Boulez was particularly fond of creating. This section further demonstrates how electronics serve the thematic conception of Anthèmes 2 by imbuing each theme with its own sonic signature. This characterizing function of electronics for the thematic identity of figures is also illustrated in Figure 17 by the way the phrase is composed of four separate themes (or cells might be more apposite given their brevity): a tremolo ponticello figure (1) , a 7-note appogiatura (2), a long-held trill (3) and finally a nervous jagged line (4). Each of these figures is rendered more sonically recognizable by being assigned its own distinctive electronic processing: ring modulation for (1), frequency shifter for (2), harmonizer for (3), and spatialized, reverberating samples for (4).

Section IV

The fourth section consists of two outer parts marked “instable” (in Anthèmes 2, b.1-11, and b.25-39; in Anthèmes 1, b.67-71 and b.80-88) consisting of trilled notes, some played as double- and triple-stops, and a central phrase (b.72–79) predominantly written in thirty-second notes. The central section uses only nine distinct pitches at a fixed register. The outer A and A’ sections of this little ternary form have a particularly symmetrical pitch organization (see beginning of A section in Figure 19).

Figure 19. Anthèmes 2, section IV, b.1-4 [© Score UE, 1997a].

In Anthèmes 1, the A section consists of twelve attacks, and A’ has eighteen attacks. Anthèmes 2 doubles the number of attacks. We look first at the pitch structure of the earlier violin solo. In A’, of the twelve trills, four triple-stops are marked ff, four double-stops are marked mf, and four single notes are marked p. The pitch symmetry appears once the top notes are grouped together according to their dynamic level [Figure 20].

Figure 20. Pitch organization of top notes of Anthèmes 2, section IV, grouped by dynamic level.

As Figure 20 shows, the A section of Anthèmes 1 features three four-note series that are all transpositions and/or retrogrades of each other, with a particularly symmetrical intervallic structure of 5–8–5 semitones. Similarly, the A’ section has three six-note series with series that have an equally symmetric intervallic structure 6–5–5–5–6 (in the last series, the last two tones, D and G#, are inverted). In the A of Anthèmes 2, a second sequence of twelve notes follows the first one that is identical to those in Anthèmes 1, but no longer follows the symmetrical plan. Similarly, in the A’ of Anthèmes 2, eighteen trills precede rather than follow the eighteen notes that appear in the earlier version, but again without the same symmetrical profile.

It might not be too farfetched to postulate that the symmetrical – indeed Webernian – pitch profile of Section IV, with series that are identical when read from right to left or left to right, may be a secret homage to the dedicatee of Anthèmes 1, Alfred Schlee, for whom the piece served as a ninetieth birthday gift on November 19, 1991. The dedication of Anthèmes 1 reads “à Alfred Schlee—en souvenir amical du 19.11.91”, Boulez having chosen a palindromic way to notate that date (since 191191 reads the same way from right to left and from left to right). Perhaps the musical palindromes of this section are a nod in the direction of the symmetrical date of Schlee’s birthday (as well as to Anton Webern—another Universal composer).

As for the electronic conception of this section, instead of using spatialization to articulate the musical text in accordance with Boulez’s usual practice, here the spatialization is used to amplify or underscore the forceful gestures of the violinist. As a result, the sound of the acoustic violin (without transformations) is abruptly shifted from one spatial position to another around the audience, using a rhythmic pattern that imitates but is not synchronous with that of the violin part. This absence of precise synchronization builds musical tension. In the contrasting middle section, on the other hand, infinite reverberation shadows the main pitches of the violin.

As for the electronic processing in this section, it presents a situation in which the violin and the electronics express opposite affects. While the violin plays violent double- and triple-stopped trills, the electronics feature calm evenly spaced notes (arco and pizzicato violin samples with infinite reverb) that contrast with these by their serenity. They create a peaceful backdrop against which the violence of the violin gestures are thrown into relief.

Section V

The short fifth section reprises thematic material already heard. In particular, after a short phrase conforming to the by now standard seven-note appogiatura, long-held trill followed by short grace-noted eighth notes, first seen in Section I (once again processed with frequency shifter and harmonizer), the central passage returns to the ‘ataxic’ material first heard in Section III: jaggedly bowed single notes, marked “nerveux et extrêmement irrégulier”. This section finally resolves into a more tranquil ambiance with the violin playing soft trills with electronics adding sampled pizzicato notes.

Section VI

Section VI.1 Violin and electronics in dialogue; Klee-like figuration

The long sixth and final section is divided into three subsections, the first of which being the only the time in the work where electronic phrases follow phrases on the violin like questions and answers, in a way that also recalls responsive chanting. The violin plays quick runs of notes followed by long trills, and as these trills fade out, very fast violin samples are triggered. This leads in to the long central section. The electronics in this section illustrate most clearly their affinity with Paul Klee’s pedagogical sketches: the violin’s single lines are followed by sampled violin pizzicato sounds that expand the line in geometrical ways: the individual violin notes are answered by sampled runs of notes drawn from preset chord reservoirs, buttressed by sound-blocks of various shapes underneath. Indeed, following Klee’s pedagogical sketches, the violin’s one-dimensional line is counterpointed by sounds that describe shapes on the pitch-time plane: a downward wedge of sound followed by a rectangle; a wedge that starts in the low register and slopes upward followed by a rectangle; or either of these shapes in reverse (rectangle followed by wedge). Some Computer Music Designers (CMD) even use a score, annotated by Andrew Gerzso and indeed Boulez himself, that indicates these shapes on the score [Figure 21], while Gerzso gave this patch the suggestive name of ‘klee-machines’.

Figure 21: Excerpt from Andrew Gerzso’s annotated performance score) from section VI.1 of Anthèmes 2, with ‘Klee-like’ shapes circled [Arch. Ircam].

Section VI.2 Play of recognition and surprise

When speaking about the return to thematic writing in Anthèmes 2, Boulez emphasized the way themes were used in the long middle passage of the last section of Anthèmes 2. As he said:

This piece is replete with such entities, which can be identified very easily. What is less easily identifiable is the order in which they occur, or rather the disorder in which they occur. We recognize a specific event, but we do not know when it will occur; we recognize them after the fact. This is what interests me – to create an effect of simultaneous surprise and recognition. [Boulez in Goldman, 2001, p. 117]

In this section (VI, b.54-163), in many ways the heart of the entire piece, there is a kind of dialogue between four very clearly defined musical objects (marked a, b, c and d in Figure 22).

Figure 22. Four themes in Anthèmes 2, section VI.2 [© Score UE, 1997a].

Media 6a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 6b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

These four motives are clearly recognizable, being comprised of the following: element a : ricochet double stops marked “calme, retenu”; element b: marked “agité, pizz.” ; element c: a violent bowed flourish marked brusque and element d: a pizzicato broken chord, emphasizing the note D and marked “calme, retenu, pizz.” Each of these themes has a distinctive “envelope”, to use the term favored by Boulez: each has a characteristic playing style, phrasing, articulation, dynamic, etc., over and above its brute pitch or duration content. Although never occurring twice in identical form, it can never be mistaken for a different thematic family member.

While recognizable, Boulez puts much store in the element of surprise, here attributed to the order in which these elements appear. And indeed, their order of appearance seems devised to emphasize their unpredictability (a b element could be followed by an a, a c or a d), which is, according to Boulez, by design. The four themes occur in the order (or indeed disorder) exhibiting in Figure 23.

Figure 23. Order of four themes in Anthèmes 2, section VI.2.

The electronics used in section VI.2 serve to further characterize each of the four themes. For element a, the ricocheted bow figure, frequency shifting is used to enlarge in a downward direction the register of the violin. For element b, two types of processing are deployed: the first uses both harmonizers and delays in order to complexify the rhythmic aspect and at the same time enlarge the register through the downward transpositions; the second creates a contrast with the “agitated” character of the instrumental writing through the use of chords created from violin samples with practice mute that are prolonged through the use of infinite reverberation. For the “brusque” third theme c, instead of underlying the forceful violin gestures through spatialization (as in section IV), here this is accomplished through the triggering of rapid and aggressive sequences made from arco and pizzicato violin samples. Finally, the quiet arpeggiated pizzicato chords of the fourth theme d use two ring modulators, much like the processing of the harmonics notes in the “letter” transitions. These ring modulators inject a complex spectrum through a comb filter tuned to a low notch frequency providing a rich inharmonic spectrum. Here the result obtained is slightly different than in the letters as a result of the slowly arpeggiated chords which add a percussive aspect to the resonance created by the comb filters. Finally, a series of chords generated from sine wave samples softly shadow the arpeggiated chords of the violin.

Section VI.3

This is the closing section of the work and is characterized by two musical ideas that progressively converge towards the central D with which the piece opens and closes [Figure 24].

Figure 24. Anthèmes 2, section VI, b.164–170 [© Score UE, 1997a].

Media 7a. Hae-Sun Kang (violin) without electronics [© Arch. Ircam].

Media 7b. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

The rhythmic regularity of the moto perpetuo-style violin part featuring nearly uninterrupted 32^nd notes creates a curiously static impression overall that contrasts with the jagged rhythmic writing of the previous sections. As the section proceeds, the musical figuration slowly and steadily converges towards the central D₅. The electronic part creates creating “clouds” imbued with a rich spectrum that shadow the solo violin. Generally speaking, these clouds are created by injecting violin samples (that are not heard directly) into an infinite reverberation module. Two distinct “cloud” layers are created and then superimposed. The musical material for both layers is based on a main pitch and a set of auxiliary pitches constructed around it. The first layer is created by choosing notes from the set of pitches at random and injecting them in a rapid burst into the infinite reverb module. The second layer is created by repeatedly injecting only the main pitch into another infinite reverb module. At the beginning of the section the main pitches shadow central pitches in the violin part. As the section progresses, the size of the pitch-set decreases and the main pitch slowly converges towards the D natural. Once both the violin part and the “clouds” have converged to this D₅, the “clouds” are unceremoniously cut off by a brief col legno battuto gesture (like in the introductory “Libre” section of the piece) [Figure 25].

Figure 25. Ending of Anthèmes 2 [© Score UE, 1997a].

Media 8. Hae-Sun Kang (violin) with electronics [© Arch. Ircam].

This dry tap on the string with the wood of the bow puts a stop to the electronic processing and to the work as a whole. Boulez said that the end of the piece was meant to be humourous effect, as if the violinist were saying by the struck col legno battuto, “maintenant, ça suffit, au revoir” (“that’s enough now, goodbye”) [Boulez in Goldman, 2001, p. 118].

Version for viola

As with Dialogue de l’ombre double (1985), which was adapted for alto saxophone (2001), and Messagesquisse (1976), which was arranged for an ensemble of violas (2000), Anthèmes 2 was adapted for viola at the request of Ensemble Intercontemporain violist Odile Auboin. Prepared by Auboin in 2008, this version was authorized by Pierre Boulez and published by Universal Edition [Score UE, 2008]. It was premiered on 30 June 2021 in Paris at the Cité de la Musique by Auboin, with electronics by Augustin Muller. The electronic processing had to be adjusted both to adapt to the viola’s lower range as compared to the violin, and to take into account timbre and playing characteristics specific to the viola.

Since some parts of the work employ audio score following, it was necessary to transpose the reference frequency of the audio analysis for the viola version. Since the processing of the harmonizer affects the transpositions themselves, these patches did not need to be modified. However, for the processing of the frequency shifter, a correction of 2/3 was applied to the patch’s output. Some adjustments were also made to the performer’s score, mostly involving changes in tempo of certain sequences, in particular those that are performed pizzicato (in section II, and VI.3 in particular) in order to accommodate an instrument in which such manœuvres require more time than on a violin. Moreover, in order to take into account the different physical characteristics of viola strings as compared to violin strings, a set of samples – especially those of pizzicato notes – was created in order to match the timbre and performance characteristics of the viola. All of the changes to the electronic part were made by Augustin Muller who, since 2017, has taken charge of all the works by Pierre Boulez produced at Ircam when they are performed.

Boulez also planned to expand Anthèmes 2 into a new work for violin and chamber orchestra, for the violinist Anne-Sophie Mutter. Anthèmes 3, as it would have been titled, had been scheduled to be performed at a concert celebrating the ninetieth birthday of Paul Sacher, in Basel on 28 April 2006, but although mentioned in Boulez’s correspondence, seems to never have got beyond its initial stages.

Conclusion

Today, Anthèmes 2 has attained the status of a classic work of live electronics. Its electronic processing succeeds in being both phantasmagorical and fundamentally sober, in keeping with the solemnity announced by the title’s allusion to the hymn. It creates tension through a dramaturgy based on stark oppositions. In its attachment to “écriture” in both its instrumental and electronic components, it encapsulates several fundamental aspects of Boulez’s musical aesthetics. Most importantly, it was designed to allow the performer to enjoy a broad degree of flexibility, to adapt her playing to the acoustic properties of the space in which the work is performed, and to make pauses or abrupt openings as desired. After all, one of Boulez’s main objectives to assigning the development of real-time electronics as one of Ircam’s main early missions, was motivated by a desire to free performers from slavishly following the inexorable unfolding of an electronic part on tape, which was the standard way of combining instruments and electronics ever since the early days of Bruno Maderna’s Musica su due dimensioni (1952). The work’s grandeur but also its flexibility shine through, unexpectedly becoming, with a nod to Mahler, a new ‘song of the earth’. Viewed at a distance, Anthèmes 2 can be seen to contain in microcosm many of Boulez’s most steadfast compositional concerns: to find ways to embrace both traditional musicianship and electronic sound, with an exploration of the ways electronics can be brought into the realm of notated musical language; to create ambiguous listening situations where perception is by turns focused or diffuse; to have musical material proliferate seemingly endlessly, whether in the quantum leap from Anthèmes 1 to Anthèmes 2 or from Incises to Sur Incises; and to approach musical texture visually or sculpturally in a Bauhaus-inspired reflection on line, form, volume and shape.

Resources

Some sections of this essay draw on and extend previous publications by the co-author, Jonathan Goldman, in particular [Goldman, 2001; 2009; 2011].

Texts

[Boulez, 1976] – Pierre Boulez, Conversations with Célestin Deliège, London: Eulenburg, 1976.

[Boulez, 1995] – Pierre Boulez, “Interview with Stephen Plaistow”, in liner notes of CD Boulez at 70, Deutsche Gramophon, GPL01, 1995.

[Boulez, 1989/2008] – Pierre Boulez, Le pays fertile. Paul Klee, Paule Thévenin (ed.), Paris: Gallimard 1989/2008.

[Boulez, 2019] – Pierre Boulez, Music Lessons, Jonathan Dunsby, Jonathan Goldman and A. Whittall (eds.), London: Faber, 2019.

[Boulez, 2025] – Pierre Boulez. Catalogue des œuvres, Éditions de la Philharmonie de Paris, 2025, dir. Alain Galliari and Robert Piencikowski, Paris: Éditions de la Philharmonie, 2025.

[Boulez et al., 2009] – Pierre Boulez, Yves Bonnefoy and Carol Bernier. Quêtes d’absolus, Jean-Jacques Nattiez and Jonathan Goldman (ed.), Montréal, Simon Blais, 2009.

[Carpentier et al., 2015] – Thibaut Carpentier, Markus Noisternig and Olivier Warusfel, “Twenty Years of Ircam Spat: Looking Back, Looking Forward”, 41st International Computer Music Conference (ICMC), Denton (USA), Sept. 2015, p.270-277.

[Dal Molin, 2007] – Paolo Dal Molin, Introduction à la famille d’œuvres …explosante-fixe… de Pierre Boulez : Étude philologique, thèse de doctorat en Arts/Musicologie, Université de Nice Sophia Antipolis, 2007.

[Goldman, 2001] – Jonathan Goldman, Understanding Pierre Boulez’s Anthèmes: ‘Creating a Labyrinth out of Another Labyrinth’, Master’s thesis, Université de Montréal, 2001.

[Goldman, 2009] – Jonathan Goldman, ‘Passage d’Anthèmes 1 à Anthèmes 2’, in Quêtes d’absolus, ed. Jean-Jacques Nattiez, Montreal: Éditions Simon Blais, 2009, pp. 34-39.

[Goldman, 2011] – Jonathan Goldman, The Musical Language of Pierre Boulez: Writings and Compositions, Cambridge, Cambridge University Press, 2011.

[Jot and Warusfel, 1995] – Jean-Marc Jot and Olivier Warusfel, “A Real-Time Spatial Sound Processor for Music and Virtual Reality Applications”, International Computer Music Conference (ICMC), Banff (Alberta, Canada), Sept. 1995, pp. 294-295.

[Klee, 1953] – Paul Klee, Pedagogical Sketches, Sibyl Moholy-Nagy (ed. and trans.), New York, Frederick A. Praeger, 1953.

[MacKay, 2009] – John MacKay, “Analytical Diptych: Boulez Anthèmes/Berio Sequenza XI”, Ex Tempore, vol.14 n^o2, 2009, p.111-141.

[Røsnes, 2023] – Irine Røsnes, “The Violining Body in Anthèmes II by Pierre Boulez”, in Linda O Keeffe and Isabel Nogueira (eds.), The Body in Sound, Music and Performance: Studies in Audio and Sonic Arts, Abingdon: Routledge, p.214-227, 2023.

[Taher, 2016] – Cecilia Taher, “Motivic similarity and form in Boulez’s Anthèmes”, diss., McGill University, 2016.

[Taher et al., 2018] – Cecilia Taher, Robert Hasegawa and Stephen McAdams, “Effects of Musical Context on the Recognition of Musical Motives during Listening”, Music Perception: An Interdisciplinary Journal, vol.36 n^o1, p.77-97.

[Van der Wee et al., 2016] – Laurens Van der Wee, Roel van Doorn and Jos Zwaanenburg, “Reconstructing Anthèmes 2: Addressing the performability of live-electronic music”, International Computer Music Conference (ICMC), Utrecht (Netherlands), Sept. 2016, p.466-470.

Archives

The following information was sourced from [Boulez, 2025]. Used with permission.

• Bibliothèque nationale de France, fonds Pierre Boulez (BnF/PB)
  About Anthèmes 1: Universal Edition score, annotated by Pierre Boulez (GR FOL-VM FONDS 148 BLZ-160); corrected galley proofs of the transcription for viola (VM FONDS 148 BLZ-9(39))
• Paul Sacher Stiftung, Pierre Boulez Sammlung (PSS/PB):

About Anthèmes 1: a) sketches ; b) draft; c) annotated photocopy of the fair copy of the initial version; d) autograph copy of the initial version ; e) corrected proofs of the initial version; f) corrected proofs of the 1992 version; g) photocopie of the 1992 edition annoted in view of Anthèmes 2 (Mappe J, dossier 5a)

About Anthèmes 2: a) sketches and drafts; b) fair copy, autograph copy; c) corrected proofs (Mappe J, dossier 5b)

Scores

[Score UE, 1992] – Pierre Boulez, Anthèmes, Vienne, Universal Edition, UE 19992, 1992.

[Score UE, 1997a] – Pierre Boulez, Anthèmes 2, Vienne, Universal Edition, UE 31160, 1997.

[Score UE, 1997b] – Pierre Boulez, Anthèmes 2 – Performance instructions, Vienne, Universal Edition, UE 31160b, 1997.

[Score UE, 2008] – Pierre Boulez, Anthèmes 2 (Viola), Vienne, Universal Edition, UE 34342, 2008).

Audio recordings

Anthèmes 1

[AR CD Atma, 1996] – Julie-Anne Derome, Solo

Anne Derome (vl)

Atma A+CD 2 2117 [CD], 1996.

Anthèmes 2

[AR CD Accentus Music, 2016] – Bach, Bartók, Boulez

Michael Barenboim (vl), Andrew Gerzso (CMD)

Accentus Music ACC30405 [CD], 2016

[AR CD Col Legno, 1998] – Donaueschinger Musiktage 1997

Hae Sun Kang (vl), Andrew Gerzso (CMD)

Col Legno WWE [3 CD] 20026, 1998.

[AR CD Deutsche Grammophon, 2000] – Pierre Boulez : Sur Incises, Messagesquisse, Anthèmes 2

Hae Sun Kang (vl), Andrew Gerzso (CMD)

Deutsche Grammophon DG 463 475-2 [CD], 2000.

[AR CD Deutsche Grammophon, 2017] – Hommage à Boulez

Michael Barenboim (vl), Andrew Gerzso (CMD)

Deutsche Grammophon DG 4797160 [2 CD], 2017.

[AR CD Les Belles Écouteuses, 2015] – Stravinsky-Boulez

Diégo Tosi (vl), David Poissonnier (CMD)

Les Belles Écouteuses LBE 10 [CD], 2015.

[AR CD Simon Blais, 2009] – Accompanying CD in Quêtes d’absolus, Jean-Jacques Nattiez ed., Montreal: Éditions Simon Blais, 2009.

Jean-Marie Conquer (vl), Gilbert Nouno (CMD)

To quote this article:

Jonathan Goldman and Andrew Gerzso, “Pierre Boulez – Anthèmes 2”, ANALYSES – Œuvres commentées du répertoire de l’Ircam [En ligne], 2025. URL : https://brahms.ircam.fr/analyses/Anthems2/