As one of the inventors of the twelve-tone technique and the first well-known composer of twelve-tone music, it makes eminent sense that Arnold Schoenberg would be understood by scholars and musicians as a traditionalist, in both the positive and negative senses. Much fruitful work has been done that shows ways in which Schoenberg carried over elements of classical and Romantic form and harmony into his twelve-tone compositions. To mention a few examples, one thinks of Richard Kurth’s illustrations of analogies to classical phrase types and tonic-dominant harmonic progressions in the opening of the Menuett from the Suite op. 25, or Ethan Haimo’s demonstration of how Schoenberg preserves the typical modulation schemes of sonata form using regions of twelve-tone rows in the opening movement of the Fourth Quartet op. 37 (Reference KurthKurth 1996: 105; Reference HaimoHaimo 2002: 225–6). On the other hand, it was Schoenberg’s obstinate tendency to hold on to classical and Romantic conventions of rhythm, form, and texture that caused Pierre Boulez the irritation he so vehemently expressed in ‘Schoenberg Is Dead’ (Reference BoulezBoulez 1952). But there is one way in which Schoenberg’s music preserved musical tradition that previous commentators and critics have hardly mentioned, perhaps the one with the most significance for long-range coherence in his twelve-tone music: what he called ‘musical idea’.

What exactly is a musical idea? Schoenberg’s explications of it in his writings were less than systematic, and, unfortunately, he never illustrated the concept with one of his own pieces, tonal, atonal, or twelve-tone, so there is room for disagreement on how to understand the term. The closest thing he provided to a textbook definition is found in the essay ‘New Music, Outmoded Music, Style and Idea’ (Reference Schoenberg, Black and SteinSchoenberg 1975c):

Note that here a musical idea is defined as a tonal piece: the initial problem which causes imbalance that grows through the course of the piece, and is eventually resolved at or near the end, is defined as an uncertainty regarding the tonal context of pitch classes C and G. And, not surprisingly, the literature that attempts to illustrate ‘musical idea’ through analysis, primarily by Schoenberg’s student Patricia Carpenter and her own students, deals almost exclusively with tonal music: Carpenter’s article ‘Grundgestalt as Tonal Function’, an insightful study of tonal problems, elaborations, and solutions in the first movement of Beethoven’s op. 57 piano sonata, is the first and one of the best examples of analytic work in this vein (Reference CarpenterCarpenter 1983).

Since the notions of ‘tonal context’ or ‘tonal problem’ are not possible in twelve-tone music, however, it is more difficult to grasp how a musical idea might serve as the framework for a twelve-tone piece. Since, in the twelve-tone style, no note should be considered any more central than any other, how can one perceive a note as foreign or distant from the centre? In my Schoenberg’s Twelve-Tone Music, I explored a number of ways in which pitch classes, intervals, and set classes can participate in narratives that involve creating an ideal state, setting another state in opposition to it, allowing that opposition to elaborate itself and branch out in various ways through the piece, and finally resolving it. Some of my analyses highlighted problems and elaborations that stem from the differences between a symmetrical pitch-class or interval pattern (presented or implied at the beginning) and various close or distant approximations of it. The symmetrical pattern is then reasserted at or near the end, and the approximations are connected to it in significant ways, as a solution. In other cases, the initial opposition and elaboration involve different partitions of different rows that create what seem like irreconcilable pitch-class or set-class elements. The solution will then consist of demonstrating how the conflicting partitions and their clashing consequences can be traced back to the original source row. Finally, a number of Schoenberg’s twelve-tone pieces, particularly later ones, include a struggle between various source row forms for primacy, which is resolved in favour of one of the potential sources at piece’s end.

The bulk of this chapter will be devoted to illustrating how musical idea is manifested in two of Schoenberg’s twelve-tone piano pieces: the Prelude from the Suite for Piano op. 25, written right at the beginning of his twelve-tone period in 1921–3, and the Piano Piece op. 33a, written in 1928–9 after Schoenberg had gained some facility at working with row pairs related by combinatoriality; ‘hexachordal inversional combinatoriality’ refers to a property between inversionally related row forms in which the corresponding hexachords have no notes in common and may be combined vertically into other orderings of the twelve-note universe. Both the Prelude and the Piano Piece express their musical idea by elaborating and resolving an opposition between a symmetrical ideal and close or distant approximations of it: the symmetrical pattern consists of pitch classes in the Prelude, and of pitch intervals in op. 33a. Given the limits of this chapter, I will not be able to give these pieces thorough section-by-section analyses, as I do in chapters 2 and 5 of Schoenberg’s Twelve-Tone Music, but instead will highlight how their problems are posed, elaborated, and resolved with a few snapshots.

Suite for Piano Op. 25, Prelude

The Prelude was the first piece by Schoenberg to be written in the twelve-tone style throughout, and a number of scholars have claimed that it does not use the row according to the conventional notion, as a single, consistent linear ordering of all twelve pitch classes. Ethan Haimo argues for what he calls a ‘tetrachordal polyphonic complex’, a division of the row into its three discrete tetrachords, which are then ordered freely between themselves (but usually preserve ordering within themselves) and often appear simultaneously (Reference HaimoHaimo 1990: 85–6). In what follows, I will sometimes count twelve-tone rows using ‘order positions’ (meaning first, second, third, etc., notes in the row), starting with 0 and ending with 11, and will highlight them in bold, so that tetrachords ordered within themselves but not between themselves might read: 4–5–6–7, 0–1–2–3, 8–9–10–11; or 8–9–10–11, 0–1–2–3, 4–5–6–7; or other such combinations. However, when these same twelve numbers (0–11) are not in bold, they represent the different pitches of the chromatic scale, regardless of octave. Therefore, C is represented as 0, C♯/D♭ as 1, D as 2, and so on. Hence, a C major triad could be represented as [047].

Part of Schoenberg’s set table for the piece, in the transcription provided by Reinhold Brinkmann for the collected edition of Schoenberg’s works, is reproduced in Figure 4.1, to which I have added a pitch-class map (Reference 396Schoenberg and BrinkmannSchoenberg 1975d: 77), while the autograph version of the table appears earlier in this volume as Figure 1.2. Haimo also reproduces this same set table, to provide evidence that Schoenberg had not yet conceived of the source row of the Prelude as a linearly ordered twelve-tone row – but I am interested in it for a completely different reason. Namely, it sets the discrete tetrachords of P₄ (the prime form beginning on pitch class 4) and R₄ (the retrograde of that same form) against one another, tetrachord by tetrachord, so that each line of the configuration creates a palindrome, and the whole also creates a symmetrical pitch-class structure. This structure then becomes the ‘ideal state’ in the piece, which is only approximated at the beginning (creating a problem), approached more closely but then completely abandoned for a different symmetrical structure in the middle (the elaboration of the problem), and finally realised in its perfect form near the end as a solution.

Figure 4.1 Part of Schoenberg’s set tables for the Suite, op. 25, with a pitch-class map

Figure 4.2 illustrates the opening of the piece, in which the ideal symmetrical shape is hinted at but not realised. The pitch-class map at the top of the example shows that when P₄ and P₁₀ are divided into discrete tetrachords and the corresponding tetrachords placed against one another, instead of the full collection of six contiguous dyad palindromes that P₄ and R₄ had created, only two are realised contiguously (<7, 1> – <1, 7> and <8, 2> – <2, 8>), while two are realised by a contiguous dyad and a non-contiguous one: <4, 5> – <5, 4> and <11, 10> – <10, 11>. In this way, the combination of P₄ and P₁₀ can only hint at the perfect symmetry that P₄ and R₄ would have created. Looking now at how these four palindromic dyads are projected in the score itself, it seems that Schoenberg has in fact attempted to highlight the available symmetries in a variety of ways: <7, 1> – <1, 7> through proximity and similar contours and articulations (accents), <8, 2> – <2, 8> through similar contours and articulations, <4, 5> – <5, 4> by means of similar dynamics and articulations, and finally <11, 10> – <10, 11> with similar articulations. These dyads account for much of the ‘balance’ that Kurth celebrates in this opening phrase’s ‘mosaic polyphony’ (Reference KurthKurth 1992: 190–6). But they still fall short of a completely symmetrical state, and that creates a problem – with its associated opportunities for elaboration and solution.

Figure 4.2 Schoenberg, Prelude op. 25, bb. 1–3

As the Prelude continues, it breaks up into subsections of the overall binary form’s A section (bb. 1–16a) that contain pairs and sometimes trios of row forms, in bb. 3b–5a, 5b–7a, 7b–9a, 9b–11a, and 11b–13a. These early sections fluctuate between pairings that yield fewer palindromic dyads and those that yield more, and also vary the number of potential two-note palindromes that are emphasised as audible motives within the texture. With b. 13, however, comes a passage that approximates the ideal more closely than anything heard before – but falls just short. It is shown in Figure 4.3.

Figure 4.3 Schoenberg, Prelude op. 25, b. 13

The lower right-hand corner of the example shows that I₄ (the inversion of the prime form that starts on pitch class 4, around that pitch class) and RI₄ (the retrograde of I₄), the row pair featured in this passage, have the potential for six palindromic dyads because they are retrogrades of one another. But only three of these dyads are highlighted in the music itself (shaded in the example): <0, 6> – <6, 0>, <4, 3> – <3, 4>, and <1, 7> – <7, 1>, the last of which is realised by using an overlap to create a three-note horizontal mirror in the middle of the left-hand part. As the registrally sensitive pitch-class map in the lower left-hand corner and the marked score at the top of the example show, the other three potential dyad palindromes are all obscured in some way. <9, 8> and <11, 10> are given as verticals in the right hand of b. 13a and answered in the left hand of b. 13b by horizontal renditions of <10, 11> and <8, 9> that have parts of other dyads interleaved between them. And the second dyad in <2, 5> – <5, 2> is reversed within the tremolo figure (marked in the score, together with the three highlighted palindromes). This is not a solution quite yet, though it comes close.

Before finding its eventual solution, however, the Prelude wanders off into one more subsection that elaborates the problem more radically than anything heard before, the climactic passage near the beginning of the large A′ section at bb. 17b–19. It is portrayed, with its rather complex pitch-class map, in Figure 4.4a. As the pitch-class map shows (once it is untangled), there are a number of contiguous and non-contiguous dyad invariances between P₄, I₁₀, P₁₀, and I₄ that enable Schoenberg to assign various pitch pairs to more than one tetrachord, and, in addition, within both row pairs the second and third tetrachords routinely begin before the first and second finish, creating multiple overlaps. All four rows contain pitch classes 1 and 7 in order positions 2 and 3, and the first tetrachords of P₄ and I₁₀ link to one another on the downbeat of b. 18 through this invariance, as do the first tetrachords of P₁₀ and I₄ on the downbeat of b. 19. The non-contiguous dyad invariances begin with pitch classes 3 and 11, which appear in order position 5 of P₄ and I₁₀, and then swap places in order position 8 of the same rows. Schoenberg uses this to create a link (expressed as repeating notes Cb5 and Eb5 in the left hand of b. 18a) between the second and third tetrachords of P₄ and I₁₀. Other tetrachords that are linked in similar ways are the third tetrachords of P₄ and I₁₀ with the first tetrachords of P₁₀ and I₄, through {4, 10} (left hand of b. 18b), the second tetrachords of P₄ and I₁₀ with the second tetrachords of P₁₀ and I₄, through {0, 2} (right hand of bb. 18b–19a), and the second and third tetrachords of P₁₀ and I₄, through {5, 9} (left hand of b. 19a).

Figures 4.4a and b Schoenberg, Prelude op. 25, bb. 17b–21

The ensuing tangle of tetrachords and pitch classes with dual meanings, so much more complicated than the simple palindromic ideal of Figure 4.1, nevertheless creates its own symmetrical shape. It is highlighted within Figure 4.4a’s pitch-class map by the white circles inside the two shaded boxes: the verticals {3, 11}, {0, 2}, {6, 8}, and {5, 9} in b. 18, balanced by {5, 9}, {6, 8}, {0, 2}, and {3, 11} in b. 19. Kurth calls this the ‘gamma palindrome’ and highlights it as the most important and perceptible of three pitch palindromes in the passage, which do not synchronise with each other and together ‘motivate [a] drive toward some greater stability’ (the loud dynamics and registral extremes also mark this passage as unsettled) (Reference KurthKurth 1992: 200–6). But in the larger context of the subsections that have preceded it, we can also understand Kurth’s ‘gamma’ as the ultimate elaboration of the work’s problem, which follows all the approaches to and departures from complete horizontal symmetry of all twelve contiguous dyads in bb. 1–17 with a completely different approach to dyad symmetry involving non-contiguous verticals. It is almost as if the piece is saying: ‘I’ve tried to attain this piece’s ideal pitch-class palindrome for seventeen bars and failed. I’m going to try a completely different kind of palindrome.’

This ultimate elaboration of the problem, this high point of instability, is followed immediately by a passage that Kurth claims to bring ‘desired stability’ (Reference KurthKurth 1992: 205), and that I understand as the solution to the work’s problem: bb. 20–21, portrayed in Figure 4.4b. In each of these measures, since retrograde-related rows are again pushed up against one another, tetrachord by tetrachord, P₄/R₄ and I₁₀/RI₁₀, there is the potential for six dyad palindromes – the ideal shape. In b. 20, this potential is not fully realised, because <7, 1> and <8, 2> do not reverse themselves. But the other four dyads in the configuration not only reverse their pitch classes, but also their pitches, so that the music takes a large step closer to perfect symmetry. In b. 21, it gets all the way to perfect pitch-class symmetry, as the middle dyad pairs overlap in a single note, <5, 4, 5>, <6, 0, 6>, and <7, 1, 7>. The one detail preventing complete pitch symmetry is Schoenberg’s transposition of A and B♭ in the left hand at the end of the measure down one octave. The passage’s function as a solution following bb. 17–19’s ultimate elaboration is made clearer, I think, by Schoenberg’s drastic reduction in dynamics from ff to pp and narrowing of the register.

Piano Piece Op. 33a

I have shown how, at the very beginning of Schoenberg’s twelve-tone period, he created a narrative spanning the op. 25 Prelude which manifests the ‘musical idea’, by suggesting a symmetrical pitch-class pattern, obscuring it further, and bringing it back into closer focus, then presenting an alternative symmetry that is nothing like the first in a climax, and, finally, realising the symmetry that was originally only suggested in a denouement. Five years later, after discovering and developing the hexachordal-combinatorial relationship between rows, he would return to the same sort of idea presentation in the op. 33a Piano Piece, expressing an old narrative in a new way. Op. 33a’s initial problem has to do with an incompatibility it presents between intervallic symmetry and row order, as shown in Figure 4.5a.

Figures 4.5a and b Schoenberg, Piano Piece op. 33a, bb. 1–9

As the example shows, the two principal (and combinatorial) rows of the piece, P₁₀ and I₃, are first presented out of order as a series of six discrete tetrachord sonorities (with the second row’s tetrachords in retrograde) in bb. 1–2, then both of them in linear order, but reversed with RI₃ above R₁₀, in bb. 3–5. The extensive reordering of notes in bb. 1–2 enables a pattern between the unordered pitch intervals of the six chords that is both horizontally and vertically symmetrical. (Schoenberg associated simultaneous horizontal and vertical symmetry with perfection in a number of his other pieces, and it even portrayed God’s perfection in Moses und Aron (cf. Reference BossBoss 2014: 332–41).) Counting intervals up from the bottom produces <1, 5, 5>, <4, 2, 3>, <6, 2, 3>, followed by a sequence of chords that reverses the previous elements and simultaneously flips them upside down: <3, 2, 6>, <3, 2, 4>, <5, 5, 1>. I call this the ‘palindromic ideal’ in Figure 4.5a. Once row order regains control in bb. 3–5, however, the pitch-interval symmetry of the opening measures disappears and is replaced by a less immediately audible symmetry, that caused by set classes: 4–23 (0257), 4–1 (0123), 4–10 (0235), 4–10, 4–1, 4–23. I call this the more abstract ‘echo’ of the ‘palindromic ideal’. The problem that op. 33a poses in its opening measures has to do with the seeming incompatibility of vertical and horizontal symmetry on the one hand and row order on the other: can both coexist? Or must row order necessarily weaken perfect intervallic symmetry?

Before answers to these questions are produced near the end of the piece, the first step in the realisation of the musical idea in op. 33a is progressively to obscure both the palindromic idea and the echo, similar to the way the Prelude op. 25 blurred its palindromic pitch-class pattern in its opening measures. Figure 4.5b shows how bb. 6–9 obfuscate the symmetries of the previous example through rhythmic displacement, as well as moving certain notes up or down by octave. (In the larger sonata form that spans op. 33a, bb. 6–9 constitute the first variation of bb. 1–5’s first theme.) In b. 6’s variation of the first chord of the palindromic ideal, C3, F3, and B♭3 rise an octave and B2 is delayed an eighth note, forming unordered pitch-interval stack <5, 5> followed by −13 (rather than <1, 5, 5>). The second chord delays its top three notes by an eighth, changing <4, 2, 3> to <+4, 2, 3>. And the rhythmic displacements and octave transfers carry on through the remaining four chords, changing what had been six horizontally and vertically symmetrical tetrachords into six conglomerations of chords and melodic intervals, all of which are unique and some of which are not even tetrachords (at the end of b. 7).

Bars 8–9 perform the same kind of obfuscation through rhythmic displacement of the set-class symmetrical ‘echo’ of bb. 3–5. To produce something like the original passage’s palindrome (4–23, 4–1, 4–10, 4–10, 4–1, 4–23), I had to group notes from different parts of the measure and from overlapping parts of the texture, creating a pitch-class segmentation that calls to mind the gerrymander – that is, manipulating the boundary line of a legislative district to favour a particular party – from partisan politics. Even with the gerrymanders, though, the sequence of set classes does not form a pure horizontal mirror: the initial pair (4–23 and 4–1) repeats. Through rhythmic and registral changes, but also through repeating parts of the row out of order, Schoenberg begins to obscure the perfect and imperfect symmetries of his opening.

After a second variation of the P theme in bb. 10–13 that continues the process of obfuscation, the subsidiary theme enters in bb. 14–18, shown in Figure 4.6a. This passage and the one that immediately follows (Figure 4.6b) play an elaborating role within op. 33a’s ‘musical idea’ that is closely analogous to the part bb. 17–19 (Figure 4.4a) played in the Prelude – after the initial symmetry is progressively obscured, the S theme casts it aside and tries to attain symmetrical perfection in a completely different way (but still using the main pair of combinatorial rows, P₁₀ and I₃). Namely, the subsidiary theme abandons the intervallic and set-class symmetry of the opening measures in favour of horizontal pitch symmetry, particularly in the right hand of the piano. Bars 14 and 15 present the first hexachord of P₁₀ as the complete palindrome <B♭4, F4, C4, B3, A3, F♯4, A3, B3, C4, F4, B♭4> (some pairs of notes are grouped vertically) followed by an incomplete version of the same. Bars 16–18 then supply the second hexachord of P₁₀, split into two pitch palindromes: <D♭5, E♭4, G5, A♭4, G5, E♭4, D♭5> and <D5, E4, G5, A♭4, G5, E4, D5>. The left hand accompanies with the corresponding hexachords of I₃ mostly in linear arrangements, forming aggregates between the hands in bb. 14–16a and 16b–18.

Figures 4.6a and b Schoenberg, Piano Piece op. 33a, bb. 14–22

This attempt to create horizontal pitch symmetry does a certain amount of violence to the ordered presentation of P₁₀ in bb. 14–18. In the following closing section, shown in Figure 4.6b, the same incentive results in even more confusion with respect to the linearity of the row form. Not only are parts of rows taken forward and backward, but also notes of the complete linear presentations of R₁₀, RI₃, and the second hexachords of P₁₀ and I₃ are missing. Bars 19–20 set R₁₀ in the right hand against RI₃ in the left, using rhythms and textures reminiscent of first theme material (this abbreviation of thematic material is my main justification for calling this section ‘closing’). R₁₀ progresses as far as order position 9, pitch class 0, and then that pitch class with its predecessors, <9, 6, 11, 0>, gets caught up in another pitch palindrome, <A6, F♯6, B5, C5, B5, F♯6, A6>, which repeats. Meanwhile, RI₃ also only progresses as far as its order position 9, pitch class 1, which likewise takes part in a smaller pitch palindrome, <D3, C♯2, D3>. In both cases, it is the emergence of the pitch palindromes that causes the row to be incomplete. Likewise, the second hexachord of I₃ that counterpoints with the second hexachord of P₁₀ in bb. 20–23a, using the rhythms and textures of the S theme, stops one note short, not reaching all the way to pitch class 9, because it gets entangled in a small palindrome, <B♭3, F3, B2, F3, B♭3>. The C theme elaborates the problem within the Piano Piece’s musical idea by showing, repeatedly and forcefully, that the alternative way of making palindromes proposed by the S theme is not an acceptable substitute, because it destroys the integrity of the ordered row. The violence it does in the pitch-class realm is made much more tangible by the forte dynamic marking and ‘martellato’ of bb. 19–20.

So now that it has become clear that pitch palindromes cannot reconcile the piece’s initial conflict between symmetry and row order, but in fact have the completely opposite effect, it remains for Schoenberg to show how those two properties can coexist within the same texture. After a fairly long development section (bb. 25–32a) where he gradually rebuilds the palindromic ideal of bb. 1–2, interval by interval, bb. 32b–34 presents the recapitulation of the P theme – portrayed in Figure 4.7. Instructors of undergraduate core theory who use op. 33a as an introduction to twelve-tone music will certainly recognise the right hand in bb. 32–33a as that place to which they send their students to find the source row of the piece in its pure, unadulterated form, presented without order changes, missing notes, or verticals to confuse the analytic process. RI₃ follows it in bb. 33b–34, but with several verticals and a short palindrome involving the third discrete tetrachord in b. 34b. The left hand in this section accompanies with the combinatorial forms I₃, followed by R₁₀ – in order between the tetrachords, but with the order within the tetrachords compromised by verticals.

Figure 4.7 Schoenberg, Piano Piece op. 33a, bb. 32b–34

Still, these measures present one of their row forms in proper order, and the other three in something relatively close to proper order. It is remarkable, then, that at the same time they are able to preserve some (but not all) of the palindromic ideal, the horizontally and vertically symmetrical pattern, of bb. 1–2. At the bottom of Figure 4.7, the discrete tetrachords of P₁₀ and RI₃ in the right hand as well as I₃ and R₁₀ in the left are stacked vertically so as to preserve the register of each note, and unordered pitch intervals between the pitches are listed. The intervals of P₁₀ and RI₃ (from the bottom up) are: <1, 6, 7>, <5, 3, 6>, <4, 6, 5>, <8, 6, 7>, <5, 4, 6>, and <7, 6, 1> – different intervals from bb. 1–2, but preserving some of the same symmetries. Most salient is the inverted relationship between verticals 1 and 6, which replicates the outside chords of the palindromic ideal in a different form. But verticals 2 and 5 also share pitch intervals 5 and 6 in corresponding locations (not inverted), preserving some of their horizontal symmetry; as do verticals 3 and 5, which preserve interval 6 in the middle position and octave-complement the intervals on the outside: 4 and 5 become 8 and 7. Finally, there are also a few vertical symmetries between the hands, marked at the bottom of Figure 4.7 with circles and arrows.

This passage constitutes the solution to op. 33a’s problem, the demonstration that vertical and horizontal symmetry and row order can indeed coexist. It is certainly true that it could have done a more thorough job of mirroring its interval stacks in the right hand. The bracketed chords after verticals 4 and 5 at the bottom of Figure 4.7 show what those verticals would have looked like had Schoenberg created an exact horizontal and vertical palindrome like the one in bb. 1–2. It would indeed have been possible for the right hand to play through these bracketed verticals in the order prescribed by RI₃, <A5, B4, F5, F♯4> and <B♭4, C6, G5, E5>, forming a perfect union of intervallic symmetry and row order. But that would have made the arch contour in the right hand less clear, obscuring an important feature that makes a connection between this passage and the opening measures.

Not every twelve-tone piece Schoenberg wrote expresses a complete musical idea – problem, elaborations, and solution – as the two examples I have discussed in this chapter do. Moses und Aron, because of its subject – Moses’s failed attempt to communicate God to his people – organises itself around an incomplete musical idea: an initial problem, representing the conflict between Moses’s words and Aron’s images, which continues to elaborate itself without ever coming to resolution (see Reference BossBoss 2014, 330–94). Other pieces with texts – for example ‘Tot’ from the Drei Lieder op. 48 – abstract a ‘basic image’ from the text and use that as an organising principle rather than an idea (Stephen Peles explains quite well how the image of a unitary entity with two opposite sides controls the partitions and intervallic and pitch-class patterns of that song) (Reference PelesPeles 2004). But, in general, the ‘musical idea’, adapted for use as an analytic framework, is an invaluable tool for understanding how Schoenberg’s music coheres and exactly how he carried on the tradition of his German and Austrian predecessors.

If there is a single, enduring quality in Alban Berg’s serial works (c. 1925–35), it is his ability to use the twelve-tone method of composition as a form of exegesis for his personal, intellectual, and musical heritage in musical narratives suffused with apparent contradictions. From his first twelve-tone composition, the second version of his song ‘Schliesse mir die Augen beide’ (1925), to his last work, the Violin Concerto (1935), Berg grappled with efforts to establish his own identity as a modern composer while dealing with issues related to personal and artistic influences from individuals such as Wagner, Mahler, Wedekind, and Kraus, as well as the overbearing figure of Schoenberg. In contrast to his former teacher, who was openly averse to external influences, Berg embraced an array of individuals as ‘ideal identities’ (Reference SantosSantos 2014), to be played out in his creative process. In doing so, Berg combined what have been generally understood as antithetical ideas in an attempt to elevate his method of composition as an overarching system that brings together his modernistic aesthetics and the art of the past through textures in which twelve-tone serialism and tonality are interwoven.

Such an approach to composition was bound to be controversial from the very beginning, as serialism was supposed to be a logical antidote to the excesses of tonality as practised by the late Romantic composers. Because Berg’s approach to serialism embraced gestures of tonality, it also attracted criticism even from members of his own circle. In 1946, Schoenberg wrote an addendum to his essay ‘Composition with Twelve-Tones’, where he engaged in a blistering judgement of Berg’s approach:

Not accepting Berg’s explanation, Schoenberg continued: ‘Though [Berg] was right as a composer, he was wrong theoretically’ (Reference Schoenberg and SteinSchoenberg 1975a: 245). It is difficult to assess Schoenberg’s sincerity when he considered Berg to be ‘right’ as a composer while mixing serialism with tonality, as Schoenberg’s main concern as a composer was to establish relational events based on the initial idea of a composition. A piece that starts with a twelve-tone series would logically develop configurations afforded by the series, and these configurations would not be tonal. His consistent position on this issue is well documented. Schoenberg’s statement puts forward, nevertheless, a conflict between the notion of the composer as composer versus the composer as theorist, and the implication that, because Berg used tonality for ‘dramatic expression’, he was less systematic in his compositional process. Such a view has helped perpetuate the notion that Berg was ‘more Romantic’ than the other members of his circle – a view that has slowly been challenged since the autograph sources preserved at the Austrian National Library were opened to scholars in 1981.

Compounding the problem discussed above is the pervasive concept of a ‘Second Viennese School’ with the figurehead of Schoenberg followed by his ostensibly faithful pupils (Reference Auner and SimmsAuner 1999). As a result, Schoenberg’s shadow remains a long one. As Taruskin puts it, Berg was ‘formerly a pupil – and still very much a disciple – of Schoenberg’ (Reference TaruskinTaruskin 2005a: 193; my emphasis). Taruskin is not alone in subjugating Berg to Schoenberg. Berg did it himself. While dedicating his opera Lulu to Schoenberg on 28 August 1934, Berg wrote:

Such expression certainly contributed to cementing Schoenberg’s approach to twelve-tone composition as the standard for analyses, a point of departure and constant reference in the interpretation of Berg’s musical language. George Perle, who established one of the most groundbreaking frameworks for analysing Berg’s music, argues defensively that ‘Berg’s characteristic practice … significantly distinguishes his twelve-tone technique from Schoenberg’s and Webern’s’ (Reference 392PerlePerle 1989: 9). In his book Serialism, Whittall argues that ‘like his fellow Schoenberg pupil Anton Webern, Berg had followed the master into the brave new world of post-tonal and total chromaticism’ (Reference WhittallWhittall 2008: 65). While there is no denying Berg’s indebtedness to Schoenberg’s musical and intellectual mentoring in his early years, the extent to which Berg followed Schoenberg in his mature years is certainly debatable, especially after the success of his opera Wozzeck (1914–22). Moreover, Berg’s differences are evident in the ways in which his twelve-tone compositions do not fit – and surely were never meant to fit – Schoenberg’s model. Berg was keenly aware of his position and approached his method of composition as a means of establishing ‘something more genuinely Berg’ (Reference BergBerg 2014). Adorno was one of the first to recognise the unique qualities in Berg’s music and openly expressed his goal of separating him from the other members of the so-called Second Viennese School. In a parenthetical comment on a letter to Berg on 23 November 1925, he put it bluntly: ‘this prattling about the “Schoenberg pupil” must stop’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 28).

Another important feature in Berg’s music is his penchant for inscribing his works with a multiplicity of extra-musical narratives, especially programmatic and autobiographical references (Reference FlorosFloros 1994; Reference PerlePerle 2001). From Adorno’s early description of the Lyric Suite as a ‘latent opera’ to the numerous essays written about Berg’s so-called ‘secret programmes’ (Reference Jarman and PopleJarman 1997; Reference PerlePerle 2001), it is clear that these features are ingrained in his approach to the compositional process. By now, it is impossible to dissociate Berg’s compositional choices from the extra-musical significations.

Together, these features encode Berg’s music with apparent antinomies that prove to be challenging to any method of analysis. Hailey puts it best:

While contradiction and paradox may seem problematic, they are the modus operandi in Berg’s compositional process and must be considered as such. Perhaps these are the features that resonated most with Adorno and may explain in part his championing and defence of Berg’s music throughout his life. For Adorno, as Morgan Rich has demonstrated, Berg’s approach to twelve-tone serialism corresponds to his working out the concept of negative dialectics – a concept usually associated with Adorno’s late thought – and the ways in which his reflections on twelve-tone music were integral to his philosophical work. In Adorno’s view, Rich observes, ‘the strict twelve-tone style stopped the dialectical process in music. Schoenberg’s “laws” stopped the work from making a way forward’ (Reference RichRich 2016: 81). As Adorno expressed it to Berg, ‘there is only a “negative” dodecaphony, being the utmost rational borderline case of dissolution of tonality (even when tonal elements appear within dodecaphony; for then they, as a construction, are coincidental in their tonality, being simply dictated by the row!)’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 71–2). Ultimately, the apparent contradictions in Berg’s music correspond to what Adorno terms a ‘category of reflection’ (Reference AdornoAdorno 2007: 144). While Geuss has argued that Berg was not interested in Adorno’s philosophical thought (Reference Geuss and PopleGeuss 1997: 38), the possibility that a two-way exchange existed between them, and that Adorno, like many others, may have influenced Berg as well is worth considering.

Theory and Practice

As I have suggested, one of the most pervasive problems in the various analytical studies of Berg’s music relates to the ways in which Berg handles serialism and tonality in his mature works. In one of the most comprehensive analysis of Berg’s music, while favouring cyclic constructions, Headlam adopts a provocative tone: ‘Berg’s later music … is not truly twelve-tone – except for the second version of the song ‘Schliesse mir die Augen beide’ – despite the presence of rows and characteristic twelve-tone techniques. It is also not the case that Berg “fused” twelve-tone techniques with tonality’ (Reference HeadlamHeadlam 1996: 195). Referring to the Bach chorale ‘Es ist genug’ in the Violin Concerto, for instance, Headlam argues that ‘its tonal language seamlessly emerges from and dissolves into the surrounding cyclically-based passages’ (Reference HeadlamHeadlam 1996: 199–200). Whittall, arguing that we cannot ignore the highly recognisable tonal passages in Berg’s music, suggests ‘the possibility that [Berg] liked the idea of using such dramatic oppositions in non-arbitrary but still potentially disorientating ways should not be rejected out of hand’ (Reference WhittallWhittall 2008: 74–5). Clearly, as Ashby has argued, ‘serialism has become more important and specific as a historiographical marker for us than it was as a compositional device for anyone in the Schoenberg circle’ (Reference AshbyAshby 2002: 399; emphasis in original). Indeed, it should not be forgotten that, when Berg started exploring serial techniques, there was no ‘theory’ of twelve-tone music, and Berg learned from an eclectic array of sources as were available to him. A set of autograph manuscripts held at the Austrian National Library, for example, demonstrates the lengths to which Berg went in analysing Schoenberg’s Suite for Piano op. 25. Of particular significance is the way in which Berg isolates the second tetrachord of the row [G♭, E♭, A♭, D] and labels it ‘tonika’ (ÖNB Musiksammlung F21 Berg 107/i, fol. 2 v), reordering the other elements so as to form a chromatic ordered set (F21 Berg 107/i, fol. 1). In another page, Berg experiments with cyclic formations, more closely associated with his own practice than with Schoenberg’s (F21 Berg 107/i, fols. 4 and 4 v).

While revisiting the origins of Berg’s approach to twelve-tone composition, Ashby has compellingly demonstrated that Berg’s approach to serialism has close affinities with the discoveries of his student Fritz Klein, who, like Josef Matthias Hauer, may stake a claim to have generated a model of dodecaphony independent, at least to begin with, from Schoenberg’s (Reference AshbyAshby 1995). In a letter to Schoenberg on 13 July 1926 (located in Box 29, Folder 11, Arnold Schoenberg Correspondence and Other Papers, Music Division, Library of Congress, Washington DC), while explaining his conception and use of the row in the Lyric Suite, which is the same one used in ‘Schliesse mir die Augen beide’, Berg was remarkably upfront about his indebtedness to Klein, particularly his borrowing the all-interval set (Figure 5.1) and the ‘Mutterakkord’, an all-interval twelve-tone chord (Figure 5.2) (see Reference Berg, Schoenberg, Brand, Hailey and HarrisBerg and Schoenberg 1987: 349–51; Reference BergBerg 2014: 203). For Berg, the axis of symmetry and the potential tonal references within the row were particularly attractive, even if they restricted the number of possible transpositions of the series (Figure 5.3). Of significance is Berg’s concern with the hexachordal content of the series and its potential for generating cyclic structures and invariant segments, which became defining traits in his musical language.

Figure 5.1 Berg’s illustration of the row set in the Lyric Suite, borrowed from F. H. Klein (Reference BergBerg 2014: 203)

Figure 5.2 Berg’s illustration of the all-notes and all-intervals chord

Figure 5.3 Berg’s illustration of axis of rotation generating the C major and G♭ chords and scales

While Berg’s use of Klein’s all-interval set and the all-interval twelve-tone chord are the most visible markers of his influence, it was perhaps Klein’s aesthetics that provided the intellectual foundation for Berg’s approach to his later compositions. Consider Klein’s statement about the results of what he called Musikstatistik [statistics of music]: ‘Since in my statistics of music all chords, from the simple triad to the complex Mutterakkord, are equal citizens in a realm of tones (the only fair estimation!), their consequences, namely tonality and extonality, are also to be considered equal manners of expression’ (quoted in Reference AshbyAshby 1995: 72–3). This comment seems to neutralise the notion of a conflict between tonality and atonality, even suggesting a lineage between the ‘simple triad’ and the all-interval twelve-tone chord. While Berg had explored some proto-serial features in his music before 1925 (Reference 392PerlePerle 1989: 1–6; Reference HeadlamHeadlam 1996: 194–216), his earliest attempt at the twelve-tone method of composition was his second setting of Theodor Storm’s poem ‘Schliesse mir die Augen beide’. The first setting, composed in C major in 1907, was dedicated to Helene Nahowsky, his future wife; the second setting was dedicated to Hanna Fuchs, after a liaison that started in 1925 (Reference Floros, Berg and FuchsFloros, Berg, and Fuchs 2008: 54). The two pieces were originally published side by side in the periodical Die Musik in 1930 and included a dedicatory note to Emil Hertzka, in celebration of Universal Edition’s twenty-fifth anniversary, in which Berg describes the works as representing the progression of music in a quarter of a century, from tonality to twelve-tone serialism (Reference ReichReich 1930). Together, the two versions capture Berg’s teleological perspective on twelve-tone serialism, from interwoven traits of tonality latent in the formation of the series to the use of musical gestures as expressions of his autobiographical impulses. Berg’s motive for publishing the two versions side by side appears to be both an affirmation of Klein’s aesthetics and a justification for his own musical language.

Berg’s extraordinary explanation of his method advances some of the theoretical precepts that underlie both Perle’s and Headlam’s approach to analysis of his music but, more importantly, positions him, to borrow Allan Janik’s concept, as a ‘critical modernist’ (Reference JanikJanik 2001: 15–36). Although Janik applies this concept to Schoenberg, it is no less applicable to Berg, as critical modernists found it necessary to become cultural critics in order to defend the principles of logic behind musical composition and appreciation and to confront the art of the past and present as major intellectual figures had done at the time. As Born argues, such a theoretical impulse, at the onset of twelve-tone serialism, was also a defining trait of German modernism (Reference BornBorn 1995: 42). Indeed, as Hall has demonstrated, Berg’s deliberately explanatory attitude towards his compositional process and musical choices is illustrated in his numerous annotations throughout the autograph manuscripts (Reference HallHall 1997). When Adorno entitled his book Alban Berg: The Master of the Smallest Link, he had a point (Reference AdornoAdorno 1991), for it is now clear that everything in Berg’s music is set with deliberate calculation, even to the smallest detail. In his Sound Figures, Adorno goes further, claiming: ‘That means that there is not a single movement, no section, no theme, no period, no motive, nor even a single note that fails to fulfill its wholly unambiguous and unmistakable formal meaning even in the most complex contexts’ (Reference AdornoAdorno 1999a: 75–6).

The Hermeneutical Impulse

If Berg’s attention to the smallest details in the composition – and, I would add, an architectonic control over the large-scale formal structures – granted him the title of ‘master of the smallest link’, then the composition of the Violin Concerto made him the master of contradictions. The context of the composition is important. Composed at a moment of great distress in the composer’s life, when he found himself in poor health and felt rejected by his own Vienna after the rise of the National Socialist Party – performances of his work had been all but banned in the Germanic world – he felt compelled to stop working on his opera Lulu and accept the commission for the concerto from the American violinist Louis Krasner. The sum of US$1,500.00 would have been a welcome relief for his financial stress. This commission also carried the promise of future performances by the well-known virtuoso as well as the possibility for Berg to validate his own compositional techniques, particularly the juxtaposition of tonality and twelve-tone serialism.

As is well known, this work is fraught with extra-musical associations. Chief among them is the dedication to Manon Gropius, the daughter of Alma Mahler and Walter Gropius, who died in April 1935. Because of Berg’s insertion of the chorale ‘Es ist genug’ from Bach’s Cantata BWV 60 and the dedication of the concerto to ‘the memory of an angel’, the work has been interpreted as a sort of requiem, as well as a premonition of Berg’s own death, which occurred on 24 December 1935 (Reference Pople and PoplePople 1997: 224).

Since the discovery of the so-called ‘secret programmes’ in Berg’s mature works, however, it is also clear that he inscribed the concerto with autobiographical narratives, connecting his present and past experiences. As Douglas Jarman has persuasively demonstrated, the concerto contains a secret programme related to Berg’s affair with Hanna Fuchs, which had started in 1925 and presumably continued up to 1935 (Reference Jarman and PopleJarman 1997; Reference Floros, Berg and FuchsFloros, Berg, and Fuchs 2008). And much as he had done in most of his twelve-tone works from the Lyric Suite to Lulu, Berg encoded both the formal and serial structures of the concerto with elements recalling and retelling that affair. In addition, as if nostalgically referring to his past experiences, Berg included a quotation from a Carinthian folk song apparently related to his past affair with Marie Scheuchl, a maid at his family estate, with whom he had a child at the beginning of the century (Reference PoplePople 1991: 34). These features alone reaffirm Berg’s compulsion to include autobiographical inscriptions in his works. More recently, Jarman has also discussed Berg’s potential overture to the National Socialists, by incorporating the motto ‘Frisch, Fromm, Fröhlich, Frei’ (‘Fresh, Devout, Happy, Free’) as descriptors of the different sections in the Violin Concerto; he also inscribed its acrostic formed by the letters ‘FFFF’ in a manuscript for the concerto. As Jarman argues, the presence of a symbol with a close relation to German Nationalism in the sketches is deeply problematic, especially after the Nazi electoral success in 1933 and their subsequent attempt to overthrow the Austrian government in July of 1934. Whether Berg used ‘FFFF’ as a symbol of resistance, as Jarman has suggested (Reference JarmanJarman 2017), or as a ‘calculated’, opportunistic ‘rapprochement’ to the Nazi Party, as Walton has argued (Reference WaltonWalton 2014: 75), its inscription in the concerto points to a network of contradictions with different layers of meaning that defies any single interpretation.

Between the private inscriptions and public messages in the Violin Concerto, it is the highly recognisable chorale ‘Es ist genug’, presented as an instrumental reinterpretation of the original message of redemption and transcendence, that keeps inviting interpretations, because it juxtaposes the musical language of the past and present, while representing the most powerful of human experiences: fear, loss, and hope. In its original context, as Eric Chafe has demonstrated, ‘O Ewigkeit, du Donnerwort’, BWV 60 occupies a special place amongst Bach’s cantatas because of its message of redemption in death, but also because of its intricate, if not unique, tonal allegory (Reference ChafeChafe 2000: 220–40). Composed for the twenty-fourth Sunday after Trinity, this cantata presents a dialogue between two of the most extreme, and perhaps most important, human feelings embodied in the voices of ‘Fear’ and ‘Hope’ in the first three movements. Following the hermeneutics of salvation, the conflict between Fear and Hope can only be resolved through acceptance of death in Christ, whose voice in the fourth movement (‘Selig sind die Toten, die in dem Herrn sterben, von nun an’) marks the shift towards the believer’s acceptance of death and life in eternity. The final movement, ‘Es ist genug’, depicts the new consciousness of the believer, who, now with his hope restored, is ready to leave everything behind and enter ‘heaven’s house’ (‘Himmelshaus’). The original text of the chorale, written by Franz Joaquim Burmeister (1633–72) and set to music by Johann Rudolph Ahle (1625–73), reads:

In light of the conflict between Hope and Fear in the initial movements, the concluding chorale characterises, in Chafe’s words, ‘the return of the believer’s viewpoint to the world below as one that has been transformed by that vision into a new sense of peace and security’ (Reference ChafeChafe 2000: 238).

While Berg described his borrowing from ‘Es ist genug’ only briefly in a letter to Schoenberg (Reference Berg, Schoenberg, Brand, Hailey and HarrisBerg and Schoenberg 1987: 466), where he indicated the relationship between the whole-tone tetrachord of the opening melody [A, B, C♯, D♯] and the last four tones of the series (transposed, of course), he must have been aware of the message of the work as a whole. In fact, the setting of the chorale in the concerto, with the alternation between the solo violin and the clarinet ensemble (Part ii, bb. 136–54), seems to reinscribe the conflict between Fear and Hope, and the new ‘consciousness’ of the believer at the end. Berg even provides the original text underlying the orchestration of the chorale.

But even here, Berg includes contradictory elements. As Walton has observed, Berg adds expressive instructions in the score that change the eschatological message of this passage in significant ways. The clarinets, whose sound emulates an organ, are instructed to play ‘Poco più mosso, ma religioso’ whereas the solo violin, portraying the inner conflicts of the individual, undergoes a shift from ‘deciso’, ‘doloroso’, and ‘dolce’, at the beginning, to ‘risoluto’ in the middle section, and finally to ‘molto espr[essivo] e amoroso’ at the end. With these instructions, Berg effectively transforms the dialogue between Fear and Hope into expressions of spiritual and sensual love.

In effect, Berg secularised the cantata just as Oskar Kokoschka had done with a series of eleven lithographs entitled O Ewigkeit, du Donnerwort based on Bach’s Cantata BWV 60 (1914) (Reference Hüneke, Heinemann and HinrichsenHüneke 2000: 388; cf. Reference KokoschkaKokoschka 1984: 39). In the sequence of illustrations, the figures of Fear and Hope are replaced with images of Kokoschka and Alma Mahler, with whom he had a relationship around that time (Reference WeidingerWeidinger 1996: 70–1). The series is therefore an allegory of life experience. As Joseph Paul Hodin points out, in Kokoschka’s O Ewigkeit, ‘art and existence are two contradictory worlds closely linked nevertheless by the mediation of man, whose condition vacillates unceasingly between being, becoming, and fulfilment’ (Reference HodinHodin 1966: 131). Ultimately, the series represents a journey of self-knowledge. In Kokoschka’s words: ‘The knowledge that comes from personal experience has an inner force. That experience which releases man from the bondage of transient existence brings the moment of eternal truth comparable to an act of birth. It is the expression of this inner truth which is socially valuable’ (quoted in Reference HodinHodin 1966: 143). Arguably, it is this journey of self-knowledge through mediation of personal experience in art that proved attractive to Berg.

And Berg would not have missed an opportunity to meditate on matters of suffering and transcendence in the second half of the concerto, which begins with a twelve-tone chord that leads to the presentation of the chorale and the set of variations that follows. This section also allowed Berg to convey not only his musical aesthetics, one that embraces serialism and tonality as equals, but also what he considered to be his musical heritage. Of particular significance is the transition to the final section of the Concerto, the ‘Höhepunkt’ of the Allegro (bb. 125–35), which functions as a bridge to the chorale. As Headlam has observed, this section is formed by a ‘monumental combination of pitch and rhythmic cycles’ where Berg lays out eighteen chords, whose top notes comprise eleven pitches, which is complemented by the F held as a pedal in the bass (Reference HeadlamHeadlam 1996: 372). In this transition, the solo violin performs seven trichords [024] transposed cyclically at a perfect fourth while unfolding the melody of the chorale [0246]. This passage leads to the initial statement of the Bach chorale and the beginning of the Adagio section (Figure 5.4).

Figure 5.4 Pitch reduction of Berg’s Violin Concerto, Part ii, bb. 125–37; after Österreichische Nationalbibliothek Musiksammlung F21 Berg 27, fols. 20 v–21 r

More important, however, is the narrative this passage conveys. In the programme notes Berg provided to Willi Reich, he described the dramatic aspects of the concerto and the role of the solo violin in the following terms: ‘Groans and strident cries for help are heard in the orchestra, choked off by the suffocating rhythmic pressure of destruction. Finally: over a long pedal point – gradual collapse’ (Reference ReichReich 1974: 179). The solo violin unfolding the whole-tone tetrachord that opens the chorale suggests an answer to the cries for help and the important role the solo violin plays in the narrative of salvation.

Indeed, Berg makes clear that in the variations that follow the entrance of the chorale, ‘the soloist with a visible gesture, takes over the leadership of the whole body of violins and violas; gradually they all join in with his melody and rise to a mighty climax before separating back into their own parts’ (quoted in Reference ReichReich 1974: 179). Starting at bar 170, the soloist is gradually joined by the strings until the concerto reaches its climax (the ‘Höhepunkt’) in bar 186 of the Adagio. At the moment of the climax, the solo violin is indistinguishable from the rest of the strings. Then, from bar 193 to 196, the reverse occurs. The strings drop one by one until the solo violin emerges again with the series P₉ (7–11 then 0–6) above statements of ‘Es ist genug’ in the violoncellos.

While Pople has related these passages to autobiographical narratives (Reference PoplePople 1991: 37), I suggest that it is a musical rendering of Schopenhauer’s concept of compassion (Mitleid), much as Wagner had done in his opera Parsifal. An excerpt from The Basis of Morality will provide a way of framing the musical narrative of the passages discussed above, particularly with regard to the relational aspect of suffering:

The transition to the chorale suggests a complete identification between solo violin and the other strings and a sudden loss of self-identification, realising the ‘pain’ reflected in the orchestra and feeling it as its own, hence the unfolding of the whole-tone tetrachord in anticipation of the chorale. Even here, Berg meditates on his musical heritage, especially his indebtedness to Wagner’s Parsifal. In many respects, the passages above are a sort of instrumental resignification of the transformation that Parsifal undergoes as he resists Kundry’s temptation in Act Two of the opera and feels Amfortas’s pain as his own, after which he realises that only through his leadership would the order of the Knights of the Grail be redeemed. In Berg’s Violin Concerto, the soloist takes the leadership by completely identifying with the string section of the orchestra. In the ‘Höhepunkt’ all differences are eliminated, and the path to ‘redemption’ is reinforced by the variations on ‘Es ist genug’. As Nicholas Baragwanath has argued, Berg’s fascination with Parsifal was instrumental in his understanding of Mahler’s Ninth Symphony and may have been even more instrumental in the ways he conceived symmetries in his post-tonal music (Reference BaragwanathBaragwanath 2004; Reference BaragwanathBaragwanath 1999). Berg also must have understood the narrative of redemption in the opera, which informed the way he wanted the solo violin to ‘act’ in the musical narrative of redemption.

While the Violin Concerto continues to reveal extra-musical meanings and acquire new ones, the sincerity of Berg’s public dedication to Manon should not be easily dismissed (Reference WaltonWalton 2014: 85). If anything, the dedication is an indication of the close relationship between the Bergs and Alma Mahler. Writing to express her condolences to Alma Mahler after the loss of her daughter, Helene Berg made a profound statement – one that captures Berg’s own sentiments towards Alma Mahler and her daughter: ‘Mutzi was not only your child – She was also mine’ (quoted in Reference StephanStephan 1988: 36). This comment reflects not only a strong empathy but also the philosophical concept of compassion (Mitleid) that underlies the narrative of suffering and transcendence of the concerto.

The apparent contradictions, if not the eclectic nature of Berg’s music, his malleable treatment of the series, and the intersections of serialism and tonality in his mature musical language continue to cause uneasiness, especially because his music does not fit any stable analytical models available to us. Headlam’s denial ‘that Berg “fused” twelve-tone techniques with tonality’ (Reference HeadlamHeadlam 1996: 195), Pople’s notion of a ‘synthesis’ of ‘various aspects of his musical world’ (Reference Pople and PoplePople 1997: 220), Ashby’s suggestion that Berg’s use of tonality in his twelve-tone works is ‘performative’ (Reference AshbyAshby 2002: 386), and Walton’s suggestion that Berg was a calculating, opportunistic individual and that aspects of his music were possibly insincere seem to confirm the inherent ambiguity in all aspects of Berg’s mature work. Whittall provides a possible way forward, arguing that ‘Berg provided incontrovertible evidence that the “mechanics” of twelve-tone technique need not inhibit the kind of intense and personal musical expression that maintained recognizable and positive links with the expressive gestures of pre-serial composition’ (Reference WhittallWhittall 2008: 84). It is arguable, as Whittall has suggested, whether Berg saw what we perceive as contradictions to be incongruous at all, in which case the problem would be ours, depending on our set of expectations and whether we are willing to overlook aspects of Berg’s music or biography.

Entering into Anton Webern’s twelve-tone music and its complex reception history is like entering into combat with the Hydra: cleave off one head of the Webern myth, and two more grow in its place, often swinging at you from opposite directions. Understandings of late Webern range widely, from that of an intrepid pioneer who, invigorated by his amicable rivalry with his former teacher Arnold Schoenberg, like the ‘Sphinx’ paved the way for the post-war avant-garde (Reference Stravinsky and CraftStravinsky and Craft 1959: 79), to a staunch preserver and guardian of the Austro-German musical tradition committed to pouring ‘new’ music into ‘old’ forms (see Reference BaileyBailey 1991); from an abstractionist with affinities with the cubism familiar from the paintings of Paul Klee (see Reference PerloffPerloff 1983), to a composer deeply inspired by the programmatic landscape tropes evoked in so many of the poems that he chose to set to music (see Reference JohnsonJohnson 1998 and Reference Johnson1999); from a frigid and elitist rationalist looking through the falseness of Romantic subjectivity (see Reference EimertEimert 1955: 37), preoccupied by ‘logic’, ‘order’, and ‘comprehensibility’ (see Reference Webern and ReichWebern 1963), to a relentless ‘expressionist’ (see Reference QuickQuick 2011; Reference CookCook 2017) and ‘middle-brow modernist’ (see Reference MillerMiller 2020), with a heightened concern for the sensuous, ephemeral, ineffable qualities of music as sound and for whom reportedly ‘knowledge of [the] serial implications was not required for a full appreciation of [his] music’ (Reference StadlenStadlen 1958: 16); or, from a fairly apolitical citizen, to someone who forsook his support for the social-democratic movement as conductor of the Labour Symphony Concerts to become ‘an unashamed Hitler enthusiast’ (Reference RossRoss 2008: 323).

So how, then, to face the Hydra of mythologies surrounding Webern’s twelve-tone work? Taking the view that, as the polemical clamour in the halls of Darmstadt and beyond has long faded away, it is otiose to keep chopping heads in an attempt to kill off the Hydra once and for all, in this chapter I wish to lay down the sword and take a step back from the embattled scenes of the past in search of a broader vantage point. Bringing biographical insights into dialogue with analytical, philological and philosophical perspectives, this chapter argues that the crux in understanding late Webern lies in understanding that the competing, often contradictory images of the composer that have emerged pose no real contradictions after all. Instead, in the same way that the Hydra’s separate heads are essentially connected entities, these different images are best understood as mediated with one another on a deeper level, representing different aspects of one and the same all-pervasive aesthetic concern: musical lyricism.

A critical shibboleth in Webern scholarship, the category of the lyric is notoriously difficult to define. Cutting across different musical styles and genres, the lyric permeates all levels of Webern’s compositional thinking, posing considerable methodological and interpretative challenges. That said, these challenges can be reframed as heuristic opportunities and a chance to rethink the very essence of Webern’s musical imagination. As Reference AdornoTheodor W. Adorno (1999b: 93) once succinctly noted: ‘Webern never departed from [the] idea [of absolute lyricism], whether consciously or not’. In this chapter, I seek to explore, in a perhaps appropriately Webernian manner of ‘six aphorisms’, how the concept of the lyric can be understood to operate in the context of Webern’s twelve-tone music. My aim is thus not to provide a systematic overview of Webern’s late repertoire, nor do I wish to put forward any interpretations of individual works. Instead, I seek to bring into focus and trace out some of the discursive levels of the lyric as a category that arguably, indeed, strikes right at the heart of the Hydra.

Lyricism as Aesthetic Self-Identity

I wish to begin with a rather curious fact: although it seems uncontroversial to regard Webern as a genuine musical lyricist – Adornians might be inclined even to say the most important musical lyricist after Franz Schubert – interestingly Webern only began to brand himself publicly as such when Schoenberg had disclosed to the members of his circle the method of twelve-tone composition in the early 1920s (see Reference HamaoHamao 2011). That Webern would forge a public identity as a musical lyricist while simultaneously developing a new identity as a twelve-tone composer is not a purely historical contingency. At the time Webern started to experiment with Schoenberg’s new method (see Reference ShrefflerShreffler 1994: 285), he was preparing many of his earlier works for publication, following his signing with Universal Edition in 1921, including the Six Bagatelles for string quartet (to become op. 9). The score appeared in print in the summer of 1924, accompanied by an evocative and often cited preface by Schoenberg. In it, Schoenberg, pre-empting potential reservations against the bagatelles’ extreme brevity, asserted that their aphoristic nature is the result of an attempt to ‘express a novel in a single gesture, joy in a single breath’, before concluding that ‘such concentration can only be present in proportion to the absence of self-indulgence’. Built into these lines is an emphatic claim. In juxtaposing the brevity of Webern’s ‘poems’ with the lengths of ‘novels’ (all quotes cited after Reference MoldenhauerMoldenhauer 1978: 193), Schoenberg advocated for an understanding of the bagatelles as valid contributions to the formation of the musical aphorism as a genre in its own right (see Reference ObertObert 2008).

Schoenberg’s preface, albeit itself somewhat elusive and not devoid of inconsistencies (see Reference Schmusch and ObertSchmusch 2012), may have made some impression on the members of the Schoenberg circle, especially on Adorno. In 1926, the year after he had joined the circle as a private student of Alban Berg and Eduard Steuermann, Adorno published a review essay on the premiere of the Five Pieces for Orchestra op. 10, conducted by Webern himself on 22 June in Zurich, which – with explicit reference to Schoenberg’s preface – identified the concern for ‘absolute lyricism’ as the linchpin of Webern’s aesthetic (Reference Adorno, Tiedemann and SchultzAdorno 1984: 513). Adorno’s essay, initially projected as a ‘theory of the miniature’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 35), can thus be read as an attempt to reinforce the interpretative vision proffered in Schoenberg’s preface and to put it on sturdy philosophical legs.

Yet despite this intellectual kinship, Adorno was quite anxious about how Webern and Schoenberg might respond to his essay. This was for a good reason, as glimpses into his correspondence with Berg reveal. Well before the premiere took place, on 25 December 1925, Adorno had shared with Berg that he was keen to ‘measure the tragic depth of his [Webern’s] [aesthetic] position’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 35), which he was later to locate in his essay in Webern’s tendency to contract the dialectical principle into the semblance of immediate expression (Reference Adorno, Tiedemann and SchultzAdorno 1984). (It is quite conceivable that Adorno is here taking his cue from G. W. F. Hegel, who in his Lectures on Aesthetics (Reference Hegel1975: 1133–4, emphasis in the original) discussed the concept of ‘concentration’ as the ‘principle’ for the lyric, admonishing that ‘between an almost dumb conciseness and the eloquent clarity of an idea that has been fully worked out, there remains open to the lyric poet the greatest wealth of steps and nuances’.) When he did not receive any feedback from Berg on this specific matter, Adorno increasingly feared that his critical take on Webern may have led to some serious irritations, possibly alienations between him and the Schoenberg circle. It was thus ‘particularly gratifying’ to him to eventually see that Berg, ever generous in his judgements and support, had only kind and approving things to say about the essay upon its publication. Reading between the lines of Berg’s response indicates, however, that Webern and Schoenberg may have been less enthusiastic. Alluding to past frictions and tensions, Berg warned Adorno that ‘a few words and turns of phrase … will once more cause offence’. In his reply, aiming to smooth potentially agitated waters, Adorno assured Berg that he had ‘increasingly warmed to his [Webern’s] works’ over the course of time and that ‘some of them … truly contain some of the purest, most beautiful lyricism that there is’, before setting great store by the fact that it is ‘precisely’ the ‘forlornness’ so palpable in Webern’s music, both at a ‘private’ and ‘historical’ level, ‘that lends it its radiance’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 57–60). It is in this sense, he implied, that his (few) critical remarks would be misconstrued if taken as self-indulgent cavilling. Instead, his initial instinct to cast Webern’s concern for ‘absolute lyricism’ in an ambivalent – to recall his own choice of wording, ‘tragic’ – light, pace Schoenberg’s much more affirmative interpretation, is undergirded by the hope that his review may actually help bolster (rather than damage) Webern’s reputation. As Adorno once envisioned with confidence, his work on Webern, not despite but because of its critical overtones, would ‘tactically … certainly be of advantage to him [Webern]’ (Reference Adorno, Berg and LonitzAdorno and Berg 2005: 35, emphasis in original).

Indeed, there is good evidence that Webern recognised the ‘tactical’ value of Schoenberg and Adorno’s writings on his aphoristic music and in fact aligned himself with their interpretations in moments where he found himself cast in a defensive position. So, for instance, in a letter to his publisher Emil Hertzka from 6 December 1927, Reference WebernWebern (1959: 15) used an expression that palpably echoes Adorno’s phrase of ‘absolute lyricism’: ‘I know, of course, that my work has very little importance regarded purely commercially. The cause of this lies in its almost exclusively lyrical nature [!] up to now; poems do not bring in much money, but after all they still have to be written.’ And in a letter dated 4 September 1931 to the conductor Hermann Scherchen, Reference WebernWebern (1945/6: 390) launched an apologetic defence of his aphoristic works clearly alluding to Schoenberg’s preface: ‘sometimes it takes a whole novel to express a single thought; and sometimes no less substantial or few thoughts are condensed into a single short poem’.

The striking confidence with which Webern, at this critical stage in his creative development, projected a public image of himself as a musical lyricist opens up some wide-ranging perspectives. Perhaps the question about Webern’s lyrical style is not one of ‘style’ at all, but rather his attitude towards the stylistic means and devices available to him at a given time and the ‘ideas’ he sought to express. In this precise sense, Webern did not compose in a certain ‘style’ – the style of ‘dodecaphony’, ‘free atonality’, or ‘late Romanticism’ – but in the ambit of lyricism. Much of the fascination that thus comes with Webern’s music lies in the sheer plethora of unique strategies that it presents to articulate highly expressive and distinctive physiognomies of the lyric.

Lyricism as Space

For the purpose of studying the ways the category of the lyric has shaped Webern’s twelve-tone thinking, his famous lecture series on The Path to the New Music (1932–3) provides some first insights. Although the lyric finds no mention in it, Webern can be shown to interpret some of the key concepts and ideas therein expounded in a decisively ‘lyrical’ light. To illustrate this issue, Webern’s curious ashtray example, presented in his lecture of 26 February 1932, is a particularly pertinent case in point. Having advocated the view that the ‘urge to create coherence [Zusammenhang] has … been felt by all the masters of the past’ (a view iterated at various stages), Webern (once again) finds himself in a position where he feels pressed to offer an explanation of what the concept of musical coherence means. Not a man of words, Webern, apparently impromptu, seeks to illuminate the issue as follows: ‘An ashtray, seen from all sides, is always the same, and yet different.’ And he adds: ‘So an idea should be presented in the most multifarious way possible’ (Reference Webern and ReichWebern 1963: 53).

While one might imagine (with some delight) Webern swirling an ashtray through the air – first holding it up still, before flipping it around again and again – the question begins to emerge what this discussion really reveals about his understanding of musical coherence. Indeed, many of the examples that Webern presents – the treatment of fugal subjects in J. S. Bach’s Musical Offering, the motivic-thematic processes in the finale of Beethoven’s Ninth Symphony, and the developing variations characterising Schoenberg’s First String Quartet op. 7 – suggest a reading of the term that renders it essentially a linear-developmental principle hingeing on the notion of becoming (see Reference Webern and ReichWebern 1963: 35, 52, and 58). Positing these examples with respect to Webern’s discussion might thus lead to an expectation that he would describe the ashtray as the subject of an (irreversible) temporal process – for example, by pondering what it would take for it to be transformed into a different object, say, a pile of fragments. This, however, is not the case. Instead, Webern’s discussion implies that it is the observer’s perspective on the ashtray that changes, while the ashtray itself remains the same. Thus, for Webern, the ‘multifariousness’ that he contends should arise from the presentation of a single musical ‘idea’ does not – in contrast to his many music examples – originate from a genealogical but a perspectival mode of musical thinking, a mode of thinking that Reference Ligeti, Metzger and RiehnGyörgy Ligeti (1984: 104) saw as the fundamental crux of Webern’s late aesthetic: the tendency ‘to treat musical time in such a way as to treat it as a spatial phenomenon’.

These nested inconsistencies can also be discerned in other parts of Webern’s lectures, such as in his famous discussion of Goethe’s ‘primeval plant’ (Urpflanze). Enshrouded in some esoteric-philosophical ideas about nature and art’s relationship to it, in Webern’s hands the Goethean primeval plant shines forth as nothing less than a (vexed) mirror of aesthetic self-legitimation. On some level, Webern conveniently exploits the genealogical epistemology built into it, both in historical and musical terms. In particular, he avers that the development of the twelve-tone method is the logical consequence of music history as evolutionary progress, and he moreover contends that the concern of past composers ‘to create unity in the accompaniment, to work thematically, to derive everything from one thing’ breathes new air in the domain of twelve-tone composition. However, in other moments of his discussion he, inexplicitly, reverses this genealogical notion into its opposite, a static one. Insomuch as the twelve-tone technique, as an ‘underlying’ method, always already guarantees ‘unity’ and ‘comprehensibility’, he argues, for instance, it has become possible to ‘treat thematic technique much more freely’, before once more making recourse to Goethe’s primeval plant but now – notably – as a paradigmatic model of structural identity: ‘the root is in fact no different from the stalk, the stalk no different from the leaf, and the leaf no different from the flower: variations of the same’ (Reference Webern and ReichWebern 1963: 40 and 53).

By pointing out these subtle yet fundamental shifts in his explications, I do not wish to suggest that there is anything wrong (or right) with Webern’s discussion. My concern is rather with the ways in which these shifts reveal a constitutive tension in Webern’s musical thinking, one that arguably tends to become all too quickly obfuscated once the categories and ideas expounded in his lectures are taken at face value or considered no more than blueprints of Schoenberg’s theorisation of the concept of musikalischer Gedanke (see Reference Schoenberg, Carpenter and NeffSchoenberg 1995). To rephrase the issue in a heretical way: what would be gained, what would be lost, by taking the sceptical-contemplative view that the late Webern may not have understood himself – or, for that matter, Schoenberg?

Lyricism as ‘Variations of the Same’

In seeking to explore the implications of his ashtray example and his discussion of the Goethean primeval plant, it seems apt to attend to Webern’s ubiquitous use of structural symmetries and permutations. Often couched in terms of a complex dialectic between ‘construction’ and ‘expression’, these salient features in Webern’s music have been the subject of enormous analytical efforts. In the following, I will draw upon two theoretical conceptions of harmonic space – the intervallic and transformational ones – as ways of exploring how Webern’s axiomatic concern for ‘variations of the same’ can be considered in analytical terms.

Figure 6.1 presents the opening of the string trio fragment M. 273, Webern’s second fully fledged foray into the ‘composition with twelve notes’ in the domain of instrumental music, drafted in spring 1925 a few months after the completion of the Kinderstück M. 267. These bars set up a ‘traditional’ discursivity that evokes the expectation of a ‘developmental’ motion: a two-bar fanfare-like homophonic ‘introduction’ is eventually broken up and ‘liquidised’ into a quasi-polyphonic presentation of distinct ‘motivic’ gestures. In what sense do these two units ‘cohere’ (zusammenhängen)? At first, this passage seems to instantiate a typical case of ‘developing variation’: the gestures emerging in b. 3 are individuated and timbrally distinct yet still operate within the harmonic and rhythmic scope set out in the opening two bars. More specifically, they are based on the melodic contents articulated in bb. 1–2, in other voices: violin 1 harks back to violin 2; and violin 2 and cello hark back to violin 1. This suggests that, in bb. 3ff., Webern was keen to expand the harmonic-rhythmic world conjured up in the opening two bars in a new textural guise.

Figure 6.1 Webern, string trio fragment, M. 273, bb. 1–5 and 2{a}, accompanied by some analytical annotations, based on a transcription of the manuscripts and sketches as provided in Reference WörnerWörner (2003: 75 and 88); the sources are archived at the Paul Sacher Foundation, Basel

Yet Webern’s sensibilities for variation arguably cut a layer deeper. The opening two bars present two complementary chromatic six-note aggregates, effectively yielding the first iteration of the fragment’s twelve-tone row: G♮, F♯, C♯, C♮, G♯, A♮, D♮, E♭, E♮, F♮, B♮, B♭. As Reference WörnerFelix Wörner (2003: 77–80) has pointed out, this row is fashioned from three consecutive statements of the symmetrical tetrachord 4–9, the constructive significance of which is highlighted by the linear motions of each voice. On the most fundamental level, one can thus understand bb. 1–2 as establishing two diametrically opposing ‘harmonies’: 6–1 (for the sake of simplicity hereafter conceived as the subset 4–1) featuring the maximised semitone (ic1), and 4–9 featuring the maximised tritone (ic6). Approached through the lens of pitch-class set theory, it is thus possible to read both chords as part of a strategy to stake out the full scope of the interval vector space, with 4–7 (in the second violin and cello) acting as the oscillating centre between both poles (Table 6.1). A fingerprint of Webern’s free-atonal and dodecaphonic music, such interval vector space opens up a vast array of possibilities to move, in a Schubertian manner, through ‘variations’, within a defined landscape.

Closer examination of these bars, including Webern’s revision of b. 2{a}, further suggests that the interval vector space may be construed as itself being, rather than the origin, the emergent product of a ‘variational’ process. As the philological reconstruction provided by Reference WörnerWörner (2003: 70–95) reveals, Webern revised b. 2{a} so as to complement the six-note aggregate presented in b. 1 and hence to obtain a statement of the full chromatic scale. This adjustment, however, comes at the price of what seems at first an infelicitous inconsistency: the first trichord in b. 2 changes from 3–3 (used throughout bb. 1 and 2{a}) to 3–2. Yet interestingly enough, when cast in the light of Klumpenhouwer network theory (‘K-nets’), this new chord (3–2) can be interpreted as sharing the same transformational logic as the opening trichord (3–3) from b. 1 (Figure 6.2a). It is, of course, not uncommon that chords with different interval properties feature an identical set of transformations. In this specific context, however, it seems not implausible to ascertain a certain degree of transformational consistency. For instance, the tetrachords 4–1, 4–7, and 4–9 shown in Figures 6.2b and 6.2c can all be construed as hingeing on the same (strongly isographic, <T₀>) transformation as said trichords from bb. 1 and 2. This analytical perspective has implications for an understanding of the semitone (ic1) which so conspicuously permeates these bars. While the ‘relational abundance’ of K-nets prompts intricate questions (not least) about the phenomenological viability of K-net-derived analytical insights (see Reference BuchlerBuchler 2007), this perspective renders the semitone conceivable as the ‘identical’ subject of a transformational ‘variation’. Thus what one hears on a material level are de facto actualisations of virtualities, indeed not dissimilar from Gilles Deleuze’s conception of the term as the differential condition of all that which manifests itself as real experience (Reference DeleuzeDeleuze 1997: chapter 4; see also Reference AhrendAhrend 2017: 34–9). Such observations offer some fascinating glimpses into the philosophical and compositional complexities of Webern’s lyrical imagination, suggesting that his concern for ‘variations of the same’ is inextricably bound up with a fundamentally altered conception of musical temporality and phenomenology.

Figures 6.2a, b, c Klumpenhouwer network interpretation of Webern’s string trio fragment M. 273, bb. 1–2 and 2{a}, as defined by Reference LewinLewin (1990) and Reference KlumpenhouwerKlumpenhouwer (1991)

Lyricism as Song

Within the topographies of Webern’s lyrical thinking, the genre of the song marks a particularly intimate place, to the extent that its significance in the context of his adaptation of Schoenberg’s twelve-tone method can hardly be overstated. At the time Schoenberg ‘discovered’ the twelve-tone technique, Webern in fact had been on a long hiatus from the composition of instrumental music. As Anne Reference ShrefflerShreffler (1994: esp. 279) has pointed out, Webern’s decision to exclusively focus on the composition of texted music following the completion of the Three Little Pieces for Violoncello and Piano op. 11 in June 1914 was above all a response to the struggles he felt during these years to compose longer works. When Webern thus turned, in the summer of 1922 with the song ‘Mein Weg geht jetzt vorüber’ op. 15/4, to the ‘composition with twelve tones’, this was not born out of an acute artistic ‘crisis’; rather, the twelve-tone technique primarily served him then as an expressive device, one of many in his toolbox, to convey musically the semantic qualities and envoiced subjectivities he sensed radiating from the poems he chose. (This may help to explain why, baffling to many, Webern’s adaptation of Schoenberg’s technique did not develop in a stepwise, evolutionary fashion but took place over many years with varying degrees of engagement and complexity.)

The fragment M. 276 for a song based on Peter Rosegger’s poem ‘Dein Leib geht jetzt der Erde zu’ allows some insightful glimpses into Webern’s working method at this critical time in the genre of texted music. As its place within the sketchbook (known as ‘Sketchbook i’) reveals, Webern began drafting ‘Dein Leib geht jetzt der Erde zu’ during the summer of 1925, at a time when he was working intensively on songs that were later to become his cycles opp. 17 and 18 (cf. Reference LynnLynn 1992: 76–9; Reference BuschBusch 2020: 211–3); as the instrumentation suggests, it seems in fact probable that the song was initially intended to be included as part of the op. 17 cycle which contains with ‘Liebste Jungfrau’ another song set to a poem from the same source, Das Buch der Novellen i (cf. Reference ShrefflerShreffler 1994: 321; Reference KaiserKaiser 2013: 106–8).

The sketch begins with a melody which is based on all twelve tones of the chromatic scale (Figure 6.3a). In the system underneath, Webern set out a(nother) twelve-tone row (placed in the centre of the sheet) which conspicuously features some of the intervals from the melody (Figure 6.3b): C♯, C♮, B♮, E♭, B♭, A♮, G♯, G♮, D♮, F♯, F♮, E♮ (Figure 6.3c). Webern, then, subdivided the row into three smaller units: two hexachords (as indicated by a double bar line), three groups of four notes (as indicated by two dashed bar lines), and four groups of three notes (as indicated by slurs). In fact, the interval content of the row reveals that it is vertically mirrored. As a corollary to these intervallic properties, the row features three symmetrical tetrachords – 4–1 (B♭, A♮, G♯, G♮), 4–7 (C♯, C♮, F♮, E♮), and 4–9 (C♮, B♮, F♯, F♮) – staking out, once more in the way illustrated in Table 6.1, the entire interval vector space (Figure 6.3d). These observations suggest that Webern did not conceive of the symmetrical dispositions of the twelve-tone row in a vacuum. While it is difficult to ascertain the exact relationship between the melody from the first system and the gestation of the row, it seems not far-fetched to understand the row as the product of a concern to first of all distil some of the intervallic features as borne out by the compositional ‘impulse’ he perceived when reading the poem, and to make these features constitutive for the whole song. In this sense, the ostensibly ‘rational’ construction of the row with all its absorbing symmetrical properties originates from a poetological – ‘irrational’ – place.

Figures 6.3a, b, c, d Webern, ‘Dein Leib geht jetzt der Erde zu’, M. 276: transcription of the sketch of the first melodic idea and twelve-tone row, ‘Sketchbook i’, p. 11, archived at the Morgan Library & Museum, New York, accompanied by some annotations highlighting the constitution of the interval vector space as illustrated in Table 6.1

After defining the basic harmonic material, Webern begins with the actual compositional process of the song (as it were). The sketches are complex, showing various drafts for individual passages. However, it is not difficult to stitch the sketches together into what could be considered a ‘complete’ version of the first stanza (Figure 6.4; cf. also Reference AsaiAsai (2021), 144–9). Through this reconstruction, it becomes evident that the musical fabric is fashioned out of two independent twelve-tone tracks (based on the same row, P₀), set out in the voice and the instrumental group. This gives the effect that the instrumental group is an iridescent reflection of the vocal line, thereby intensifying the elegiac qualities evoked by the text.

Figure 6.4 Reconstruction (modified transcription) of Webern’s fragment ‘Dein Leib geht jetzt der Erde zu’, M. 276, ‘Sketchbook i’, p. 11, archived at The Morgan Library & Museum, New York

Webern begins the compositional process by setting out the melody for the first two lines (which right from its inception seems to be set in stone): ‘Dein Leib geht jetzt der Erde zu, / Woher er ist gekommen.’ Webern is here clearly guided by a concern to use all twelve notes of the row, and to do so in such a way that the twelve notes are distributed equally over the two lines. This concern to map the twelve notes onto the formal structure of the poem, however, may have posed some practical challenges for Webern insomuch as the number of syllables used in each line (eight and seven, respectively) does not match the number of notes reserved for each of them (six). The compositional solution Webern finds is insightful. Rather than ignoring the irregular number of syllables and sticking rigorously to the distribution of one note per syllable, he makes a few adjustments: he repeats the first, second and seventh notes so as to maintain the even distribution of six plus six notes per line. In this way, he aligns the presentation of the twelve-tone row with the predetermined formal structure of the text. Curiously, for the stanza’s third and fourth lines – ‘Der Seel’ wünscht man die ewige Ruh’, / Bei Gott und allen Frommen’ – Webern at first seems to take a more flexible approach. He reserves for the nine-syllable third line the first seven (not six) notes of the row; and for the seven-syllable fourth line he in fact adds one note, setting out the word ‘allen’ as a three-note melisma. As a result, the row is used up before the fourth line has come to an end. But this decision, too, is quite conceivably motivated by a form-syntactical consideration. The notes used for the line’s last word ‘Frommen’ are yet again recruited from the beginning of the row, lending the stanza a framing effect which is possibly intended to contribute to a sense of closure while at the same time offering interlocking options for continuation.

Webern appears to have abandoned his work on the song at this advanced stage. The reasons may remain unknown. It would be his last setting of a poem by Rosegger. He would thereafter devote himself exclusively to the poetry of Hildegard Jone, an artistic connection that would inspire with the Three Songs from ‘Viae inviae’ op. 23, the Three Songs op. 25, Das Augenlicht op. 26, and the two Cantatas opp. 29 and 31, some of his most iconic explorations of the dialectical relationship between vocal expressivity and musical construction.

Lyricism as Silence

The Symphony op. 21, completed in June 1928, three years after the string trio fragment M. 273 and ‘Dein Leib geht jetzt der Erde zu’ M. 276, is commonly considered to mark a sea change in the development of Webern’s late style. Already some cursory glimpses into the field of metaphors that emerged right after Webern’s death may give a taste. In his 1949 monograph on Schoenberg and His School, Reference LeibowitzRené Leibowitz (1949b: 210–7) discerned in Webern’s Symphony a turn to ‘greatest purity’ and an ‘extraordinary economy of means’, identifying in the work’s ‘almost complete immobility’ a tendency towards the ‘emission of isolated tones’. This mode of reception, which would only a few years later inspire Herbert Eimert’s (controversial) coinage of the term ‘pointillism’, was also shared by Reference Adorno and SchwarzAdorno (2015: 18) who, though considerably more sceptical in his philosophical assessment, similarly saw in the Symphony a ‘peculiar [penchant for] simplification [eigentümliche Simplifizierung]’ and sense of ‘utmost demureness [grösste Zurückhaltung]’. How profoundly puzzling and enigmatic Webernians found the stylistic veneer of the post-op. 21 works is perhaps particularly apparent in a fervid exchange between Franz Krämer and Glenn Gould:

Purity, simplification, reticence. Despite the profusion of metaphors used to describe Webern’s ostensibly new lyrical style, there is a shared understanding that the post-op. 21 works evoke a strange sense of silence. Indeed, Webern’s treatment of the rest as a constructive rather than rhetorical device (cf. Reference LoLo 2015; Reference SyroyidSyroyid 2020) was considered such a defining feature of the late works that, in his lectures on ‘Twentieth-Century Tendencies in Music’, held at Columbia University from July to August 1948, Edgard Varèse heralded Webern as ‘the poet of the pianissimo, of mystery and silence’ (typescript, Edgard Varèse Collection, Paul Sacher Foundation). In fact this trope was so pervasive that only seven years later Reference EimertEimert (1955: 36) was able to call it a ‘cliché [Klischeebild]’.

A representative example of the idiolect that has sparked this mode of reception is Webern’s final variation (coda) from the second movement of the Symphony (Figure 6.5a). Built on the basic row and its retrograde, this passage largely comprises individual dyads, melodic fragments, and, indeed, a striking number of rests which are directly tied to the harmonic-formal organisation. Three out of the eleven bars in fact have full bar rests, and the use of compound crotchet rests adds to the scene two more ‘silences’ of roughly the same length. (The sense of ‘symmetrical’ lengths is obfuscated by the change of tempo.) The setting of the row running simultaneously ‘forwards’ and ‘backwards’ corresponds with the symmetrical rhythmic-formal disposition: as shown in Figure 6.5b, the passage is mirrored in b. 94. Fed into such a constructive metabolism, these crotchet and full bar rests can be considered to mark a negative presence. It is in this precise sense that in Webern the ‘silence’, structurally determined, enters the status of ‘material’, and thus is materialised.

Figures 6.5a and b Webern, Symphony, op. 21/ii, final variation (reduction), accompanied by some analytical annotations

Given the tight relationship between rests and harmonic organisation, it is not hard to see why this type of musical thinking was regarded as a precursor to what Reference StockhausenKarlheinz Stockhausen (1959: 12) came to identify as the cornerstone of post-war serialism: the ‘attempt to put the time-proportions of the elements in order, by means of a series’. Any such ‘proto-serial’ interpretation of Webern is not uncontroversial, however. As can be glimpsed in Peter Stadlen’s first-hand account, Webern considered the Symphony by no means a caesura in his development but rather a natural continuation of the expressive idiom that he had cultivated in his previous works. Going into detail about Webern’s disappointment when a performance of the Symphony in Vienna (to which Stadlen had accompanied him) reduced the work to no more than ‘seemingly unconnected little shrieks and moans’, Stadlen reports that the dissatisfied composer, by that time himself a much-celebrated conductor, demonstrated to him how the music was initially conceived – namely, essentially, as a rich discourse of expressive gestures. Stadlen takes this discrepancy as the starting point for a razor-sharp reflection. Relating the difficulties in communicating to the musicians the plasticity of embodiment Webern was apparently hoping to obtain to issues of ‘metrical complexity’, he wrote: ‘not too many things going on at the same time, but too few things at the required time … and so we are robbed of one of the basic prerequisites of all musical understanding: our ability to feel the regular beat of the metre and to relate to it the rhythms we listen to’ (Reference StadlenStadlen 1958: 10–6). Indeed, as Reference BaileyKathryn Bailey (1995) has shown based on a philologically rigorous analysis of the sketches for the Symphony op. 21, the Piano Variations op. 27, and the String Quartet op. 28, there is good evidence that Webern treated rhythm and metre as two fairly independent parameters, to the extent that he, seemingly with ease, could change the metre of whole passages at various stages throughout the compositional process apparently without fearing that these surgeries might interfere with the rhythmic identity of the gestures he sought to express.

These insights, I wish to venture, can be interpreted as bringing yet another lyrical quality of Webern’s ‘silences’ to the fore, one that is less defined by virtue of their (material) ‘presence’ but rather the engendering of what could be termed (phenomenological) ‘presencing’. As suggested in Figure 6.5c, the ‘pulse’ of the Symphony’s final variation, though notated in $\begin{array}{c}2\\ 4\end{array}$ , can no less (im)plausibly be heard in $\begin{array}{c}3\\ 4\end{array}$ . This metrical vacillation causes a bewildering effect. While due to the symmetrical setting the final gesture F♮⁵–B♮² falls, unlike in the corresponding b. 89, onto the second (weak) beat of the bar, if conceived in triple metre this gesture falls yet again onto the first (strong) beat. In so doing, it insinuates a sense of continuation that never materialises. Couched in Edmund Husserl’s terminology, the consecutive triple-metre pulse can thus be understood as instantiating a trace of ‘retentive memory’ through which, virtually, the final gesture – ‘protentively’ – travels beyond the final bar line. In this sense, the final gesture is at once ‘closing’ the work and staring into the ‘openness’, freezing in this climate of structural ambivalence to a ‘tone-now [Tonjetzt]’ (Reference Husserl and HeideggerHusserl 1964: §§11, 38, and 39) that, ecstatically, seemingly stands outside of time.

Lyricism as Politics

As deeply fascinating as Webern’s lyrical imagination is on some level, it undeniably also comprises a troubling political dimension. This is perhaps nowhere else more poignantly encapsulated than in his admiration for the poetry of Stefan George. Webern had set several of George’s poems to music around 1907 to 1909, the famous years in which he had embarked upon his self-proclaimed ‘path’ to atonality, and published many of them between 1919 and 1923 as opp. 2–4. Later in his life, Webern seems to have seen his interest in George’s poetry vindicated, through disturbing signs. As Hans and Rosaleen Reference MoldenhauerMoldenhauer (1978: 526–32) were able to reconstruct, in a letter to his friend Josef Hüber in December 1940 Webern heralded George’s poem collections The Star of the Covenant and The New Reich as prophecies of a new social world order that he saw now – at a time the Wehrmacht had invaded Poland, Denmark, Norway, the Netherlands, Belgium, Luxembourg, and France, and Mussolini’s Italy had occupied parts of north Africa – become reality. And still two years later – following the Wehrmacht’s first setbacks – he evidently turned to George’s poetry as a source for optimism (see also Reference BaileyBailey 1998: ch. 8, esp. 172–3). To be sure, the sources known today indicate that Webern’s views of National Socialism may have been more ambiguous than an isolated reading of his correspondence with Hüber suggests (see Reference KronesKrones 1999). But these biographical documents do raise some far-reaching questions. While Webern’s interest in poetry itself may not have instigated his enthusiasm for the war, it stands to reason that he, personally prone to succumbing to authorities and consistently in pursuit of securities and stabilities in his private life, found in the new-symbolist tropes he felt so drawn to throughout his lifetime a resonance chamber for a type of identity-thinking that retrospectively tallied all too well with Nazi ideology. This renders Webern’s musical lyricism, as little as it seems to have in common with Nazi cultural politics at first glance, politically septic.

The question however of how, if at all, this ideological dimension is manifest in the fibre of Webern’s compositional thinking taps into some formidable methodological challenges. For Reference TaruskinRichard Taruskin (2009: 397; see also Reference Taruskin2005a: 734–41), the case is surprisingly clear. With reference to the heaped occurrences of the B-A-C-H cipher through the technically ‘dehumanised’ String Quartet op. 28, he paints a picture of Webern (alongside Schoenberg) as a relentless ‘chauvinist’ for whom ‘Bach was a third Bach, a national as well as a universal figurehead … [whose] elaboration of the technique of absolute music … vouchsafed German domination’. And he proceeds to cock a snook at Carl Dahlhaus as the key post-Adornian advocate for the concept of aesthetic autonomy, contending with heretic joy that not even Webern’s ‘absolute’ music is unencumbered from ideology.

Once read as calling out large strands of Webern reception for depoliticising the composer, Taruskin’s biting polemical attack, while valuable, arguably throws the baby out with the bathwater. By stripping the concept of aesthetic autonomy from the heuristic potential it holds for understanding the relationship between music and politics, Taruskin’s account may be considered somewhat myopic. As Reference JohnsonJulian Johnson (1999: 223) has argued, ‘art does not offer a critique of society by having nothing to do with it, but by reordering and reformulating social categories in aesthetic form’. With Johnson’s caveat in mind, identifying musical ciphers as if they were traffic signs is in effect to retreat to an essentialist position, one that arguably all too quickly runs aground at the question of how these meanings are negotiated in the individual work. Indeed, as Reference Ahrend, Heister and SparrerThomas Ahrend (2018: 32) has suggested, the musical structures to which Webern’s particular ‘psycho-social disposition’ gave rise are best understood as fulfilling an aesthetic rather than a personal function, and thus ‘dynamised’ in the individual work they may as a matter of fact ‘undermine [their initial status as] merely preconceived representations of order’.

The irony is that Taruskin, if he had been willing to pursue a perspective drawing on aesthetic autonomy, could have found in his arch-enemy Adorno a well-disposed interlocutor. Adorno remained wary of certain aspects of Webern’s aesthetics throughout his lifetime. In particular, in his post-war writings on the composer it becomes palpable how he recoiled from Webern’s late works. ‘The fear that the act of composition might damage the notes leads to a vanishment [of subjectivity] … hardly anything happens anymore; intentions [in the music] scarcely make any impression, and instead he [Webern] sits in front of his notes and their basic relationships with his hands folded as if in prayer’. In my reading, the issue for Adorno was thus not simply that in Webern the rational patina of the twelve-tone method had hardened into the dogma of orders (Gesetze) but, more specifically, that the ‘rich interplay’ facilitated through this hardening produced no musical moments of immanent transcendence (Reference AdornoAdorno 1999b: 101–2, translation amended). What Adorno recognised was rather that the differential relations – Reference WhittallArnold Whittall (1987) felicitously speaks of ‘multiple meanings’ – woven into Webern’s tightly controlled fabric annul any motions of even the slightest dialectical sparkle, into a state of ‘oscillations’ (see Reference Ahrend, Heister and SparrerAhrend 2018: 32). To overstate the issue slightly: in his search for ‘Hegel’ in a desperate attempt to save the dialectic in Webern, Adorno only found that the composer had turned the quasi-Heideggerian vice of tautological ontology into a virtue. Adorno, the Hegelian, captured this critical twist in his own appropriately dialectical terms, as follows: ‘In Hegel’s Phenomenology we encounter at one point the disconcerting phrase “fury of disappearance”: Webern’s work converted this into his angel’ (Reference AdornoAdorno 1999b: 94). Put differently, what made Webern’s ‘absolute lyricism’ so ‘tragic’ for Adorno is that it remains precisely underdetermined as to whether it obsecrates unity (‘variations of the same’) or difference (‘variations of the same’).

There is a remarkable moment in the third movement of the First Cantata op. 29 that allows some deep glimpses into what, in a post-Adornian vein, I like to think of as Webern’s musical obsecration (Figure 6.6). Entrenched in the theosophical discourses of its time (see Reference AbbateAbbate 2018), the text that Webern chose to set – an extract from a (lost) poem entitled ‘Transfiguration of the Charites [Verwandlung der Chariten]’ which Jone had sent to him in early 1939 – casts Apollo’s music for the Gods in the light of solemn metamorphosis. According to Jone’s own interpretation (Reference Jone1959: 7), the ‘Verwandlung’ mentioned in the title rests essentially on three steps: firstly, the text associates Apollo’s music-making with ‘inexpressibly melancholy’, the ‘deities’ of which are then ‘silenced’ and ‘absorbed in … eternal meaning’, before eventually an ‘amazing transformation takes place’ that amounts to a revelation of ‘joyful astonishment’. The final lines read: ‘Charis, the gift of the highest: the grace of mercy glistens! / bestows herself in the darkness of the developing heart as dew of perfection [Vollendung]’. The way Webern musically renders the ‘silencing’ of the ‘deities of melancholy’ is aesthetically insightful. Following a transition played in the strings and harp that unmistakably represents Apollo’s ‘blessed strings’ (bb. 34–8), to the words ‘all the former names have faded away in sounds’ the music eventually bursts out quietly into a fully fledged arrangement, with four different rows running in parallel (using notably all four row types on the same transposition step), played in stretto, and which ‘liquidises’ the two subjects staged in the opening through tightly knit fugal-variational processes (bb. 39–43) (see Reference BaileyBailey 1991: 292–302, 342, 396–7). It is as if Apollo’s ‘sound’ has collapsed onto itself, and we now, in piano, begin to vaguely gain a sense of the ‘former names’ reverberating before they ‘fade away’ into oblivion. This compositional realisation, it strikes me, epitomises the aesthetic model of Webern’s musical obsecration. By literally sounding out the structural-semantic depths of Apollo’s ‘sound’, this passage, highly differentiated, asserts only itself, rendering the notions of transcendence and presence in terms of an ontological double-bind.

Figure 6.6 Webern, Cantata No. 1, op. 29/iii, bb. 34–43 (reduction)

How can this passage be understood in political terms? Webern turned to the composition of the Cantata four months after the annexation of Austria into Nazi Germany and apparently found in this text the appropriate missing piece to bring this work to completion. In her contribution to the special Webern issue of Die Reihe, published ten years after the end of the Second World War, Jone invited a reading of the Cantata essentially as an anti-war piece of music, as a piece of consolation and comfort composed during the darkest of times. Recalling how she had heard the Cantata for the first time in August 1940, in the company of Webern and his student Ludwig Zenk, she wrote (not timid about speaking for all three of them): ‘the music, heard by us here in the neighbourhood of the bells, is no other than the sparkle of the grace of Grace, in the midst of the war. We cannot forget the war while listening to the music, but we are given something to take back into the dark with us and to give us light’ (Reference JoneJone 1959: 7). This account seems difficult to square with all the evidence known to us today about the war enthusiasm Webern (and Zenk) harboured at that time (see Reference HommesHommes 2010). Without meaning to perpetuate superfluous speculations over Webern’s intentions, one may wonder whether it is not also conceivable that Webern construed the text in a nationalistic-heroic light and specifically perceived in the ‘former names’ reverberating through Apollo’s ‘melancholic’ sound those not-yet-realised forces that he also perceived in George’s poetic vision. But if that was the case, the redemptive power of transcendence Jone claimed to be inscribed into Webern’s setting would stand revealed as the ultimate terror of presence. Was Webern’s other-worldly lyricism – according to Reference EimertEimert (1959: 32), ‘an outsider’s world in the extremest sense’ – perhaps all too painfully worldly after all?

Milton Babbitt has regularly been accepted as one of the earliest adopters of what has come to be known as integral, total, or, most often in its European flavour, multiple serialism. Many European composers of the mid-twentieth century, including Pierre Boulez, Karlheinz Stockhausen, Luigi Nono, and Jean Barraqué have been central to this movement, and painted with a broader brush, it would include contributions by the likes of Olivier Messiaen and Elizabeth Lutyens. What sets Babbitt apart from this group encompasses both his compositional techniques and his roots as an American musician. In the following, I will concentrate on the former, with at the very least an awareness of the latter.

Milton Babbitt grew up in the city of Jackson, Mississippi, but also spent a significant amount of time with a branch of his family in Philadelphia. He played the clarinet from an early age and was a member of a variety of ensembles during those years. His awareness of musical structure would seem to be precocious. He narrates becoming aware of local and long-range note relationships in a performance of Weber’s Oberon overture and mentioned on several occasions receiving scores of modernist music, including some works of Arnold Schoenberg, from an uncle who regularly travelled in Europe. His study with Marion Bauer in New York City reinforced his interest in the most recent developments in music composition (Reference BabbittBabbitt 1976).

While Babbitt wrote a handful of pieces employing more traditionally tonal techniques, some of the earliest fragments available show that he had absorbed the lessons of Arnold Schoenberg’s method of composition employing twelve notes only related to each other from the very start (see Reference BrodyBrody 1993). Owing to his activities during the Second World War, Babbitt did not start publishing music until 1947, the year of the Three Compositions for Piano and the Composition for Four Instruments. With these two works, Milton Babbitt set the stage for what was to become a career-long development of a remarkably fruitful and flexible compositional technique.

Babbitt’s compositional interests grow from a close reading of both Arnold Schoenberg’s and Anton Webern’s twelve-tone techniques. However, while both Schoenberg and Webern saw their music as connecting with and furthering the traditions of European, in particular Germanic, composition, Babbitt was interested in exploring what he saw as the profound differences between the first principles of scale-based music and those of music based on successive orderings of the total chromatic. Both Schoenberg and Webern, each in his own way, sought to infuse such traditional formal practices as the sonata-allegro or theme and variations with the relational possibilities derivable from the use of twelve-tone rows. Babbitt, on the other hand, was interested in imagining a music whose every element of formal practice might derive ab novo from those same possibilities (Reference BabbittBabbitt 1976).

This is not to say that Babbitt was totally disconnected from the musical past, especially his own musical past. But his position with regard to making music was inevitably different from that of his European predecessors. He was an American, and while he had a solid grounding in Old World musical traditions, he was also steeped in the rich variety of American music making as well. Nor was he intent on throwing over the received instrumental traditions of Europe. While he was a pioneer in electronically produced music, part of his adoption of the synthesizer can be attributed to his apparent frustration with many of his experiences with live performance (see Reference BabbittBabbitt 1958, Reference Babbitt1962, Reference 367Babbitt1965, and Reference Babbitt and Hines1970). But he remained until the very end of his life dedicated to music as something that was made by living players in real time. In fact, with the exception of three solo synthesized works, Babbitt’s use of pre-recorded taped music was generally coordinated with one or more live performers, and those compositions that use synthesis are a relatively small corner of his work as a whole. Babbitt’s writing for traditional instruments might be, or might have been at one time, found extremely demanding and well outside of what would have been considered idiomatic, but his actual use of traditional instruments was largely conservative in nature, drawing on well-established playing techniques and frequently recognising the different capabilities of instruments as a factor in how his musical imagination could be brought to sounding life through them.

A fundamental factor of twelve-tone composition as Babbitt understood Schoenberg’s compositional practice derives from the profound difference between what a note, or pitch, or pitch class, might mean in a tonal context as opposed to the context of the twelve-note aggregate. In traditional tonal music, a sounding pitch takes on meaning from its context within a given diatonic collection. The pitch class C, for instance, is without meaning until it is heard as embodying a scale degree. Scale degrees in tonal music are therefore the smallest unit of structural, or grammatical, meaning, with pitch being the articulator thereof. In music based on a sequence of aggregates – complete or for all intents and purposes complete presentations of the twelve pitch classes – aggregates are the smallest unit of structural meaning, taking on their individuality from the ways their constituent elements, the twelve pitch classes, are distributed within them. Aggregates compose the heard surface of the music; twelve-tone rows, deployed in a variety of ways, therefore can become a way of controlling how aggregates are structured and how they can then be deployed in chains of associational relationships (Reference BabbittBabbitt 1976).

I have gone into this in some detail in order to make a fundamental point that Babbitt was to take on in a variety of ramifications: an aggregate represents a total compendium of possibilities (the twelve equal-tempered pitch classes), which adopts a recognisable profile by the ways those pitch classes and the intervallic relations amongst them are distributed within it. It is possible to generalise this into a wide variety of musical situations and give it a name: the idea of maximal diversity. This became a kind of guiding principle, which saturates Babbitt’s technical developments throughout his creative life. Such a principle can be read as being completionist, but it need not be so. One could imagine a list of possibilities that itself was not complete, but which contained no repetitions, such as all of the trios and duos of a group of six different instruments. Such lists occur in a variety of instances throughout Babbitt’s life, but they exist alongside lists that are in fact complete; their shared characteristic is a lack of repetition (Reference BernsteinBernstein 2016).

Babbitt recognised that this principle could be articulated in a variety of ways in multiple musical dimensions, not just in pitch. But he also recognised that each of these dimensions was limited and determined by the different ways whereby listeners could perceive relationships within them. The linear nature of pitch in register is made cyclical by the ability to perceive octaves, and thus pitch class. Time is also linear, but not inherently cyclical, although cyclicity can be made manifest through compositional means. Dynamics are linear, but absolute intensity is not how people tend to hear. In fact, intensity can be a factor not only of some absolute decibel measure; it is also readily mediated through the means by which a sound is produced. Babbitt’s music reflects a keen awareness of the difference amongst instruments, for example, not so much by changing its qualities based on how a given instrument is played, but by taking advantage of the ways different instruments (or voices) can traverse similar pitch and intervallic landscapes. Thus, for Babbitt, the idea of total serialism was not an arbitrary application of abstract ideas to perceptually or structurally incommensurate musical dimensions. Rather, it involved a subtle awareness of both the similarities and dissimilarities of how we perceive the various dimensions conjoined in a musical utterance. In order to impart a greater understanding of his practice, I will deal with each musical dimension individually in a process of limning a sketch of Babbitt’s compositional technique.

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As mentioned above (p. 108), Babbitt derived a great deal of his manner of treating pitch from both Schoenberg and Webern. From Schoenberg, he adopted the technique of combining more than one member of a row class to form an aggregate. Schoenberg’s primary way of doing so has become known, largely from Babbitt’s own writings, as inversional hexachordal combinatoriality, in which two rows are combined so that the first six elements and the last six elements of each form aggregates. From Webern, Babbitt adopted the technique of deriving a row from a single ordered trichord, representing the four traditional twelve-tone transformations within the body of the row itself (see Reference Babbitt, Peles, Dembski, Mead and StrausBabbitt 2003).

These two techniques combined yielded the trichordal array, a structure that in various guises underlies much of the music of Babbitt’s first compositional period and persists in one form or another throughout his career. Figure 7.1 shows the trichordal array found at the outset of his Composition for Four Instruments. This example additionally shows how the trichords are deployed at the opening of that work, but one may read the example simply as a presentation of a trichordal array.

Figure 7.1 Trichordal array composed into fifteen subsets of four elements

As one may observe, each line (or ‘lyne’, the term coined to described individual strings of pitch classes in a musically uninterpreted array) forms an aggregate based on the four transformations of a trichord type, in the same way as the four quadrants of the array (arising from the hexachordal combinatoriality of the two distinct pairs of lynes) and its four columns (Reference KasslerKassler 1967). This has the effect of spreading the influence of any given trichord out over three different aggregate interpretations. Should one interpret such an array as projected by two pairs of similar instruments, then one can readily track how a given trichord could be heard as part of a lyne articulated by, say, a flute playing in counterpoint with the other three instruments; as contributing to an aggregate formed by a pair of like instruments, for example a flute and a clarinet; or as contributing to a combined texture of flute, clarinet, plus a pair of stringed instruments.

Trichordal arrays provide opportunities for flexibility in a variety of ways. First, as may be seen in Figure 7.1, individual lynes do not necessarily have to be made from members of the same row class; indeed, in most cases they cannot be and still yield the same range of trichordal transformations in every position. Second, in creating such structures out of individual trichords, it is possible to use different orderings of constituent trichords, or even to vary the number of trichord types being used in their realisation. In the Composition for Four Instruments, Babbitt used two different orderings of two different trichord types over the span of the work, combined in a carefully controlled variety of ways. While indeed one may construct a row class in which the elements are made from one each of these four possible orderings, no actual member of this row class appears at the surface of the music. While a row is a particular ordering of the twelve pitch classes, a row class is the collection of all those rows that may be related by a set of operations. Thus, the classical forty-eight-member row class would include all those rows related by transposition, inversion, and retrograde in all possible combinations. Several of Babbitt’s works from the late 1940s and 1950s explore the range of possibilities inherent in the construction of trichordal arrays.

A second opportunity for compositional flexibility afforded by trichordal arrays entails the ways aggregates may be realised on a musical surface. I suggested that lynes might be articulated by individual instruments, but register or playing manner within a given instrument may be used as well. In his compositions using trichordal arrays, as well as those using different kinds of array structure, Babbitt explored a wide variety of ways of projecting his musical elements.

In any array with multiple lynes, pitch or pitch-class order is only specified within lynes but remains undetermined between lynes. This affords many opportunities for compositional interpretation and the creation of surface details that can be used to coordinate with details projected in different passages of the piece. A particular basic pattern that Babbitt regularly used with trichordal arrays may be found in the ways trichords are displayed in Figure 7.1.

In this example, each aggregate divides its trichords into either a grouping of one trichord and three trichords, or two pairs of trichords, or all four trichords at once. Since there are four possibilities for doing the first, three for the second, and one for the last, such a pattern will require two iterations of a trichordal array to be complete. These two iterations are normally related to each other using some basic twelve-tone transformation. We can think of this kind of pattern both as a series of partitions of four elements or as a particular ordering of the fifteen non-zero subsets of four elements, in this case trichords. As can be noted in the current example, the disposition of a single ordering of a single trichord type has enabled the array to be disposed to present all possible transformations of the ordered trichord in all possible combinations and locations. This, of course, is another manifestation of what I have suggested is a guiding principle of maximal diversity in Babbitt’s work.

Such a disposition of trichords still does not determine completely the composition of any given aggregate in an array, but it does limit the possibilities in intriguing ways. Tracking all the possibilities Babbitt used for working within these constraints is beyond the scope of this essay, but doing so allows one to realise the balance between the self-imposed rules of play and the inventive response to opportunities thus provided that is always a lively presence in Babbitt’s music.

The pattern found in Figure 7.2 with trichords is something Babbitt employed with other musical dimensions as well. In the case of the Composition for Four Instruments, Babbitt used an analogous pattern applied to the ensemble as a whole to determine the piece’s fifteen sections. It also informs the number and variety of combinations of his four different ordered trichords over the span of the piece. This means that the last section of the work, analogous to the combination of all four lynes in the array of Figure 7.1, is the only passage in which all four instruments participate, with all four ordered trichords. As the pattern appears in reverse order at this point in the work, it is only the opening aggregate of the final section in which all four ordered trichords and all four instruments are sounded together. This is illustrated in Table 7.1 and Figure 7.2.

Figure 7.2 Trichordal disposition in the last section of Composition for Four Instruments

Much of Babbitt’s music of the late 1950s and early 1960s shows his interest in extending his compositional practice. Works such as All Set (1957), the Composition for Tenor and Six Instruments (1960), Post-Partitions (1966), and Philomel (1964) each take new steps in creating an unfolding counterpoint of lynes derived in whole or in part from a work’s row class. From this developed a practice that underlies much of his later music, the use of all-partition arrays. Like a trichordal array, an all-partition array is comprised of lynes unfolding simultaneously, but unlike the earlier practice, all-partition arrays feature a unique disposition of lyne segments for each aggregate. Babbitt devised several all-partition arrays based on four, six, or twelve lynes (there is one example of an eight-part array, employed in his Third String Quartet (1970)). In general, Babbitt’s all-partition arrays are built from hexachordally combinatorial lyne pairs, the number of which are determined (usually) by the number of distinct pairs of complementary hexachords found in a work’s row class. Thus, for example, an all-partition array whose underlying row class is built using the hexachord type 014589 would only contain two hexachordally combinatorial lyne pairs, given that there are only two distinct pairs of such hexachords. On the other hand, an all-partition array built with 012678 would have three lyne pairs, while ones built using 012345, 023457, or 024579 would contain six lyne pairs, owing to the number of distinct pairs of hexachords available in each type.

Each such all-partition array contains all the possible combinations of lyne segment lengths to form its aggregates. Table 7.2 is a chart of the seventy-seven possible ways of partitioning twelve parts into lyne segments of various lengths, while Figure 7.3 is a short segment of a four-part array composed of the thirty-four ways of combining lyne segments of various lengths derived from at most four parts.

Table 7.2 The seventy-seven possible ways of partitioning twelve parts into lyne segments of various lengths

Figure 7.3 The opening block of a four-part all-partition array

Since the construction of such arrays by hand is fairly difficult, and because they are easily adaptable for multiple interpretations, Babbitt tended to reuse the same relatively small number of arrays in several pieces. These pieces remain distinct from each other due to the individuality of both lyne projection and aggregate composition, but listeners can often infer ‘family resemblances’ amongst pieces sharing arrays. All-partition arrays also impose a kind of rhythmic flux on a composition, owing to their constantly changing aggregate shapes. An aggregate containing ten elements in one lyne and two in another will, depending on how lynes are being projected, sound quite different from an aggregate using four trichords, or three tetrachords, or six dyads. The greatest potential difference between two aggregates in a twelve-lyne all-partition array will of course be between the aggregate that is made of a single row in one lyne and that which is made from one element each in all twelve lynes. This difference should also imply the range of possible aggregate composition, from the totally restricted (a single row in one lyne) to the totally free (each lyne having a single element). A couple of vivid musical examples arise in the piano work Post-Partitions, where the registral sweep of the opening bars is contrasted in the middle of the piece where an aggregate is projected in the middle octave of the piano; one may also point to a passage heard not long after the opening of Relata I (1965), where, after a lot of activity throughout the orchestra, one can hear a trombone slowly and solemnly uttering a long string of notes against a held sonority. Both of these passages absolutely depend on the varying shapes of the aggregates within their arrays.

One additional concept that emerges in this period of Babbitt’s music derives from his techniques for transforming an array. It is easy to see how one might perform the familiar twelve-tone transformations of transposition, inversion, and retrogression on an array as a whole, but to this Babbitt added the circle-of-fifths transformation (or multiplication by 5 (or 7), mod 12), and a technique of inverting each distinct lyne pair by the index number (a representation of the inversional axis) that would preserve its hexachordal content. In the former case, the result is an array that preserves all of the distributional aspects of the original, while shifting intervals in predictable ways. This technique is not usually found within a composition but can be seen to relate arrays of two different pieces. The latter case, however, occurs frequently within a given work and can have a dramatic effect on the musical surface.

Inverting an array around a single axis will preserve columnar aggregates but will map the hexachordal contents of lyne pairs onto each other in predictable ways. Inverting each lyne pair by its own axis preserves the hexachordal content of each lyne pair but plays havoc with the columnar aggregates of the array. The result has been called ‘weighted aggregates’, in that under this kind of transformation what had been an aggregate in the original array can appear with multiples of a given element, and with the loss of other elements. Overall, the content of the array will still contain an even distribution of all twelve elements, but locally the flow of pitch classes will be varied. One of the consequences of this transformation can manifest itself in the sudden appearance of element duplication in the musical surface, articulated as unisons or octaves between those means by which Babbitt is projecting the array lines. A vivid moment of this latter operation may be heard at the midpoint of the Fourth String Quartet (1970), in which a unison A blossoms out in octave doublings in the passages that follow.

Having established a practice based on all-partition arrays, Babbitt moved on to seeing how these themselves could be combined in ever more complex networks of polyphony, referred to as super-arrays. In the orchestra piece Ars Combinatoria (1981), Babbitt unfolds four transformations of the work’s array simultaneously, articulating once again a version of the list of the fifteen subsets of four, in this case not just of trichords, or individual instruments, but of complete twelve-part all-partition arrays, each presented by its own ensemble drawn from the orchestra as a whole. Much of the music that occupied him to the end of his career engaged with such counterpoints of counterpoint, at times piling up a dizzying number of simultaneously unfolding strands of music, as in, for instance, his Sixth String Quartet (1993).

Yet, ideas and preferences found in his earliest work may still be perceived in the later music. The Head of the Bed (1982) returns to the ensemble of the Composition for Four Instruments, used here to accompany a soprano. The ensemble unfolds a super-array based on a frequently reused four-part all-partition array, while the voice part is composed using trichordal arrays disposed as they had been in the earlier work. The super-array is divisible into the fifteen subsets of four elements, here represented by how many of its constituent arrays are present and yielding the same collection of instrumental subgroups found in the earlier work, albeit in a different order.

With relatively few exceptions, Babbitt’s catalogue of music displays an ever more complex exploration of the implications of some of his earliest decisions about how to treat pitch within the context of relations amongst aggregates. Register and instrumentation in various combinations form the basis for creating means of distinguishing amongst simultaneously unfolding strands of pitches, be they individual orderings of trichords, hexachords, or the total chromatic, or combinatorial pairs of rows, or complete arrays, or polyphonies of arrays.

Babbitt’s treatment of rhythm, however, is a more varied affair. For Schoenberg, traditional ways of thinking about rhythm and metre can be quite easily derived from his roots in earlier practice. Recognisable dance rhythms, waltzes, and marches proliferate throughout his twelve-tone compositions, bringing with them their attendant associations both of affect and of accentuation within the bar. Babbitt, on the other hand, was not so much interested in re-enlivening traditional practice as he was committed to exploring the possibilities inherent in the radically different ways of construing relationships afforded by aggregate composition.

His initial excursions into interpreting these new pitch relationships into the temporal domain dealt with issues of absolute duration, susceptible to the kinds of transformations he was using with pitch. The Composition for Four Instruments offers a good example of this, although he had worked with a similar structure in the second of the earlier Three Compositions for Piano. Figure 7.4 illustrates the durational pattern composed out in the ensemble work.

Figure 7.4 Duration patterns in Composition for Four Instruments

While the Composition for Four Instruments employed a duration string of only four elements, subsequent works used duration strings derived from their underlying twelve-tone rows. The Second String Quartet (1954) is one of the more consequential pieces using this approach. But as may readily be imagined, this kind of translation of pitch to duration is not only a perceptual challenge but is non-commensurate with regard to things like interval preservation under various kinds of transformation. This caused Babbitt to seek another way of handling issues of time, one that would better afford parallelisms with his pitch procedures.

Babbitt’s solution has been called the time-point system (see Reference BabbittBabbitt 1962). At its heart is the use of metre to create a cyclical division of time. Just as the perception of octave equivalence allows a cyclical division of register, so in the time-point system the perception of a regular metre creates a series of ever-repeating cycles. If a bar, representing a single module, is divided into twelve attack points, one can construct a temporal analogy for the twelve-note equally tempered realm of pitch. Obviously, there are considerable differences, both abstract and perceptual, between the pitch and time domain, but by using time points as described here, Babbitt was able to make far closer analogies between pitch and rhythm than in his earlier practice (Reference MeadMead 1987). Figure 7.5 illustrates some of the issues addressed above.

Figure 7.5 Time-point rows and an aggregate realisation

One of the consequences of this approach is the restoration of a more traditional interpretation of rhythm and metre. While in some music of the twentieth century bar lines are reduced to serving as placeholders to help read a score or part, in many time-point compositions it is useful to be able to recognise downbeats, pick-ups, subdivisions of various kinds, and so on. This is not to say that metrical interpretation is not active in earlier Babbitt; in fact, one of the interesting things about the Composition for Four Instruments is how tempo and the maintenance of the work’s absolute duration scheme interact to offer reinterpretations of large-scale repetitions of patterns. But with the advent of time-point composition, Babbitt’s music affords a whole range of engaging metrical interpretation.

One example will serve to illustrate this. The Third and Fourth String Quartets were written within a year of each other but use complementary ways of altering tempo. In the case of the earlier work, a basic pulse present throughout the composition is frequently reinterpreted so that modular length can change from section to section. Some sections are notated in $\begin{array}{c}3\\ 8\end{array}$ , others in $\begin{array}{c}3\\ 4\end{array}$ or $\begin{array}{c}6\\ 4\end{array}$ , with the underlying eighth-note pulse always constant. Bar length, and thus modular length, changes, and with it the sense of rate of turnover. In the case of the later quartet, the bar length is a constant throughout, but the notated tempo changes. The differences of temporal change between these two works is striking and is due to our way of hearing the modulus in each case.

The use of the time-point system allowed Babbitt to create arrays of time-point rows, usually employing the same array structure found in the pitch domain. And just as the lynes of his pitch arrays are often distinguished by register, so Babbitt turned to dynamics to provide an analogue for projecting time points. Sometimes, this would lead him to use twelve different dynamic levels, but frequently he would use a single dynamic level to project a combinatorial pair of time-point rows, just as a single register might be used to unfold the analogous combinatorial pair of pitch-class rows in his arrays.

This might at first seem to be a kind of false equivalency, but Babbitt was well aware of the inexactness of fit between structures in pitch and structures in time. This led him to adopt a greater degree of freedom in his exploration of the temporal domain over his career. Unlike the pitch domain, the temporal domain in Babbitt’s music demonstrates a number of different interpretations. Babbitt devised several different ways of treating time spans and added to these basic techniques a further way of subdividing the spans he created. In many works, a given timespan created by some means or other would be subdivided by some even number of attacks, not all of which would be sounded. The clue to these additional attacks may be heard in how they are realised as pitches. As mentioned above, pitch-class arrays are susceptible to interpretations based on the partial orderings determined by the lyne segments found in any given aggregate. Frequently, Babbitt would use this flexibility to create whole or partial cross-references to segments present elsewhere in the array. This was by no means his only approach to composing out the aggregates of his arrays, but it was one that appears frequently.

The foregoing is at best an overview of Milton Babbitt’s developing approach to composing in the total chromatic and his use of various kinds of analogues to his thinking in pitch in his approach to handling rhythm. Much is left out; there are a number of pieces in which he moves in directions that he does not bring in to his central set of techniques. The underlying approach to constructing both rows and arrays in Philomel is never quite followed up in later work, and certain pieces such as The Crowded Air (1988) depart quite substantially from the technique of the music that surrounds it. Nor have I touched in any kind of comprehensive way on the variety of strategies Babbitt used to compose out the details of his arrays’ constituent aggregates. There is a danger of imagining that Babbitt’s composing was in some way algorithmic, that once an array had been selected for pitches and rhythms, and once the parameters for instrumental and registral projection had been determined, then the rest would follow trivially. But this could not be further from the case (see Reference MailmanMailman 2019). Babbitt’s compositional technique sets limits on the choices he could make in the process of writing, but it did not make those choices automatically. He once remarked that one the hardest things for him to do in starting a new piece was getting the previous piece out of his mind (personal conversation with the author).

A more fruitful way of thinking about Babbitt’s compositional technique is to see it as the creation of a musical space within which he could be creative: the establishment of a set of constraints that allow any given compositional action to have consequences, to create contingencies, to induce echoes of itself that can spread through a work. Just as Schoenberg yearned for a compositional technique that would allow him to navigate the total chromatic in ways that could replicate the structural depth he perceived in the music of Haydn, Mozart, and Brahms, so Babbitt sought ways to explore the implications of Schoenberg’s insight into a fundamentally new way of construing notes, not as representations of scale degrees, but as means to individuate aggregates. Furthermore, while Babbitt’s compositional techniques grew over his career, their evolution was accretive in that ideas and approaches evident in his earliest published works persisted amidst all of his developments right up to his final compositions. And despite his work with the RCA Mark II synthesizer, Babbitt’s conceptions of instruments and the voice had strong roots in traditional performance practice as a way of inflecting the idiosyncrasies of his musical imagination.

In its own way, Babbitt’s musical practice echoes the balance between tradition and the avant-garde one finds in Schoenberg’s and Webern’s music. The difference, of course, lies not merely with the issue of compositional technique, but in what tradition each composer found himself. For Schoenberg and Webern, it was the legacy of nineteenth- and eighteenth-century European practice. For Babbitt, it included a strong European heritage, but one heard from the vantage point of the New World, and it also included a very strong legacy of those Americanisms found in jazz and popular song (Reference MaggartMaggart 2020; Reference BrodyBrody 1993). Babbitt had an encyclopaedic knowledge of the American Songbook, with firm grounding in Jerome Kern and George Gershwin, and his youthful musical experience growing up in Jackson included not only playing clarinet in the local orchestra but playing in a variety of informal pick-up bands as well. Scholars have likened his approach to his own arrays as having an affinity to the revisiting of lead sheets in jazz as much as they are a new development from the first principles of twelve-tone composition (Reference MailmanMailman 2019). And while Babbitt’s music might seem a radical departure from earlier compositional practice, it is by many measures another instance of the American tendency to put together unexpected combinations of influences, just to see what happens.

Writing from Buenos Aires to John Cage in 1954, Pierre Boulez stated:

The decade of the 1950s, in fact, witnessed a great transformation in the compositional practice of Pierre Boulez. The usual narratives of serialism during this decade have tended to dwell on Boulez’s experiments with multiple serialism in Structure Ia (1951), where the composer applied the operations common to twelve-tone music in a one-to-one mapping of other parameters such as duration, articulation, and dynamics. The practice of multiple serialism represented a significant contrast with the more conventional form of serialism that Boulez had successfully practised since 1945. It did, in fact, expand the serial principle by extending it to other parameters, thus breaking with familiar formal structures and opening up possibilities for common structural underpinnings between various parameters (Reference DecroupetDecroupet 1995a), but this experiment was tremendously short-lived. Boulez presented radical deviations from a straightforward application of multiple serialism as soon as the second and third movements of that work, Structures Ib and Ic (Reference Boulez1952) (Reference BoulezBoulez 2004). Although this technique appeared in other works, such as Polyphonie X (1951) and (briefly) Structures II (1956–61), it was eventually abandoned.

The desire to expand the serial principle, however, did not end with it. The ensuing works, like Le Marteau sans maître (1952–5), Pli selon pli (1957–62/89), and the Third Piano Sonata (1955–7/63), which brought Boulez to the pinnacle of his reputation within the European circle of composers, are those that truly redefined serialism. Yet, with the exception of Le Marteau, which is often presented as an extension or loosening of serial practice, illustrating Boulez’s much cited references to a dialectic between freedom and control (cf. Reference Boulez and ThéveninBoulez 1991d; Reference GoldmanGoldman 2011: 39), narratives of twentieth-century serialism rarely discuss their serial practice (Reference SalemSalem 2018). In what follows, I will discuss how Boulez’s redefinition of serialism took place and its motivations, as well as its musical implications and ramifications. Ultimately, the chapter shows how, through this redefinition, serialism remained an important element of Boulez’s compositional technique until the end of his career. Furthermore, Boulez’s serialism was an essential forerunner of future trends, rather than a culmination of an abandoned practice.

In the quotation that opens this chapter, Boulez talks of expanding the series, as well as the serial principle. It might be useful to examine both of these ideas in turn. The works he refers to are Oubli signal lapidé (1952–3) and Le Marteau sans maître (Reference O’HaganO’Hagan 2007: 35; cf. Reference Campbell, Campbell and O’HaganCampbell 2016). In Le Marteau, Boulez develops three distinct serial techniques (Reference DecroupetDecroupet 2005; cf. Reference KoblyakovKoblyakov 1990; Reference MoschMosch 1990; Reference HaasHaas 1990; Reference PiencikowskiPiencikowski 1980 and Reference Piencikowski, Newsom and Mann2000), all of which expand the series by generating blocs sonores (Reference Boulez and ThéveninBoulez 1991e: 128; Reference DecroupetDecroupet 1995b: 120; cf. Reference SalemSalem 2018), vertical collections of notes of variable size that can function as the basis for pitch organisation. This desire to organise various parameters (notes, durations, articulations, dynamics) in groups, and thus free up possibilities in terms of texture, timbre, and temporality, was the primary motivation for the deviations from straightforward application of multiple serialism (which were achieved chiefly through grouping notes based on their equivalence in smaller modular spaces) in the second and third movements of Structures I.

Of the techniques used in Le Marteau, the most far-reaching, in the sense that it influenced subsequent methods of pitch generation for the remainder of Boulez’s career, was the technique of pitch-class multiplication. As Figure 8.1 shows, pitch-class multiplication consists of a process where two sets are combined to form a larger set, by replicating the intervals of one set (figured from a chosen anchor note), over each of the notes of the other set. Initially, Boulez incorporated this technique in the larger context of a multiplication table. These tables expand the series in a very literal sense. Each system of the table contains several embellished series, that is, partitions of the series transposed systematically by the intervals of the row itself and embellished by the intervals within the partitions themselves. Figure 8.2, from ‘Séquence’ (Third Piano Sonata), illustrates the multiplication table as an embellishment of the series most clearly (Reference Decroupet, Decroupet and LeleuDecroupet 2006). The partitioned twelve-tone series appears at the top of the example. Each note of the row recurs at the top left of each of the twelve sequences of six chords that make up the pre-compositional sketch. Each of these sequences of chords consists of the partitioned row transposed to start on successive notes of the row and embellished (depending on which of the six systems it is on), by the intervals within each of the six partitions. For instance, in the last system of the table, the partitioned row is transposed to start on E♭ and C♯ (the notes of the last of the partition of the row, taken in order from top to bottom). Each of these transposed rows is embellished by a transposition of the same at the interval between E♭ and C♯ (two semitones down). Similar tables were used for works such as Structures II (1956–61), Doubles (1958), and Domaines (1961–68) (Reference KoblyakovKoblyakov 1990: 32; Reference LosadaLosada 2014; Reference LosadaLosada 2017; Reference Losada and IllianoLosada 2019a; Reference LosadaLosada 2019b).

Figure 8.1 Pitch-class multiplication as described by Boulez. e*c (ec) results from realising each one of the ordered pitch-class intervals that occur above the bass in e (the multiplicand) over each pitch-class of c (the multiplier)

Figure 8.2 Annotated reproduction of pre-compositional table for ‘Séquence’, from Third Piano Sonata.

Paul Sacher Foundation, Pierre Boulez Collection (Mappe H, Dossier 2 f,1)

This practice creates an identity between the relationships governing local and large-scale structures, a criterion that had been important for Boulez throughout his career (Reference Boulez and ThéveninBoulez 1991e: 116–17; cf. Reference Piencikowski and HäuslerPiencikowski 1985 and Reference Piencikowski1993; Reference DecroupetDecroupet 2012 and Reference Decroupet, Campbell and O’Hagan2016; Reference LosadaLosada 2008, Reference Losada2014, Reference Losada2017 Reference Losada and Illiano2019a, Reference Losada2019b, Reference Losada2019c). Figure 8.3 presents a graph that illustrates how the desire to preserve the same structure on the local and larger level explains the transpositional structure of the multiplication table as a whole. The graph in Figure 8.3a reflects the relationships embedded in the partitioned row (Figure 8.3b), stressing the transpositional relationships between the highest notes in each partition of the row, which function as anchor notes. If the nodes of the graph are filled with pitch classes, the graph represents the partitioned row (moving clockwise from the very top node, which represents the first partition of the row). If they are filled with each of the sets of the partitioned row, the graph represents a vertical or horizontal trajectory through each of the columns or systems of the multiplication table. Finally, if the nodes are filled with the partitioned row itself, the graph represents the entire left side of the multiplication table. This explains the transpositional structure of the table, which is determined by the intervals between the anchor notes. Simultaneously, each of the shaded radial subgraphs in Figure 8.3a, which reflect the intervals embedded in each of the partitions of the row, represents the transpositional relationships that govern the corresponding system of the table.

Figure 8.3a Transformation graph modelling the partitioned row and other levels of structure in ‘Séquence’, from Third Piano Sonata

Figure 8.3b Partitioned row for ‘Séquence’

Crucially, this type of structural organisation creates important harmonic relationships, defined by common tones, common subsets, and varying degrees of chromatic saturation, which embody a hierarchical organisation. The multiplication table also expands the series in terms of density, thus permitting a degree of flexibility at the local level, where the pitch classes can be disposed of with a certain freedom and are not subject to a strict temporal disposition. Furthermore, in several of these works, multiplication tables organise parameters beyond pitch (especially duration). This practice has several advantages over the former approach to multiple serialism when applied to other dimensions. Chief amongst these advantages is the organisation into groups, which enables the composer to avoid the pointillistic sound world that emerges from having each note associated with its own dynamic, articulation, and duration marking.

Reaching beyond the goal to ‘expand the series’, Boulez’s desire to ‘expand the serial principle’ transcended the development of multiplication techniques, as is reflected in his insistence that:

After the composition of Le Marteau, Boulez did in fact, gradually reduce his reliance on extensive pre-compositional tables of the type shown in Figure 8.2. Two crucial influences led to radical changes in his compositional approach, what I term the redefinition of serialism (Reference Piencikowski, Campbell and DecroupetPiencikowski 2016; cf. Reference Salem, Campbell and O’HaganSalem 2016). These were the influence of mathematical trains of thought on his techniques of composition and the influence of music from other cultures on his approach to temporality, timbre, and texture. I will examine each of the influences in turn.

A turning point in Boulez’s career was his exposure to the logical empiricism of Louis Rougier (Reference RougierRougier 1956; cf. Reference Decroupet and AlbèraDecroupet 2003a; Reference NicolasNicolas 2005 and Reference Nicolas, Goldman, Nattiez and Nicolas2010; Reference CampbellCampbell 2010; Reference LosadaLosada 2019c), which had repercussions on his musical technique that allowed him to reach many of the goals outlined in the quotation cited immediately above. In his writings, Rougier argues that that the fundamental axioms of a system, instead of apodictic or assertoric truths, in certain cases may simply be optional conventions (Reference RougierRougier 1920: 199; Reference Marion, Nemeth and RoudetMarion 2005: 158–59; cf. Reference LosadaLosada 2019c). He states, furthermore, that ‘a reasoning should be independent of the object upon which one reasons … Only the relations imposed upon these notions by the postulates and the definitions must intervene in the deduction’ (Reference RougierRougier 1920: 199). Crucially, ‘the axiomatic method makes it possible to construct purely formal theories which are networks of relations, schemes of ready-made deductions. Consequently, the same form can be applied to various subjects, to sets of objects of a different nature, on the sole condition that these objects respect among themselves the same relations as those stated between the undefined symbols of the theory’ (Reference RougierRougier 1956: 1001). Rougier’s ideas transformed Boulez’s approach to serialism by providing him with the motivation to expand the serial principle in two fundamental, and radical, ways. In the first place, they made Boulez increasingly less reliant on a generative twelve-tone row and extensive pre-compositional sketches and more prone to reappropriate previously used materials as the basis for new works. On the other hand, they led to solidification of a practice already common to Boulez: that of applying networks of relationships, chosen from the possibilities embedded in the source material, in different contexts. This had important consequences for his harmonic language.

The reappropriation of previously composed materials became an essential feature of Boulez’s compositional process (cf. Reference TissierTissier 2012; Reference SalemSalem 2014, Reference Salem, Campbell and O’Hagan2016, and Reference Salem2019). On the one hand, he developed a tendency continually to revise works, as I will discuss shortly. In many cases, however, the practice of reusing materials did not have a strong aesthetic basis, since the material stemmed from unpublished works, and recognition of the source materials was not the goal. Instead, it reflected a gradual diminishment in the importance placed on the nature of the source materials and a proportional increase in the emphasis on proliferation of materials, through techniques of development based on relationships embedded in the material itself. As a result, from this point on in his career, his works gradually moved further away from an underlying twelve-tone basis. Simultaneously, a number of techniques of development, roughly summarised in Figure 8.4, became standard to his compositional process (Reference LosadaLosada 2019b). Although many of them (transposition, inversion) stem directly from serial procedures, what distinguishes them is how they replicate the relationships embedded in the materials itself, their application in the vertical and harmonic dimensions simultaneously, as well as repeated application in a single dimension as the material proliferates in the course of the compositional process. Combined with the other techniques (intervallic combination, chordal thickening, chromatic saturation), they enabled different ways of generating crucial harmonic links between foreground and middle-ground events, creating a method of composing out that Boulez described as inhabiting the diagonal dimension and opening up a new realm of possibilities for hierarchical structure (Reference LosadaLosada 2019d).

Figure 8.4 Summary of serial developmental techniques

To illustrate, Figure 8.5 explains the basic principle that generates several pages of material from Éclat (1965) from the opening chord of his unpublished work Don (first version 1960, for piano and voice). In this example the intervallic structure of the opening chord of Don (the last chord in the progression), determines the transpositional relationships in the progression. The transpositions retrograde the series of intervals (defined in register) embedded in the chord. The technique is a type of pitch-space multiplication and is also akin to a rotational array. The result of this scheme is a common tone, B♭4, that is a significant element of the harmonic content of the piece, creating a hierarchical structure. On the musical surface, the various chords are deployed with flexibility in terms of ordering. Even when deployed horizontally they are often perceived as stretched-out simultaneities.

Figure 8.5 The consequence of transposing a chord by the retrograde of embedded pitch intervals (in registral space) is a common tone in pitch space

The above example illustrates the conceptual similarities between the technique and multiplication and rotational arrays. In fact, rotational arrays, and arrays built on the simultaneous transposition of a series by the intervals of the series and their inversion, underlie virtually all of Boulez’s works written after 1971 (Reference Dal Molin, Decroupet and LeleuDal Molin 2006, Reference Dal Molin2007, Reference Dal Molin2009, and Reference 374Dal Molin, Campbell and O’Hagan2016; Reference GoldmanGoldman 2011; Reference TissierTissier 2012; Reference O’HaganO’Hagan 2021). These encapsulate many of the same structural relationships embedded in multiplication tables, including isomorphic relationships at various levels of structure and an emphasis on common tones. They also generate harmonic sonorities that share large, common subsets embellished by additional notes, thus permitting continuity in the musical language in a non-dodecaphonic context (Losada 2021).

These are the technical underpinnings of Boulez’s redefinition of serialism. They allowed Boulez to realise the goal of composing without extensive pre-compositional sketches, instead creating the sketches along the way. Although hierarchy is essential to his conception, it is not determined in advance: it is achieved through variation principles (generative principles) that work in both the horizontal and vertical realm. His satisfaction with the potential of these techniques can be seen in the following comment in a letter to Stockhausen from late 1957: ‘now that we have a basic technique that is sufficiently broad and solid, we must work madly on the poetics’ (Karlheinz Stockhausen Collection, Paul Sacher Stiftung). This outlook explains why Boulez essentially stops writing theoretical texts on music for about a decade after 1965 (Reference GoldmanGoldman 2011: 39). Having solidified his compositional technique, Boulez was ready to focus on the aesthetic realm. This aesthetic component accompanied the transformation of this compositional approach and had far-reaching influence in several fields of inquiry. It derived from a multitude of influences, many of which, like the ideas of John Cage, affected most mainstream European composers of the time. I would like to focus, however, on those that were important to Boulez as an individual. These are encapsulated in the concept of the ‘rhizome’ and the influence of music from other cultures.

The rhizome relates to the creative alternative to organicism embedded in Rougier’s logical empiricism (see Reference Losada and IllianoLosada 2019a). Rougier states that ‘there exist an unlimited number of equivalent notions and propositions that can be chosen as primaries, without any being imposed by right of nature’ (Reference RougierRougier 1956: 1001). As has been noted by many authors, Boulez’s works from this time period can be grouped into families of works that share common materials. The nature of the relationship between the different works, however, varies widely. While some works share common materials with others without any audible link between them (for example, the Third Piano Sonata and Domaines, which are based on pre-compositional tables derived from retrograde inversional related rows), others have clear musical links. Some works are re-compositions or revisions of others (for example, Figures Doubles Prismes (1963/8) compared to Doubles (1958)), while others constitute expansions of movements, smaller sections, or materials from another work (for example, Domaines for clarinet and instrumental ensemble compared to Domaines for solo clarinet, or Éclat, with respect to the first version of Don, for voice and piano). In Boulez’s practice, from here on, even works that share a common pre-compositional basis typically exploit different properties embedded in the materials themselves, creating a multidirectional (non-organic) network of relationships between different works and sections within individual works. This approach, embedded in the concept of the rhizome, was far-reaching in its influence. It appears in Boulez’s sketches from the late 1950s and early 1960s. It was adopted and developed by the philosophers Gilles Deleuze and Félix Guattari in the 1970s (Reference CampbellCampbell 2010: 143–5), indicating that they may have taken this idea from Boulez.

As Luisa Bassetto and Rosângela Pereira de Tugny have stated, the music of other cultures was another crucial aesthetic influence on Boulez, transforming his approach to texture, timbre, and timing, in addition to the question of what constitutes the work itself (Reference Bassetto and AlbèraBassetto 2003 and Reference Bassetto2014; Reference Pereira de TugnyPereira de Tugny 1998 and Reference Pereira de Tugny, Decroupet and Leleu2006). This influence was not superficial, nor did it consist of a straightforward appropriation or imitation. As I argue in a recent article (Losada 2021), Boulez’s interactions with the ‘other’ illustrate Gianmario Borio’s penetrating assessment of how artists like Boulez were forerunners of post-colonial thinking (Reference Borio, Ginnattasio and FacciBorio 2009; Reference Berio and De BenedictisBorio 2013a). In Boulez’s music, elements inspired by music from other cultures impress themselves indelibly into the creative procedures and are fundamental to his redefinition of serialism. In my view, this interaction is an example of ‘productive reception’ in the sense presented by Maria Moog-Grünewald (Reference Moog-Grünewald and RallMoog-Grünewald 1993) and shows elements of ‘critical listening positionality’ described by Dylan Robinson (Reference RobinsonRobinson 2020), though it is important to note that Robinson (and others) would probably consider this extraction to be problematic. From my standpoint, however, as a person whose identity can only be described as resulting from the confluence of many different cultures, these interactions between different cultures do not seem problematic when they invert established schemes of dominance and invoke a change in the way we listen to and conceive of the work of art, reflecting a deep understanding of the musical and cultural contexts.

Boulez, highly critical of composers writing music primarily based on exoticism, sets his approach in relief, by emphasising what he admired about Debussy, and specifically how Debussy permitted elements from the music of other cultures to transform his musical language without imitating or making direct reference (and thus exploiting) the original context (Reference BoulezBoulez 1967: 6; Reference Boulez, Oesch, Arlt and HaasBoulez 1984: 142–3; Reference Boulez and ThéveninBoulez 1991i). Boulez also clarifies how he uses instruments from other cultures in order to destabilise dominant hierarches (Reference Boulez, Oesch, Arlt and HaasBoulez 1984: 140).

In order to grasp the depth and quality of this influence on the music of Boulez, it is important to understand some crucial aspects of the composer’s professional trajectory (cf. Reference LosadaLosada 2021b). In 1946, after completing his studies with Messiaen in the Paris conservatory, and having started to achieve recognition through some of his compositions, like the Sonatina, Boulez expressed an interest in being an ethnomusicologist (Reference BassettoBassetto 2014). In fact, he planned a research trip to Cambodia, with the Guimet Museum, but this trip was never realised owing to the start of the Indo-China War. However, Boulez realised many transcriptions of music from the Far East and Africa during this time.

Boulez acknowledged the influence of the music from other cultures on his approach to temporality. This is manifest in the way texture and timbre interact with timing to create an exploration of musical space. In the first place, it affected his sense of timing within the works, imbuing them with a greater degree of flexibility. On the other hand, it affected his conception of what constitutes a work of art in itself. Both of these ideas, and the acknowledgement of the influences from the Far East, are embedded in the following quote from Boulez:

In the realm of timbre, Boulez mentions that the xylorimba refers to the African balafon, the vibraphone to the Balinese gamelan, and the guitar to the koto from Japan (Reference BoulezBoulez 1986d: 341).

Following Boulez’s lead, many scholars have commented particularly on the influence of the music from the Far East (Reference GriffithsGriffiths 1978: 28; Reference Bradshaw and GlockBradshaw 1986: 159; Reference DecroupetDecroupet 2005: 44). Far fewer have commented on another crucial influence on Boulez, that related to his experiences in Latin America. The same year as Boulez’s failed research trip to Cambodia, he was appointed music director of the Compagnie Renaud Barrault. Although Boulez did not travel to Africa or the Far East during this formative period, his position with the Compagnie Renaud Barrault allowed him to realise three extended tours of Latin America. These were in 1950, 1954, and 1956 (Reference Bassetto and AlbèraBassetto 2003; Reference Campbell, Campbell and O’HaganCampbell 2016).

These Latin American tours proved to be crucial to Boulez’s development as a composer, partly because of the pieces that he was working on during that time. Edward Campbell has provided crucial information regarding these trips, which makes it possible to see the extent of the importance of this experience (Reference Campbell, Campbell and O’HaganCampbell 2016; Reference SalemSalem 2018). During the tour of 1950, Boulez worked on an abandoned project, a setting of Mallarmé’s ‘Un coup de dés’. During the Latin American tours of 1954 and 1956 respectively, however, Boulez worked on two pieces that carried him to very centre of the circle of European composers. As mentioned above (p. 125), during the tour of 1954 he worked on Le Marteau, specifically, on the ‘Commentaire III de “Bourreaux de solitude”’. During the tour of 1956 he worked on the Third Sonata.

A few concrete influences can be attributed to these experiences. Campbell has noted how, in his 1954 tour, Boulez met with the brothers Augusto and Haroldo de Campos, founders of concrete poetry, in São Paulo. They spoke of Pound, Joyce, Cummings, and Mallarmé’s ‘Un coup de dés’ (Boulez to Souvtchinsky, quoted in Reference Campbell, Campbell and O’HaganCampbell 2016: 11). Given this, it is interesting to note, as Campbell does, the relationship between Augusto de Campos’s poems from 1953 and 1954 (for example, ‘dias, dias, dias’), which explore the idea of alternative trajectories distinguished by colours, and the score for Boulez’s Third Sonata, a work which was first conceived, according to a letter from Boulez to Stockhausen, around December 1954 (Reference LosadaLosada 2018). This throws interesting light on the debate about lines of influence between European composers regarding ‘open’ elements in composition (Reference O’HaganO’Hagan 2017: 187). The open work, which refers both to works that lack a specific predefined trajectory, incorporating elements of choice, and to works that are subjected to perpetual recomposition and revision to the point that many remained as works in progress to the end of the composer’s life, became an essential feature of Boulez’s compositional approach for the remainder of his career.

Musical influences, principally affecting temporality and timbre, were important as well (Reference O’HaganO’Hagan 2007) but were always integrated into the musical language, transforming it from within, rather than invoking or imitating an extraneous context (see Losada 2021). As stated above (p. 135), Boulez explains the incorporation of instruments from other cultures as a means to destabilise dominant hierarchies, which is made possible by the profound incompatibility in the aesthetic contexts (Reference Boulez, Oesch, Arlt and HaasBoulez 1984: 140). The movement Boulez was working on during his South American tour of 1954, the ‘III Commentaire’, incorporates clear timbral influences. The beginning of the work shines with the bright, propelling rhythm of the claves, while the end is characterised by timelessness in the repetitions of the bongos and maracas attacking simultaneously (this texture is reminiscent of the method of playing the birimbao). In an interview with Peter O’Hagan, Boulez acknowledged other influences, like the timbral contrast between harp and flute of the music of Peru, which is essential to the timbral and spatial worlds of the ‘Improvisations sur Mallarmé’ in Pli selon pli (quoted in Reference Campbell, Campbell and O’HaganCampbell 2016: 23; cf. Reference Bassetto and AlbèraBassetto 2003). In spite of acknowledging the influence of the Latin American music in matters of texture and rhythm in this interview with Peter O’Hagan, in other places Boulez disclaims any musical influence from Latin America, claiming that the influence was spiritual and not musical (Reference BoulezBoulez 1967: 4). This most likely reflects the fact that the musical influences were not in the realm of pitch, nor were intended as imitation, but instead transcended into other dimensions, such as texture and temporality, which, in fact, had a more profound influence on future trends, as I will discuss in the conclusion to this essay (pp. 138–9). For example, in the interview with O’Hagan, he acknowledges the influence of the contrast between percussion and voice of the candomblé. This can be linked to the contrast between smooth and striated time that underlies much of his music from this time (including the examples from Le Marteau and Pli selon pli above), as well as his development of the concept of resonance, perhaps best represented in the play between resonant and non-resonant instruments that is basic to his conception of Éclat, which reaches beyond extending the dimension of time into that of musical space.

Campbell provides important information showing how the Latin American tours were essential to Boulez’s conducting career, since they gave him a first opportunity to conduct a symphony orchestra in a comparatively safe context, which boosted his confidence (Reference Campbell, Campbell and O’HaganCampbell 2016: 21–2). The strides he made in the transformation of his compositional process during the same time period, indicate that the Latin American tours were essential to his development as a composer, giving him the distance and perspective necessary to truly explore new realms and break boundaries and to allow influences from the music of other cultures to re-emerge in his compositions. As Boulez wrote to Souvtchinsky on a 1956 postcard containing an image of one of the Inca ruins in Peru:

To summarise, Boulez’s redefinition of serialism consisted of developing a palette of developmental techniques that could be applied simultaneously to the horizontal and vertical dimensions and at a compositional, rather than a pre-compositional stage, which imbued them with an unprecedented degree of flexibility, as they could proliferate while the composer worked on individual passages. This perspective sees the development of newer trends in Boulez’s music, not as an extension, or loosening, of the serial practice, but as developments that were made possible by his redefinition of serialism. The mathematical premises underlying his focus on techniques that developed relationships built into the material itself, resonate with those embedded in transformational theory. For this reason, the music is ideally suited to analytical techniques that invoke that theory, as embodied in the work of David Lewin (Reference LewinLewin 1987; Reference LewinLewin 1993). Its structure results from anchor notes and important common tone relationships that provide the basis for larger-scale harmonic structures and allowed Boulez to explore the so-called diagonal dimension, allowing for the flexibility in the treatment of musical time.

Such flexibility in the compositional approach enabled an opening up of the aesthetic realm that had important repercussions in the development of future trends. Many of Boulez’s works from this time (for instance, Éclat) were groundbreaking in their exploration of time and space informed by the concept of resonance. The major transformation of his compositional techniques during this time period, with their harmonic structures characterised by large, common subsets embellished by additional notes, can also be seen as resulting from a broader exploration of the concept of resonance, which provides the primary inspiration for all the timbral references described above (Losada 2021). Such focus was behind Boulez’s far-reaching influence on a younger generation of composers, particularly through his work at IRCAM (Institut de Recherche et de Coordination Acoustique/Musique). He had a crucial influence on subsequent developments in composition in fields. The influence of such aesthetic issues (exploration of time and space) on electronic music is straightforward enough. Scholars have also commented on the relationship between Boulez’s blocks of sounds and early experiments in the electronic studio (Reference Piencikowski and NattiezPiencikowski 2002; Reference DecroupetDecroupet 1995a). By understanding the importance of the concept of resonance to Boulez’s later works, one can also make a case of his influence on the aesthetics of spectralism, which developed at IRCAM in the 1970s. In fact, spectral composer Tristan Murail describes spectral music as an aesthetic concerned with ‘sound evolving in time’ (Reference FinebergFineberg 2000: 2; cf. Reference MurailMurail 2005).

Beyond the aesthetic realm, technical influences are important as well. The serial developmental techniques underlie the relationship between acoustic and electronic components in Boulez’s most influential electronic works. For instance, in Répons, a work which propelled him again to the very forefront of composers, Boulez translates his most important serial techniques to the electronic manipulations that are embedded in the work (Reference GerzsoGerzso 1984). In these precise technical connections the root of Boulez’s motivation for founding IRCAM can be seen, a cooperation between scientists and artists to create a technology that can give voice to the artist’s technical and expressive ideas. Similarly, Boulez’s exploration of sound structures through repeated proliferation of his techniques of development in the vertical realm (for instance in the Third Sonata (Reference O’HaganO’Hagan 1997 and Reference Ahrend2017) and Doubles (Reference LosadaLosada 2018 and Reference Losada2019b)), along with his aesthetic position that explored the boundaries between perception and non-perception, prefigured crucial developments in compositional trends that explored the boundaries between sound and noise essential to sound mass composers such as Penderecki and Ligeti (Reference 370BoulezBoulez 1976: 51–2; cf. Reference LosadaLosada 2014, Reference Losada2017, Reference Losada and Illiano2019a, and Reference Losada2019b; Reference Decroupet, Decroupet and LeleuDecroupet 2006). This discussion shows how, far from an abandoned practice, Boulez’s expansion and redefinition of serialism resulted in works and approaches that opened up new avenues for composition and continue to be relevant to composers worldwide to this day.

Karlheinz Stockhausen was one of the first European composers to write serial music (or – to distinguish it from the dodecaphony of, for instance, Schoenberg, Berg, and Webern – multiple serial music). He is also one of its most high-profile representatives: for Stockhausen, serial thinking was a complex and life-long ‘mental attitude’ which went beyond composing (Stockhausen 1963i: 48; Stockhausen 2014c). With the start of serial composing in the early 1950s up until the end of his life, Stockhausen played a role in countless compositional, technical, and aesthetic innovations, something which is also reflected by a range of new terms applied to his musical works. Such terms include point music, group composition, statistical field composition, moment form, process composition, variable music, formula composition, scenic and multi-formula music, and more. In a nutshell, it can even be said that Stockhausen’s entire work is marked by serial thinking, even if some phases – such as his ‘intuitive music’ – seem distinct at first glance. The chronological cornerstones of his serial work comprise the ensemble piece Kreuzspiel (1951) and the Klang cycle – The 24 Hours of the Day – which came about between 2004 and 2007. Below follows a necessarily brief walk through the work, which stops at selected points, which will serve to explain the foundations and the constants, but also the creatively changeable dimensions of Stockhausen’s serial thinking.

In summer 1951, Stockhausen participated in the Darmstadt New Music Courses for the first time. He met the Belgian Karel Goeyvaerts (cf. Reference DelaereDelaere 2010 and Reference Delaere2011; Reference Misch and DelaereMisch and Delaere 2017), who had the first (multiple) serial composition in Europe under his belt with his Sonata for Two Pianos, which he had just completed. Goeyvaerts studied at the Paris Conservatory until 1950, where he became familiar with Olivier Messiaen’s ‘Mode de valeurs et d’intensités’, which inspired him to create the sonata. In Darmstadt back in those years, there was much being said about the twelve-tone music of Arnold Schoenberg, Alban Berg, and Anton Webern. With the ‘Mode’, Messiaen went one step further than the composers of the Vienna School, who had only arranged pitches in rows: he organised the parameters of pitch, duration, volume, and attack intensity in the form of ‘modes’. Goeyvaerts took the step towards complete serial design in the second movement of his sonata. Fascinated by the novelty of this music, following the 1951 Darmstadt Courses Stockhausen composed Kreuzspiel for oboe, bass clarinet, piano, and three percussionists, his first own comprehensive serial composition. In the run-up to 1953, other works of this type followed in close succession: Spiel for orchestra (1952), Schlagquartett (1952, revised in the same year as Schlagtrio for piano and two timpanists), Klavierstücke I–IV (1952–3), Punkte (1952/62) and Kontra-Punkte (1952–3), as well as the electronic Studie I (1953) and II (1954). Stockhausen soon described these works as ‘point music’, a term Herbert Eimert had coined in 1952, to describe the auditory impression of isolated successive tones. At the same time, Stockhausen wrote his first theoretical essays, in which he attempted to explain and clarify the new type of composition.

Basic aspects of his serial thinking were distinct even in Kreuzspiel, in that the serial organisation of a composition always represents a complex and procedural structural principle which arose from a superordinate work idea. From individual elements to large shapes, everything musical in the work is there to be seen, and with this the entire serial organisation is in a coherent context. In Kreuzspiel, for example – as the title indicates – it is about the ‘idea of a crossing of temporal and spatial processes … in 3 stages’ (Stockhausen 1964c: 11). Stockhausen selected a twelve-tone series as the basis of the regulations to be applied to the material, which he linked with two groups of six different dynamics, twelve intervals, and twelve durations (Reference BlumröderBlumröder 1993: 39–56). With this, though, following additional serial predeterminations with regard to the musical material, at the stage when the music would be played the matter was not one of initial exposure of the initial series with subsequent derivations or permutations; rather, it was about the procedural emergence and passing of the initial series, whereby it undergoes an ‘inner change’ (Reference BlumröderBlumröder 1993: 56).

On a more general level, in his essay on the ‘Criteria of Point Music’, Stockhausen speaks of the ‘subordination of tones to a unified principle’, hence idea of the work. Important factors here include the ‘singularity’ of the work idea, and ‘lack of contradiction’ between the idea and the material regulations and the equality of all individual parts. The ‘single element’, in turn, is ‘the tone with its four dimensions: duration, intensity, pitch, colour’ (Stockhausen 1963e: 18–19). As a matter of fact, in the case of ‘point’ compositions, an individual sound is the largest unit. This is because the determinative procedure aims to tie together different sets of characteristics that emerge at the interfaces of individually characterised single tones. In contrast to earlier composition methods, the individual tone acquires a completely new status in that it carries within the idea of the whole thing – by which it was generated – as a structural moment. In his ‘Work Report’ (on work undertaken between 1952 and 1953), Stockhausen formulated this as a premise of point composition: ‘To begin with, all form should set out from the point from the individual tone – and flow back into it’ (Reference Stockhausen and SchnebelStockhausen 1963a: 36).

This new type of concentration on the individual tone as the ‘largest formal unit’ can also be explained by the demand for ‘unification’ and ‘lack of contradiction’ within the superordinate structural principle, since the functional tonality of the tones is no longer determined by that which goes before and after them (Stockhausen 1963f: 76). With this, an additional aspect comes into play: the expansion of serial composition to all sound parameters meant a radical abandonment of previously regulative techniques of musical organisation. Stockhausen was well aware of this fracture: following the period of the Nazi dictatorship and the Second World War, he intended to preside over a rebirth of music with serial composing. In 1953, he emphatically wrote in the essay ‘On the Situation of the Métier’: ‘It should not be forgotten, however, that seldom has a generation of composers had so many opportunities and been born at such a fortunate point in time: The “cities are erased” and we can start from scratch again irrespective of ruins and “tasteless” remains’ (Stockhausen 1963i: 48). For Stockhausen, serial composing was a ‘new musical language’, which, after the ‘derailment of German Romanticism’ (Stockhausen 1963i: 48), opened up the possibility of overcoming subjective and national tendencies:

Like other composers, Stockhausen appealed to Anton Webern in particular: it was in Webern’s twelve-tone works that he saw an expanded compositional predetermination, if still bound to the idea of the series, most strongly mapped out. Stockhausen also analysed Webern’s music from a serial perspective: in the Concerto for nine instruments op. 24, ‘some once-chosen Gestalt (theme, motive)’, in Stockhausen’s eyes, was no longer essential. What was essential was ‘rather the proportional sequence chosen for pitches, note values and dynamic levels’. The ‘Schoenbergian thematic serial principle’ was replaced by a procedure whereby a certain number of parameters – in a constantly changing combination – served as a sort of ‘structural mediation’ (Stockhausen 1963g: 26). While Stockhausen felt a ‘contradiction’ between the use of twelve-tone series and the recourse to traditional principles of sentence formation and form design in the case of Schoenberg, Webern’s music offered him a starting point which he viewed as legitimate from the perspective of musical history. With the first serial point compositions, traditional ‘“Gestalts” – themes, motives, objects’ have been replaced by ‘a series of the most latent and striking transformations and renewals’. ‘The same thing is never heard twice’, Stockhausen insisted. ‘Yet we have the distinct feeling that we do not fall out of an unmistakable, extremely unified construction. A hidden cohesive force, related proportions: a structure. Not the same Gestalts in a changing light, but instead: various Gestalts in the same light that permeates everything’ (Reference Stockhausen and SchnebelStockhausen 1963a: 37).

In the early 1950s, Stockhausen consequently understood the serial organisation of material as ‘a sort of support that keeps us from slipping’. To him, in its strictest form, it was necessary to retain this support until one was able to speak the new musical language ‘without mincing matters’ (Stockhausen 1963i: 48). However, in all Stockhausen’s work, he never viewed his serial organisational forms as a rigid grid. Flexible handling of pre-established organisational structures is most clearly evident in the numerous ‘inserts’ in his works (cf. Reference Assis, Grant and MischAssis 2016). At the end of the 1970s, Stockhausen confessed that he had initially composed his works in one go before considering them ‘finished’, but then, occasionally, ‘almost in a state of fear that the whole thing was too theoretical’, withdrew to consider ‘sound ideas’ which were ‘not accommodated in the system’ (Stockhausen 1989c: 323). In Gruppen for three orchestras, for example, in the highly complex four-part serial work structure, three longer free musical sections were inserted (cf. Reference MischMisch 1999b). Only with this alternating combination does the work gain its specific dramaturgical element, something which is possible only because of the temporary rejection of serial strictness. Elsewhere, what this means is that ‘inserts are always what are left out during the planning stage. They are not just events; they are always the events which are missing. … Inserts are the necessary additions in an organism’ (Stockhausen 2014j: 311). Stockhausen’s hint that he always composed the large form of a work ‘intuitively and the microstructure mentally’ (Stockhausen 1978b: 577) complements this description of the relationship between serial order and compositional freedom.

Although early serial composing was based on the model of twelve-tone music, and the starting point was often a series of pitches, from the start composers acknowledged the challenge of finding comparable and above all practical forms of organisation for the other parameters: length, volume, timbre, and so on. Simply dividing these parameters, like pitch, into twelve equal parts led to unsatisfactory results, since an addition of rhythmic values does not correspond to the logarithmic principle of twelve tempered halftones within an octave. With Kreuzspiel, Stockhausen limited the dynamics to six values, which he used twice. In Klavierstück III, the ‘specific organisation of the material, and as such the entire composition’ are based on the principle of a serial order each element of which comprised three determinants (Reference BlumröderBlumröder 1993: 123). These include, for example, three dynamic values (piano, mezzo forte, and forte), three metric units of three, four, and five eighth values expanded into a series by multiplication, and a pitch organisation based on two sets of three four-tone groups and two three-tone groups, alongside permutations in units of three and so on (cf. Reference BlumröderBlumröder 1993: 123–37).

The serial organisation of Kontra-Punkte for ten instruments, on the other hand, is based on units of six. Stockhausen initially formed, for example, six different timbres: ‘3 different types of pairs of wind instruments and 3 string instruments with strings which are struck, plucked and stroked’. In the course of the work there unfolds a process which begins ‘in a diverse world of sound’, in which all timbres are to be heard; gradually the timbres are subtly reduced, until only ‘a unified, unchanged output can be heard’, the struck strings of the piano (Stockhausen 1964h: 20).

In 1953, with Studie I, Stockhausen composed the first piece of electronic music comprised solely of sine tones. Until this point, the parameter of timbre had been something that was not serially determined in compositions for traditional musical instruments, and this allowed electronic media to create completely new and work-specific timbres. What served as a starting point for Studie I was a sequence of five proportions which resembled a falling minor tenth (12:5), rising major third (4:5), falling minor sixth (8:5), rising minor tenth (5:12), and falling major third (5:4). A frequency selected at the beginning was multiplied with the factors of these proportions (Stockhausen 1964b: 24), so that further permutations for a sufficiently large number of frequencies could then be derived from the resulting frequency series. With the help of a permutation procedure based on a series of six, sound mixtures were then formed from the frequencies. The principle of ‘mixing sound mixtures from simple tones’ generates the ‘mould construction’ of the entire composition: ‘Sounds form sound mixtures (“Sound groups” – vertical); sound mixtures form sequences (“sound groups” – horizontal); sequences form structures (“sequence groups” – horizontal or vertical); meaning that a uniform proportion of the whole work can be determined from a group series’ (Stockhausen 1964b: 26; Stockhausen’s italics).

As is shown based on these short work contexts, the term ‘series’ rapidly undergoes a modification with the advent of Stockhausen’s serial composing. It no longer refers only to pitches, durations, volumes, and timbres; rather, it refers to the sequences of numbers and proportions which generate the structure of the entire composition. In 1953, Stockhausen’s overall definition of the ‘serial principle’ is:

One key work that fully implements this principle is Gruppen. The core of the work is one half of a symmetrical all-interval series, from which the entire work structure was derived, as if from a genetic code. As in Studie I, Stockhausen used mainly the interval proportions of this series: he transferred them in consistent ratios and in this way generated a structural space–time continuum (cf. Stockhausen 1963h; Reference MischMisch 1998 and Reference Misch1999b). This also solved two fundamental problems. For one, there existed a convincing classification system for the time level comparable to the pitches, with which Stockhausen worked from a permanent octave, which – like the pitch octave – is divided in logarithmic intervals and is transposable. Also, the new organisational system generated larger formal units. The details of these longer musical sections were handled by Stockhausen partially in accordance with statistical criteria – only the framework conditions were determined by the superordinate plan. The single tone was no longer the largest unit to be formed; rather, it was a so-called group of tones. The dominant experiential qualities of these group continued to be determined serially: ‘Soon, however, I broadened the exclusively “point” conception of form. I hit upon group composition. In group series, pitches are grouped together according to mutual superordinate characteristics. And yet the individual pitches, which are to be heard grouped together, are still the point of departure’ (Stockhausen 1963f: 76).

At the start of the 1950s, Stockhausen had postulated a system of strict handling of the row-bound organisational forms, for the purpose of avoiding echoes of the previously regulative musical language. During the 1950s, he gradually loosened his self-imposed strictness; however, he did it without abandoning the essential principles behind his serial thinking. One consequence on a technical level was the development of group composition. However, the complexity of serial notation influenced not only audio perception but also musical interpretation. After all, an extreme differentiation in the rhythmic area brings with it ‘factors of uncertainty’, which influence ‘temporal precision … in performance’ (Stockhausen 1963h: 126).

In order to ensure creative use of this inaccuracy, Stockhausen responded with statistical determinations of musical properties, and introduced the term ‘field’ into his terminology: ‘series of field sizes’ and ‘field proportions’ operate in ‘statistical field composition’; the abrupt ‘shift from “point” to “statistical” temporal perception’ was ‘yet a further motive for statistical field composition’ (Stockhausen 1963h: 129). ‘The statistical conception of form works with approximative determinations. It deals with degrees of density of note groups; degrees of pitch register, of direction of motion; degrees of velocity, of change of velocity, of average intensity, of change in intensity; degrees of timbre and of timbral mutation’, Stockhausen stated (Stockhausen 1963f: 77).

Aleatoricism, polyvalence, and variability are effective both at micro and macro levels in many of Stockhausen’s compositions. In Zeitmasze for five woodwinds (1955–6), there exist five different ‘pace settings’ (the time measurements of the title) which combine precise time determination with flexible time design – ‘played sequentially and simultaneously’: ‘1. twelve tempos on a chromatic scale between single and double speed (bb. 60–120), measured according to clock time; 2. As fast as possible; 3. Start extremely quickly and slow down approx. four times; 4. Start at a speed approx. four times slower until ‘as fast as possible’; 5. As slow as possible’ (Stockhausen 1964g: 46; cf. Reference KohlKohl 2017).

For the electronic composition Gesang der Jünglinge (1955–6), Stockhausen had a boy sing verses from the Apocrypha to the book of Daniel. Even though he introduced the creation of unknown, never-before-heard timbres into electronic music, this was when the human voice was, for the first time, included in the context of the new medium. The sung recordings were subjected to an extensive serial design process, which operated with, for instance, a series of seven intelligibility levels (cf. Stockhausen 1964i, 1964a, and 1964e; Reference Decroupet and UngeheuerDecroupet and Ungeheuer 1998; Reference Heike, Misch and von BlumröderHeike 1999; Reference ToopToop 1981). There is also a mediation between electronically generated sounds and sung speech sounds, music and speech, sinus tone complexes and sung chords, and so on. Much is serially scaled and formed, while other things are designed according to statistical criteria. In Gesang der Jünglinge, space is also used as a musical parameter for the first time in Stockhausen’s output: in the four-channel (originally, five-channel) composition, the sound results are distributed across the four tracks of the recording and over the four loudspeakers during performance in a concert hall, according to serial criteria. In this way, the work constitutes the prelude to a series of other Stockhausen pieces which are composed as space music (cf. Stockhausen 1963d; Reference 389Misch, Misch and von BlumröderMisch 1999a).

Stockhausen designated the location at or from which sound is generated a “topic” (Stockhausen 1963d: 152–75), which is to say an additional new parameter in addition to pitch, volume and timbre. The spatial dimensions were gradually expanded, a function not least of the available technical possibilities: Telemusik (1966), Kontakte (1958–60), and Hymnen (1966–7) are four-track; Sirius (1975–7) is eight-track; in the opera cycle Licht (1977–2003), there is a cubic loudspeaker model in Oktophonie from Dienstag aus Licht; the electronic music with sound scenes from Freitag aus Licht is twelve-track. The pinnacle of spatial polyphony is represented by Cosmic Pulses, the thirteenth hour of Klang (2004–7): Stockhausen composed twenty-four sound layers, each of which has its own tempo, overlapping with the others in the piece and, then, a total of 241 different ‘space orbits’ (Stockhausen 2014b: 65), distributed over eight speakers, for the individual sections of these sound layers.

If the large-scale layout of a composition is variable, then Stockhausen would also speak of ‘polyvalent form’ in such cases (cf. Stockhausen 1963b: 241). Klavierstück XI (1956) is probably the best-known example. This is composed of nineteen musical sections which are irregularly distributed on the score sheet. The interpreter can start with any group and also connect the following sections together ‘unintentionally’ (Stockhausen 1964j: 69). The sound groups are serially composed in detail and precisely notated, but superordinate qualities, such as tempo, the basic dynamic degree, and the attack intensity, are only determined by the respective previous group.

The Momente, that is ‘moments’, for soprano, four choir groups, and thirteen instrumentalists (1961–2) (Stockhausen 1964j, 1971b, and 2014h), too, are ‘no finished work with a clearly defined beginning, form flow and end; rather, they are an ambiguous composition of independent events’ (Stockhausen 1964l: 130). The idea of the ‘moment’ continues the group principle in technical terms, except with a higher level of serial ‘freedom’ and technical independence. The Momente combine many of Stockhausen’s compositional experiences since 1951. In this regard, they are key, not just with respect to length and complexity. One central aspect is the ‘abolition of the dualism between vocal music and instrumental music, between sound and silence, between sound and noise’ (Stockhausen 1964l: 130). Stockhausen transferred numerous qualities of electronic music into vocal composition, thereby establishing ‘sounds scales’ of ‘articulations’ and ‘noises’ (Stockhausen 1964l: 131–2). Using their hands, feet, and mouths, choir singers continuously generate noises, with and without aids. Underpinning this are scales which provide unvoiced, noisy consonants between vocal and instrumental sounds, and vowels between breathing and singing.

In the 1960s, there were two trends to be observed in Stockhausen’s musical work which reflected further relaxation of the initially strict rules of serial composition. For one, in electronic compositions like Telemusik (1966) and Hymnen (1966–7), he fell back on already existent forms of so-called ‘found music’ (cf. Stockhausen 1971d; Reference Erbe and von BlümroderErbe 2004). For a second, he granted far-reaching freedoms to those who interpreted his instrumental works. In Telemusik, forms of cult and folk music from different countries served as source material; in Hymnen, the source material was forty or so national anthems from all over the world, ‘the most familiar music imaginable’ (Stockhausen ([0-9]+): 122). While such a recourse to traditional, pre-existing musical material was something that Stockhausen could hardly have conceived of in the early 1950s (cf. Stockhausen 1971d: 80), in the context of increasing globalisation and mobility, he would establish a new, integrative concept of ‘world music’ or rather ‘universal music’ associated with the utopia ‘music of the whole world, all countries and races’ (Stockhausen 1971d: 75; cf. Reference Schumacher, Misch and von BlumröderSchumacher 1998; Reference Gruber, Misch and von BlumröderGruber 1998; Reference Heile and HeileHeile 2009). Also, the serial handling of material properties would became increasingly multipurpose on the path to technical composition from 1970 onwards: in Hymnen, Stockhausen developed the ‘intermodulation’ procedure, with which, for example, ‘the rhythm of a hymn was modulated with the harmony of another hymn, and the result was in turn modulated with the constellation of timbres and with the melodic course of electronic sounds’ (Stockhausen 1971c: 98).

Stockhausen’s instrumental compositions of the 1960s were marked by a significant increase in interpretational freedom. In parallel, the term ‘organism’, which Stockhausen was already using in previous contexts as far as characterisation of his works was concerned, gained greater significance. Process compositions such as Plus–Minus (1963), Solo (1965–6), Prozession (1967), Kurzwellen (1968), and Spiral (1968) are based on serially designed form gradients which are ‘enlivened’ in detail by those performing, allowing one to experience the ‘structure formation process’, which is to say ‘the emergence and fall of multi-layered processes’ (Stockhausen 1971f: 86). The processes applied in the scores enable individual ‘multiple interpretations’, as well as the integration of newer, unspecified materials for the creation of ‘musical beings’ or ‘living organisms’ (Stockhausen 1971e: 40). Live electronic media are also frequently used. The scores now define, for example, ‘structural parts’ and ‘shape types’, and the ‘overall trend resulting from changes’ or ‘level of change’, such as through ‘transformation signs’ (like plus and minus symbols) (Stockhausen 1971e: 43–6), which can mean higher, louder, longer, greater and lower, quieter, shorter, less. Unpredictable materials frequently considered by Stockhausen include sound outputs from a shortwave receiver: interpreters look for an output from the radio device and respond to it according to the fixed process given in the score.

The creative role granted to performers as the work was played peaked at the end of the 1960s in the text compositions that Stockhausen brought together under the description ‘intuitive music’. These are purely verbal instructions which – when following the basic principle of serial scaling – form the opposite end of the spectrum from the strictly structured selective compositions of the early 1950s. The interpretations of these texts should not be improvisations of material already known; rather, they should continue to live up to the dictum of innovation by sharing experiences about ‘the limited scope of the rational’. Following the many ‘stages of primarily rational music’, Stockhausen was now concerned with ‘discovering different archetypes of musical processes through the different texts, each of which leads to their own musical happenings’ (Stockhausen 1971a: 124). The zeitgeist of such years is also reflected in the spiritual dimension, in which one may find elements of the ‘intuitive’: traces of Fluxus and Happenings, hippies, the Vietnam War, the sexual revolution, and the student movement can also be found in Stockhausen’s work.

However, once again, the ‘mental-spiritual [das Geistig-Geistliche]’ facet hints at another constant which has not yet been discussed: Stockhausen’s music, from his first work to his last, features a religious overtone (cf. Stockhausen 2014g: 214 and 2014e; Peters 1999 and Reference Peters2003; Reference UlrichUlrich 2006). Stockhausen originally grew up in a Catholic environment, in the Bergisches Land near Cologne. In a way that paralleled his own life experiences, and encounters with other countries and cultures, later on in his life he would distance himself from Catholicism in favour of an expanded universal belief. The conviction that the universe is sensibly ordered by the divine was and remained a central factor. The same principle of divine order and perfection is reflected in the small and the large, and in nature and art. However, music is not just a depiction of cosmic order; at the same time, it also serves as a tool of ongoing worship of God. This conviction is the main thread of all Stockhausen’s works and at the same time the cornerstone of his serial thinking. After all, from the start, Stockhausen understood the overriding structural principle of a work as a reflex of the ‘universal order’. As early as 1953, he was occupied with the question of why composers attempted to organise ‘everything existing in a composition … by one unified principle’ (Stockhausen 1963i: 46), which is to say ‘the proportions of the series’:

This view is just as central to intuitive music as it is to the formula composition developed by Stockhausen from 1970 onwards (Stockhausen 2014e: 151–2).

The year 1970 marks a climax in Stockhausen’s compositional career. The Federal Government sent him to the world exhibition ‘Expo 70’ in Osaka, Japan, as a prominent representative of the German music scene. In the spherical concert hall – built by the architect Fritz Bornemann in line with Stockhausen’s plans for Germany’s contribution – his works were presented for five-and-a-half hours a day for almost six months. It was a site for listening to a compilation of electronic and current instrumental compositions which were projected to the public through loudspeakers in surround sound. In this environment, following a long phase of indefinite, polyvalent and intuitive music, Stockhausen once again composed a comprehensive, serially determined work: Mantra for two pianos. For the first time, a so-called formula served as the musical nucleus of the work. The principle of composing with one or more formulas characterises Stockhausen’s work from Mantra onwards, right up until the completion of the Licht heptalogy.

Stockhausen had defined the serial thinking of the 1950s as a dualistic kind of thinking based on gradual mediation between opposing pairs, but, in contrast, he also described formula composition with the metaphor that, now, it was possible to transform ‘a mouse in a glass’ (Stockhausen 2014a: 193; cf. Stockhausen 2014d: 274–5). The term ‘formula’ suggests different things: the magic formula in the sense of a magic word, a formula as known from a scientific perspective, but also Einstein’s dream of a universal formula (Stockhausen 2014d: 275). For Stockhausen, formula thinking was, at the same time, a global constant, which can be traced back to Franco-Flemish isorhythm, to Indian ragas and talas or to archetypes of Chinese or Greek music. Johann Sebastian Bach, Olivier Messiaen, and Anton Webern were Stockhausen’s key figures in music history, and they knew about ‘the ancient tradition of forming things with archetypes’, he claimed (Stockhausen 2014i: 28). Stockhausen regarded formula composition as a ‘differentiated further development of serial music … including the intermediate stages (namely: aleatoricism and indeterminacy or variable determinism)’ (Stockhausen 2014i: 26), which brings back some essential qualities of pre-serial music which had previously been in a state of paralysis: melody, echoes of tonal harmony or the use of key intervals of tonal music, repeatability, singability, and tangible, concise figures and variative shape formation (cf. Stockhausen 2014k: 307–8). Nevertheless, the formulas themselves and the act of composition comply with serial regularities which are highly complex. A formula is no abstract sequence of sound properties, but rather a musical structure which is catchy, melodic, rhythmically specific, and individually characterised in many different ways. All musical characteristics, which were initially determined in mutually independent series of numbers and proportions when serial composition first started, are now synthesised in the formula (cf. Stockhausen 2014f: 254).

After Stockhausen had written works using a formula – such as Mantra (1970), Inori (1973–4), and Sirius (1975–7) – between 1977 and 2003 he composed his opera cycle Licht, based on a unique so-called ‘super-formula’. The super-formula for Licht is a three-part melodic structure lasting around one minute, which served as a matrix for the twenty-nine-hour heptalogy. In addition, the action of the cycle is included, at an embryonic level, in the music-genetic material of the super-formula. In the term ‘multi-formular music’, Stockhausen summarised the further development of formula technology thus:

The three levels of the super-formula represent the three main characters of Licht: Eva, Michael, and Luzifer. Each formula is based on core pitch material: Eva’s melody has twelve chromatic semitones, Michael’s has thirteen, and Luzifer’s has eleven. Seven horizontal sections make up the basic material for the seven opera days. On the basis of the core pitches, Stockhausen composed ‘core formulas’ for Michael, Eva, and Luzifer, which differed melodically, rhythmically, and dynamically. These were supplemented by a variety of musical characteristics and events unique to each one. Each formula includes not only pitches, durations, intensities, timbres, and (where appropriate) spatial positions. Also included are echoes and pre-echoes, improvisations, scales, pure and timbred breaks, modulations, rhythmic characterisations, sounds, and semantic details.

Ultimately, the super-formula for Licht results from the vertical combination of the three individual formulas. All musical contexts of the opera cycle are generated from them, the compositional structure becoming increasingly condensed and moulded through segmentation, spreading or compressions, concatenations, overlaps, transpositions, insertion of segments, and other procedures. Musically, each formula represents one of the three main figures: Eva’s formula is particularly melodic, featuring rising-falling-rising fine glissandi, with a central interval of a major third. The direction of Michael’s formula is a descending one: characteristic intervals are fourths along with a ‘floating tritone’ at the end; the main characteristic is the dynamic; the formula contains a triple echo. The Luzifer formula melody begins with tone repetitions in elevenths, followed by a passage which ‘jumps up twice and falls each time thereafter’, and is pervaded by dissonant intervals like sevenths and tritones, along with odd-numbered rhythms such as fifths, sevenths, thirteenths, or ‘irregular complexity’ (Stockhausen 1989b: 357–8). Luzifer’s formula also includes noises, unvoiced consonants, improvisations, and a double falling echo. The three cosmic spirits Eva, Michael, and Luzifer appear in the various sections of the opera, where they sing, play, and dance.

The movements of the musicians are normally fixed in terms of composition. The figure of Eva is linked to the basset horn, Michael is connected with the trumpet, and Luzifer’s instrument is the trombone. For each day of the week there are individual timbres, symbols, scents, elements, and more, depending on the topic of the weekday. For the events in Licht, Stockhausen drew on numerous cultural and historical sources, such as religions, mythologies, fairy tales, or collectives of literature. Even biographical information was included in the scenario. In Licht, Stockhausen consistently put forward the basic idea that manifested itself in his earliest years of composing: he wanted to ‘develop worlds from one core’. That is to say, ‘Licht is nothing more than a galaxy developed from a single core formula’ (Stockhausen 2014i: 26). Stockhausen’s music, which is neither expressive nor subjective or emotional, aims at what is universal, timeless, binding for all. This characteristic is reflected not least in the temporal cycles which are the subjects of his compositions: in Sternklang (1971) Stockhausen translated constellations into notes; Sirius (1974–7) is a work about the four seasons of the year; Tierkreis (1974–5) is music dedicated to the twelve zodiacal signs; Der Jahreslauf (1977/91) illustrates the temporal course of millennia, centuries, decades, and years; the Licht cycle stages the seven days of the week. The last major cycle, incomplete at the time of Stockhausen’s death, Klang, is dedicated to the hours of the day, but ends with the twenty-first hour, Paradies. In Klang, Stockhausen returned to a simpler serial process based on a double all-interval series. The sketches of the Klang cycle show that most of the hours were composed without complex predeterminations. As Stockhausen put it in the 1950s, stating it as the goal of serial notation, he wrote Klang, so to speak, ‘as if one had grown a beak’ (Stockhausen 1963i: 48).

Looking back at Stockhausen’s complete oeuvre, the consistency and scope of his serial thinking are conspicuous. The associated ‘mental attitude’ can be described as a fruitful mixture of deep faith, well-founded knowledge about the cosmos and nature, and an almost inexhaustible artistic creativity and creative power, coupled with the standard of always making heard something musical that was new and unknown, again and again. One of the essential premises of serial composition lies in equal rights for all elements of a work while at the same time allowing for consideration of their diversity. This is associated with a departure from the hierarchical thinking that characterises tonal music above all else. Stockhausen was deeply convinced of the sustainability of serial thinking, not least because it opened up a wide range of compositional integration options and rejects subjective expression in favour of general, cosmic truths.

Among the Italian composers engaged with the redefinition of musical language through (multiple) serialism, Luigi Nono was the first to articulate a theoretical reflection about this technique. As it is demonstrated through Nono’s correspondence with Bruno Maderna and Karlheinz Stockhausen, his earliest conversations about serialism, of an entirely private nature, date back to 1951 to 1952. However, it was only in later years, between 1956 and 1957, that Nono decided to take up a public discussion of serial technique from the perspective of its historical foundation. Considering that multiple serialism – that is, an approach that treats multiple musical parameters in a serial manner – was conceived around 1950 to 1951, and that composers had been positioning themselves around the new technique since then, Nono’s initiative may appear tardy. At that time, however, the theme of history as a dialectical process was at the centre of Nono’s thought, which was influenced by both Marx and Gramsci.

In the summer 1956, Nono took part in a seminar organised by Hermann Scherchen and centred on the analysis of Schoenberg’s Variations op. 31 and Webern’s Variations op. 30 (Reference NonoNono 1956; cf. Reference SchoenbergSchoenberg 2011). It was in this context that Nono developed his earliest (public) reflections on serialism, which he illustrated in a short article published in the same year examining the development in the way in which the series had been employed beginning from Schoenberg’s Serenade op. 24 and the main theme of his Variations op. 31 up to the work of Boulez, Stockhausen, and in Nono’s own latest composition, Il canto sospeso (1955–6) (cf. Reference Nono, De Benedictis and RizzardiNono 2018b). Also in 1956, Luciano Berio had invited Nono to contribute an analytical article to the first issue of his journal, Incontri Musicali (Nono to Berio, 10 January 1956, Paul Sacher Foundation, Basel). In response, Nono wrote a detailed analysis of the ‘Thema’ of Schoenberg’s op. 31, which he further developed for a lecture that he gave in Darmstadt in 1957 and later published under the title ‘The Development of Serial Technique’ (Reference De Benedictis and RizzardiDe Benedictis and Rizzardi 2018b).

The main purpose of both the 1956 article and the 1957 paper was to demonstrate a direct continuity in compositional strategies between Schoenberg and the music of the so-called Darmstadt School (a term first more widely popularised by Nono in his 1957 essay, though coined at least a year earlier (cf. Reference WehagenWehagen 1956)). In these writings, Nono implicitly opposed the theories that Boulez had been promoting since 1951, especially Boulez’s argument regarding Schoenberg’s presumed ‘confusion between theme and series’ in his ‘serial works’, an opinion that was well entrenched among many composers in the Darmstadt music circles (Reference Boulez and ThéveninBoulez 1991f: 212).

Nono’s analysis of the op. 31 theme aims, in particular, at overturning Boulez’s theories. From Nono’s perspective, the foundation of serial composition lies precisely in the combinatory possibilities implicitly underpinning the thematic process which generates the variations devised by Schoenberg. Nono’s argument also rested on his interpretation of the BACH motif in Schoenberg’s Variations as ‘a thematic-formal element independent of and pre-existing the row itself!’ (Reference Nono, De Benedictis and RizzardiNono 2018b: 129). In Nono’s view, this motif acts as a secondary combinatory texture, traversing the entire composition. In spite of its implicitly polemical stance, however, Nono’s approach only found limited resonance among his peers. The text of his 1957 Darmstadt lecture was published in German only, and the portion on the Variation’s theme did not appear in Incontri Musicali, simply because of a disagreement with Berio over the style of the essay. Ironically, Nono’s article was replaced by another one by Henri Pousseur that advanced the argument that Nono had attempted to reject – namely, the discontinuity between the thematicism of Schoenberg’s twelve-tone technique and the foundation of the New Music (cf. Reference 393PousseurPousseur 1956; Reference De Benedictis and RizzardiDe Benedictis and Rizzardi 2018b: 148–9).

It should be observed that, by 1957, Nono’s serial technique had already been developing from the simultaneous definition of multiple sonic parameters towards the construction of sonic fields. For Nono, however, going back to examine the conceptual continuity between series and theme was, at that time, a way to demonstrate a consistency in the evolution of his own technical choices since the beginnings of his career. It is thus necessary to clarify how this continuity can be verified in time going back to Nono’s earliest experiences with the twelve-tone technique and, so, to his earliest attempts as a composer tout court. While describing this earlier portion of his musical output, it would be reductive and historically inaccurate, however, to discuss Nono’s first experiences with serial or proto-serial technique without a parallel consideration of Bruno Maderna’s procedures, because the didactic workshop in which the latter had invited him to take part in Venice in 1946 would soon become a creative workshop, where the analysis of early and contemporary music was inextricably connected with compositional experimentation on the grounds of shared aesthetic and technical premises.

As is well known, the catalyst that encouraged Maderna and his pupil Nono’s transition to serialism was their encounter with Hermann Scherchen during the conducting course that Scherchen directed at the Venice Biennale in August and September 1948. Scherchen engaged as his assistant for this course his former pupil Hans-Joachim Koellreutter, who had emigrated to Brazil in 1937. During his several-month-long stay in Italy, Koellreutter strengthened his relationship with Maderna and Nono, who in November 1948 attended a course on twelve-tone music that he taught in Milan. Nono’s personal notes from that course show that Koellreutter based his teaching on Paul Hindemith’s theories, in particular the idea of tonal relationships founded on acoustic ‘natural’ laws and the consequent classification of intervals according to their own ‘melodic’ and ‘harmonic strength’, directly derived from Hindemith’s Unterweisung im Tonsatz. At that time, Nono and Maderna were both already familiar with Hindemith’s treatise, and they had been adopting its main principles since their earliest attempts at coordinating advanced twelve-tone techniques with a serialisation of durations and/or rhythms (Reference GuerreroGuerrero 2009; cf. Reference Nono, De Benedictis and RizzardiNono 2018a: 27). Many of the rules that Koellreutter proposed in his class, however, revolved around his taxonomy of ‘melodic’ rows (where ‘tense’ intervals prevail), ‘harmonic’ rows (with a majority of ‘calm’ intervals), and ‘compensated’ rows, balanced between the two. These appear in just these terms in both Nono’s and Maderna’s notes and musical sketches at least until the end of 1951. Beginning from this moment, such a classification of musical material would be permanently inscribed within the compositional technique of both Nono and Maderna, and its influence would extend throughout their use of twelve-tone technique and beyond it in their respective properly serial and post-serial phases.

Works such as Liriche greche (1949), Maderna’s first serial composition, and Nono’s opus primum, the Variazioni canoniche sulla serie dell’op. 41 di Arnold Schönberg (1950), are the result of the assimilation of Hindemith’s ideas via Koellreutter and already demonstrate how both composers distanced themselves from the Viennese School models that their Italian colleagues Luigi Dallapiccola, Riccardo Malipiero, Riccardo Nielsen, and Camillo Togni were more or less slavishly following in the same years. Leaving aside other formal elements that referred to pre-classical if not to Renaissance models, in Nono and Maderna’s works the tone row is not only presented in its retrograde, inverted, and transposed forms but is also subject to permutation, sieving, and proliferation. Most importantly, the tone row is not the only musical material to receive systematic treatment: note durations, while organised independently at first, are later coordinated with the tone row itself. The most significant aspect of Maderna and Nono’s compositional strategy is their creation of tone rows based on the expressivity implied in their intervallic content and their reliance on intervallic quality for the determination of the row’s transformations. This is a recurring aspect in Nono’s serial works of the following years.

On many levels, the aforementioned Variazioni canoniche sulla serie dell’op. 41 di Arnold Schönberg is an exceptional debut composition. Already in its title, Nono announces his intention of applying a process of transformation of the original pitch material, intended as a ‘theme’ but only in an abstract sense, with no regard to (or for) the historical form of the variation. By taking to extremes a typical compositional practice of the Viennese School – that is, the deduction of formal consequences from the intrinsic characteristics of the basic pitch material – Nono begins from the distinctive structure of Schoenberg’s row, whose symmetrical configuration is repeated as such also within its hexachords; indeed, each individual movement of the Variazioni canoniche is built on the ‘mirror image’ (Spiegelbild) principle. Furthermore, in accordance with the principle of intervallic ‘calmness’ and ‘tension’, Nono generates a first variation on Schoenberg’s row by deriving from it three permuted rows completely different from the original – one of them with a prevalence of fourths and major thirds, another one based on tritones, semitones, and minor thirds, and a third one which is more differentiated. The preliminary sketches show that Nono meant to start from each of the three rows that he had generated, plus the original one, to build four distinct episodes differentiated from each other according to their degree of ‘tension’. This project would never be realised, perhaps because Nono preferred to exercise more direct control over the intervals. Yet such a project exemplifies the consistency of Nono’s proto-serial thought, which at that time already tended towards a simultaneous coordination of multiple sound parameters. Indeed, the Variazioni canoniche adopt a systematic device for the assignment of durations, a serie base (a ‘basic row’, as Nono called it in his sketches) consisting of six different units: five individual duration values respectively equalling 8, 7, 6, 5, and 4 semiquavers plus another value corresponding to 3+2+1 semiquavers that works as the only germ of the motivic material used in the entire work (cf. Reference Rizzardi, Borio, Morelli and RizzardiRizzardi 2004: 13). It should be noted that such a treatment of durations is unique in Nono’s work. Its relatively abstract character did not appear again in his later compositions, which are mostly based on pre-existing rhythmic models. Indeed, a first association between the pitch and the duration series underpins the complex double mirror canon of the first movement, ‘Largo vagamente’, but it is only in the following movements (‘Andante moderato’ and ‘Allegro violento’) that a systematic coordination between pitches (permutations of rows divided in six dyads) and durations (permutations of six values) can be clearly observed.

The coexistence of increasingly sophisticated techniques of proliferation and pre-compositional organisation of pitch material on the one hand, and of systematically organised rhythmic structures on the other, is a feature of the compositional procedures of both Maderna and Nono beginning in 1951. In that year, Maderna devised a technique that Nono would also soon adopt, and which would be remarkably successful: namely, a system for the transformation of the basic pitch material in the direction of a rhythmic and harmonic pre-organisation based on the graphic representation of pitches. Maderna sometimes refers to this technique using the term mutazione (‘mutation’) or describes it, along with Nono, as a ‘(magic) square’ treatment. The originality of this technique consists in the use of a basic pitch series for the automatic generation of chains of derived series not just of individual pitches, but also of different elements that may be either note aggregates or ‘empty’ positions (Figure 10.1a). Using this method, it is possible to create a reserve of material that is already intimately related to the rhythmic and harmonic components and can thus foreshadow the musical form. Maderna first adopts the magic-square technique in a composition entitled Improvvisazione per orchestra (1951) and will use it, in increasingly complex ways, until his Concerto per pianoforte e orchestra (1959). Luciano Berio acknowledged his use of it in his Nones (1954) (personal communication, 2000) and Serenata (1957) (Reference Berio and Osmand-SmithBerio 1985: 65). The title Improvvisazione emphasises the self-organisation of the musical material, and the resulting organisation presents itself as having an intentional reference to fifteenth-century isorhythmic motets: the concatenation of the sequences of pitches/chords/rests corresponds to the color inserted atop the taleae, represented by repeated and systematically ordered (dance) rhythmic patterns (Reference Rizzardi and DelaereRizzardi 2011).

Figure 10.1a Composizione per orchestra [No. 1] (1951).

Sketch of the precompositional material for bb. 17–25, Archivio Luigi Nono (facsimile)

Figure 10.1b Composizione per orchestra [No.1] (1951). Score realisation of bb. 17–25 (Ars Viva Verlag).

Nono adopted the same ‘mutations’ technique in his Composizione for orchestra (1951), a work that was premiered in the same concert in which Maderna’s Improvvisazione was first performed. In Composizione, Nono’s implementation of this technique was both more consistent and at the same time less reliant upon the automatic elements of the ‘mutational’ compositional process than Maderna had been in his work. Only in one out of the five ‘episodes’ of Composizione are all the elements – pitch organisation, chordal aggregates, distribution of durations and rests – rigorously based on ‘mutations’ of the original row (Figure 10.1b). Whereas in the first movement the duration of neighbouring notes is determined by the ‘calm/tension’ factor intrinsic to each given interval, the prevailing structural feature of the four remaining movements consists of a contrapuntal arrangement of rhythmic modules predetermined from the transformations of a basic tone row. Nono actually in all of the ‘episodes’ of his Composizione [No. 1] for orchestra uses a series of nine sounds, assigning the remaining three to the timpani in the percussive movement that ends the work (Reference Rizzardi, Borio, Morelli and RizzardiRizzardi 2004, 47–59).

In Nono’s immediately preceding work, Polifonica–Monodia–Ritmica (1951), movements are similarly organised by means of compositional devices, each producing a different kind of development of the original material. In Polifonica, the first, extensive movement of this work, Nono’s tendency to make serial techniques instrumental in the achievement of specific poetic goals can be observed for the first time. In this case, the building of a progressive development from silence into noise and finally into the individual pitch (that is, to melody) that can be in turn used for contrapuntal construction is realised through an automatic process of reduction and progressive ‘indifferentiation’ – until annihilation – of the basic tone row (see Figures 10.2a, 10.2b, 10.3) that allows him simultaneously to obtain both the pitch material and the distribution of durations, up to the point where a predetermined rhythmic model intervenes. This model is based on a motive that, according to Nono, alludes to a traditional Afro-Brazilian candomblé rhythm (‘Jemanjá’), which is in turn deconstructed and permutated through serial procedures (Figure 10.4). Polifonica’s successor, Monodia, sees the first appearance of a form that would regularly appear in Nono’s later music. This monodic form is the outcome of an entirely linear process resulting from the concatenation of derived, regular twelve-tone rows that are symmetrically organised: ‘harmonic’ rows prevail at the far ends of the chain and ‘melodic’ ones predominate towards the centre. Nono derived this form from a number of transformations (for which he had employed the ‘mutation’ technique for the first time) but eventually omitted any vertical implications from the outcome of such transformations. The harmonic component of Monodia, which is implicit to the ‘calm/tension’ division, already prefigures the linearisation of harmonic groups that Nono, although in a different technical context, would use in his Canti di vita e di amore of 1962.

Figure 10.2a Polifonica–Monodia–Ritmica (1951). Generation of ‘degrading’ intervallic material of the opening four-part canon of Polifonica (bb. 1–40)

Figure 10.2b Polifonica-Monodia-Ritmica (1951). Precomposition of the opening four-part canon of Polifonica, derived tone rows from the O form and rhythmic organization (bb. 1–40)

Figure 10.3 Polifonica–Monodia–Ritmica (1951). Four-part canon (bb. 1–40) built by reading each of the four derivations right to left, bottom up, beginning with sparse sounds and gradually filling the space

(score, Ars Viva, excerpts: bb. 1–28)

Figure 10.4 Polifonica–Monodia–Ritmica (1951). Serial permutations of the Afro-Brazilian rhythm (‘Jemanjá’) employed in the movement Polifonica

(sketch, Archivio Luigi Nono; facsimile)

The following cycle of compositions on lyrics by Federico García Lorca (1952–3), and the Due Espressioni for orchestra (1953) further expand the development of complex rhythms deriving from folk models (Reference Borio, Borio, Morelli and RizzardiBorio 2004). In these works, however, the organisation of pitches temporarily departs from twelve-tone materials. As Nono himself would recall in 1987:

However, even when these pre-existing musical materials are chosen because of their allusive or symbolic value – in La Victoire de Guernica (1954), for instance, Nono borrows the melody of the Internationale – they are always transformed through serial procedures: rhythmic motives are systematically decomposed and permutated, and pitches are subject to ‘square’ treatment until all the notes of the total chromatic are obtained. Such compositional choices depart from the more abstract experimentations of Nono’s contemporaries, and because of this they earned him quite a few criticisms. While Maderna himself reproached Nono, albeit in general terms, for the literary drifting of his recent works, Stockhausen made much more detailed criticisms in his private correspondence to Nono, accusing the Italian composer of inconsistency in his use of serial techniques. In a letter dated 9 May 1953, in particular, Stockhausen comments on Nono’s Epitaffi in the following terms:

In his response, which he only wrote two months later, Nono rejected Stockhausen’s argument, but without further elaborating. Yet it is striking that, from the end of 1953, Nono began to steer towards that ‘homogeneous sonic world’ typical of total serialism, which in 1955 would lead to Canti per tredici and, more importantly, Incontri. In Canti per tredici, Nono began to employ the most neutral pitch material possible, the all-interval series, which he would regularly use in all of his works between Il canto sospeso (1955–6) and Cori di Didone for choir and percussion (1958). This series also appears in Composizione per orchestra n. 2: Diario polacco ’58 (1959) and – together with other kinds of series – in the azione scenica (‘scenic action’) Intolleranza 1960 (1960–1).

In Incontri, a tone row mostly based on major and minor seconds does not transform or generate anything and always presents itself in its original form, while all the other sound parameters (duration, timbre, and dynamics) change. The work is made of two mirroring macrosections, parts of a perfectly symmetrical compositional process. These two blocks are internally differentiated by extension and polyphonic density, dimensions that are simultaneously regulated according to the numerical principle of the Fibonacci series. The title Incontri (Encounters) refers to the interpenetration of two symmetrical structures, each characterised by the merging of two complementary expressive characters. But even leaving aside its symbolic implications and private allusions, this is a manifesto score. The clarity of its structure prompted an early wave of scholarly musical analysis that contributed to propagating the image of Nono as a rigorous serialist composer, and which would lead later generations of researchers to overlook the originality, complexity, and incessant development of his technique (cf. Reference WennerstromWennerstrom 1967: 217–33; Reference StenzlStenzl 1972; Reference PiencikowskiPiencikowski 1988). However, what appears to be an exercise of serialist rigour and coherence is nothing but Nono’s earliest codification of a musical constructivism focused on the complexity of sound phenomena, an integral part of a long-term development.

Nono himself expressed criticisms about serialist hyper-determination, especially after 1960, even distancing himself from his own most rigorous applications of this technique, as, similarly, did Boulez (cf. Reference BoulezBoulez 1986a). In the autumn of that year, Nono, who had just emerged from a public debate with Stockhausen (discussed below, p. 171) about the serial treatment of Il canto sospeso, privately wrote that the ‘theocratic’ principle of total determination had always been extraneous to him: ‘in Varianti (1957) I came as close to that principle as possible, as far as study, self-discipline and result analysis are concerned. But it has mostly been distant from me’ (Reference Mila, Nono, De Benedictis and RizzardiMila and Nono 2010: 48). And in 1969, during an interview, he added (perhaps more lucidly):

While from the standpoint of Nono’s poetics it is possible to position his highest degree of involvement with generalised serialism in the years between 1955 and 1959, the composer’s later distancing from this technique seems to circumscribe and minimise its value as a technical principle and to prioritise instead the functional value of systematic compositional processes. This interpretation may be reductive, but it is certainly true that Nono invests serialism with different functions and meanings over time.

Speaking about Nono’s output based on the use of compositional systems and procedures connected with serialism, some scholars have interpreted this timeframe, 1955 to 1957, as a ‘second serial phase’, followed by a ‘third phase’ represented by the works that he composed between 1957 and 1959 (cf. Reference SchallerSchaller 1997). Rather than depending on a rigid timeline, we would like to suggest a kind of bipartition, which is instead articulated around specific developments in Nono’s work regarding the application of serial principles to musical structures derived from a text. This subdivision hinges on Il canto sospeso (1955–6), a work fraught with innovations and changes from the perspective of Nono’s compositional technique that inaugurate his research of a ‘new expressiveness in the song’ (Reference Nono, De Benedictis and RizzardiNono 2001: 432).

Originally chosen because of their poetic contents or their ethical and political message, these texts provided the starting ground for the selection of all the musical materials (see Figure 10.5). Indeed, it is the structure intrinsic to the verbal material (from the ‘quantitative’ perspective of formal subdivisions, of verses, of single words, and so on down to the number of syllables and vowels) that determine the choice of the basic ‘fields’ (following Nono’s own description) that regulate durations, speed, intervals, density, and every other parameter.

Figure 10.5 Typescript of Luigi Nono with text selection and sketches for Cori di Didone

(Archivio Luigi Nono)

It was the peculiar intonation of the text in Il canto sospeso that sparked the well-known debate that divided Nono and Stockhausen after 1957. Again, five years after a letter in which Stockhausen had expressed his annoyance regarding the ‘resorting to subjectivity’, the reliance on ‘predetermined expressive content’, and finally ‘pathos of the intonation of Neruda[’s poem]’ (4 September 1952, Archivio Luigi Nono), the controversy was framed on the level of compositional technique, whereby such technique is put at the service of a text intentionally loaded, both ethically and politically. After his initial disapproval of the programmatic approach adopted in Epitaffi per Federico García Lorca, Stockhausen seemed unwilling to understand the treatment of text in Nono’s compositions following La Victoire de Guernica (1954), a work in which his serial compositional practice had clearly evolved, visible, too, in the involvement of choral ensembles. Stockhausen’s accusations of poor ‘observance’ of serial precepts on Nono’s part eventually moved from a personal to a public level with his anathema incorporated into ‘Sprache und Musik’, a lecture that he delivered at Darmstadt during the New Music Courses of 1957 (cf. Stockhausen 1964d; English translation: Stockhausen 1964e). The specific target of Stockhausen’s analysis was the second movement of Il canto sospeso, which the German composer interpreted according to serial or statistical criteria that were very distant from Nono’s compositional horizon. Take, for instance, Stockhausen’s Gesang der Jünglinge (1955–6), where the voice is elaborated along with the electroacoustic material according to specific ‘scales of intelligibility’ and through permutational structures conceived for the purpose of preserving the intelligibility of the text and to separate its use as sonic material from its semantic value (cf. Reference Decroupet and UngeheuerDecroupet and Ungeheuer 1998).

Nono’s vocal writing technique had precise motivations, strictly related to the content of the text chosen, whose intelligibility, however, ended up being almost precluded; his conception diverged from Stockhausen’s, who was puzzled by this apparent contradiction and attacked Nono precisely on this issue: ‘Why, then, texts at all, and why these texts?’ (Stockhausen 1964d: 158). What is the point of ‘serialising’ such weighty and meaningful texts – he asked – if musical structures end up completely preventing the listener from understanding even a syllable? As Stockhausen put it:

Nono’s reply to Stockhausen came in the form of ‘Text–Music–Song’ (1960), a public lecture that he also gave in Darmstadt (Reference Nono, De Benedictis and RizzardiNono 2018c). However, Nono’s reticence to discuss the technical aspects of his own music led him not to reply with analytical demonstrations, ultimately leaving the actual ‘serial structure’ of Il canto sospeso unrevealed. Instead, Nono adopted a defensive strategy, motivating his choices from a historical perspective, taking, among others, Schubert and his Lieder as an example. Although he employed a different technique from Schubert’s, Nono argued, ‘the two structural elements, namely sound and word, interpenetrating one another, and the one not being subordinate to the other, form a new and autonomous whole’. And he concluded: ‘Composition with the phonetic elements of a text serves today, as in earlier times, to transpose its semantic meaning into the musical language of the composer’ (Reference Nono, De Benedictis and RizzardiNono 2018c: 154 and 178).

And yet, a response based on the analysis on the second movement of Il canto sospeso would have sufficed to effectively reply to Stockhausen’s criticisms and explain the peculiarities of his serial compositional technique in 1955–6. In hindsight, such an analytical response would have also shed light on the preconditions that led to the eventual overcoming of this same technique and, perhaps, would have helped to avoid further misunderstandings in the relationship between text and music in Nono’s works.

When discussing serialism in Nono’s works based on a text (that is, in most of his compositions from the 1950s), it is important to consider that the choice of parametric materials starts directly from the text (see Figure 10.5 and cf. Reference De BenedictisDe Benedictis 2006). Through various transcriptions and gradual text modifications, syllable counts, selection of key words, and the subsequent (re)coding of such words into numbers then associated with the coordination of musical parameters, Nono managed to create a structural grid of the various musical elements that was predetermined by and from the verbal material. In the specific case of the second movement of Il canto sospeso (the sole section for voices only, from the nine movements of which this work consists) it should be immediately pointed out that the compositional technique adopted by Nono presents numerous similarities with movements no. 6b and, especially, no. 9. Not by chance, these three sections are also connected by the content of their respective texts (drawn from Reference Malvezzi and PirelliMalvezzi and Pirelli 1954), whose main theme invites a conscious acceptance of death in the name of a better future. The textual similarities between the three movements find a counterpart in the use of a shared compositional technique that could be called ‘uninterrupted sound [suono continuo]’ and that entails a multidimensional scanning of the text (and its consequent dissolution and perceptual unrecognisability). If one considers that, in Il canto sospeso, the same basic musical material is coordinated with perpetually changing permutational systems that are often chosen depending on the local context – and, in the vocal sections, always according to the semantic of the text – perhaps the most productive question that one must ask in order to understand how Nono chose his coordination principles in his text-based works should be (paraphrasing Stockhausen): ‘why a structure at all, and why this one?’

In the case of movement no. 2 of Il canto sospeso, the analysis reveals how Nono, by means of a rigorous serial procedure, adapted the (musical) form to the (text) content and built a structure that is flexible enough to distribute the chosen text across voices according to specific expressive intentions. The entire movement consists of fifty bars (bb. 108–57 in the score) in a fixed $\begin{array}{c}2\\ 4\end{array}$ metre. The basic duration is the crotchet (the tempo is steady: c. 60–66): the result is a total of 100 abstract ‘tiles’ on which sound agglomerations can be placed. On a formal level (and as a direct consequence of the implementation of serial materials), the movement is divided in two parts: the first is more extended and corresponds to bb. 108–42; the second (bb. 142–57) is a coda of sorts, consisting of a proportional canon. More specifically, the movement is based on the following materials and principles of parametric coordination:

• Durations: In the movement, four duration values are used: the quaver, ; the triplet quaver ; the semiquaver, ; and the quintuplet semiquaver, , which reflect the different possibilities in the division of the crotchet into two, three, four, or five parts respectively. Such values, which regulate the speed, are coordinated with a ‘neutral’ duration series, a Fibonacci sequence made up of twelve factors (six ascending factors followed in symmetrical fashion by an equal number of descending factors), 1–2–3–5–8–13–13–8–5–3–2–1. This series is repeated fifteen times (bb. 108–42) by means of a method of continuous rotation that shifts the first number of the series to the end during each cycle (Table 10.1), though Nono inverts the last two factors in the twelfth iteration. Nono does not employ this method in the second part of the movement (bb. 142–57), in which the duration factors in the series 13–8–5–3–2–1–1–2–3–5–8–13 are linearly associated with each single duration value. In the movement as a whole, the rotation and the coordination of the factors of the Fibonacci series with the four duration values thus determine formal proportions and speed of the sound events.

• Pitches: The only tone series used in the entirety of Il canto sospeso is the all-interval series beginning with the pitch A. In the second movement, this series is repeated nineteen times with no permutations or transpositions, rigidly following the distribution of durations in both the sections of the movement (cf. Table 10.1).

• Dynamics: In the same movement, dynamics are regulated by a series of twelve different intensity values:

This series adopts the same criteria for the selection and the rotation applied for the duration series, although in this case the implementation and statistical distribution of the dynamic series operate vertically (and not horizontally as in the case of durations) and a higher degree of freedom can be observed. The series is repeated fifteen times in constant rotation (Table 10.2). In the second portion of the movement, dynamics are freely associated with pitches in relation to the expressive meaning of the text. Moreover, it is important to observe the exception of the two last pitches E and E♭, which are assigned the same dynamic factor.

Table 10.1 Il canto sospeso, no. 2: table coordinating the all-interval series with the duration Fibonacci series (I–XV: bb. 108–42; XVI–XIX (proportional canon): bb. 142–57)

	A	B♭	A♭	B	G	C	F♯	C♯	F	D	E	E♭
I	1	2	3	5	8	13	13	8	5	3	2	1
II	2	3	5	8	13	13	8	5	3	2	1	1
III	3	5	8	13	13	8	5	3	2	1	1	2
IV	5	8	13	13	8	5	3	2	1	1	2	3
V	8	13	13	8	5	3	2	1	1	2	3	5
VI	13	13	8	5	3	2	1	1	2	3	5	8
VII	13	8	5	3	2	1	1	2	3	5	8	13
VIII	8	5	3	2	1	1	2	3	5	8	13	13
IX	5	3	2	1	1	2	3	5	8	13	13	8
X	3	2	1	1	2	3	5	8	13	13	8	5
XI	2	1	1	2	3	5	8	13	13	8	5	3
XII	1	1	2	3	5	8	13	13	8	5	[3]2	[2]3
XIII	2	3	5	8	13	13	8	5	3	2	1	1
XIV	3	5	8	13	13	8	5	3	2	1	1	2
XV	5	8	13	13	8	5	3	2	1	1	2	3
XVI–XIX	13–8–5–3–2–1–1–2–3–5–8–13 (once for each duration value)

Table 10.2 Il canto sospeso, no. 2: table coordinating the dynamics series with the all-interval series

The compositional device is set in motion by the preparation of four uninterrupted temporal levels (or ‘time lines’), each associated with one of the four duration values (from the quaver to the quintuplet semiquaver). Pitches are then systematically distributed in the time lines in coordination with the duration factors of the Fibonacci series (see Figure 10.6, showing what may be understood as the first stage of this process, and Figure 10.7, the final draft as seen in the printed score).

Figure 10.6 Il canto sospeso, no. 2: schematic rendering of the first three rotations of the parametric series

Figure 10.7 Il canto sospeso, no. 2: the final outcome of Nono’s compositional device as represented in the score

(Ars Viva AV 50)

The first step consists in the pairing, from top to bottom, of the first four pitches of the series (A–B♭–A♭–B) with the first four duration factors (1–2–3–5). Once the first pitches of each time line are set, an automatic method (the ‘uninterrupted sound’ technique) is executed, whereby the pitch-duration pairs are organised in sequence in the available time line without leaving any pauses or gaps. Besides determining instances of rarefaction and thickening in the temporal flow of sound events, the rotation of the Fibonacci series avoids situations in which a given pitch ‘prevails’ upon the others and is thus instrumental in creating an equal distribution of durations and pitches. The final result is a sort of ‘virtual temporal space’ filled with sound agglomerations that incessantly vary in pitch, duration, and intensity.

As mentioned above, this compositional process is interrupted from b. 142 onwards. Starting from the sixteenth iteration of the tone series, Nono abandons the ‘uninterrupted sound’ technique to build a proportional canon in which the Fibonacci series (read from the longest duration, 13, to the shortest one, 1, and backwards in a mirror-like trajectory) is associated with each time level in a linear fashion. Thus, the density of sound events is modulated along a horizontal trajectory, a compositional choice that, as will soon be made clear, is a product of the treatment of the text. The automatism of this procedure apparently makes the interval the only element that allows the author some degree of choice; indeed, it should be reiterated that the arrangement of pitches across different registers is at the composer’s complete discretion. The analysis of the movement’s text structures, however, reveals that this seemingly neutral compositional grid is intentionally designed around specific expressive goals.

The bipartition of the movement itself and the corresponding diversification in the implementation of the serial material depend on the intention to isolate the last two verses of the text (excerpted from a letter by Anton Popov, a teacher and journalist sentenced to death in Bulgaria):

The whole process of scanning and distribution of the text across voices and registers is not constrained by any compositional device and exclusively depends on the author’s choices. Two separate treatments of the phonetic material, exactly corresponding to the bipartition of the movement, can be identified: from b. 108 to b. 142 the text ‘floats’ between registers (it expands or contracts depending on the time-flow system shown on Table 10.1), and its distribution is linear, despite the syllabic deconstruction across the various voices. From b. 142 to the end, instead, the text is condensed, creating a sort of ‘semantic block’. This contrast is motivated by the only word that is repeated twice in the whole text: ‘muoio’ (‘I am dying’, bold in the text quoted above). Strikingly, Nono develops his proportional canon at the point at which this crucial word is repeated (bb. 142–57). Precisely in that moment, the Fibonacci series reaches its highest duration factor (13) and is placed in the central register (C₂) starting from the longest duration value (quaver). This way the word ‘muoio’ is clearly uttered (and made perceivable), expanded on a single line by a single voice (the second alto, bb. 142–47).

All the musical structures in this work are dependent on the textual architecture. First of all, Nono selects specific words and decides to repeat them in succession, overlapping iterations or placing them apart from each other, almost as if creating a ‘hypertext’: ‘muoio’ (×4); ‘mondo’ (×2); ‘splenderà’ (×4); ‘luce’ (×2); ‘non [è]’ (×6); ‘nulla’ (×4); ‘sono’ (×2); ‘morti’ (×3); ‘milioni’ (×4); ‘uomini’ (×2). The sum of these repetitions, not present in the original text, gives as a result: ‘I’m dying / word / will shine / light / is nothing / millions have died.’ A crucial role in such a process of semantic reinforcement is assigned to the enhancement of particular vowels, which intensifies the sound density. For their organisation (contra Stockhausen 1964d: 158), Nono does not make use of tables or serial procedures. Every vowel is in fact always related to the word (or the syllable) uttered in that moment. It is an authentic ‘vowel spectrograph’ that accompanies the scansion of the text and reinforces its content (Nono employed this technique in almost all of his serial works for solo voice or choir). It should also be observed that Nono operates this scansion and distribution of the text across voices, registers, and duration values, adopting expressive devices that recall Renaissance madrigalisms. The four iterations of ‘splenderà’, for example, are associated with the shortest duration values (the quintuplet semiquaver and the semiquaver) according to an ascending succession of registers from the lower to the higher voices (bb. 111–5: second tenor, second alto, first alto, first soprano) that emphasise the word’s meaning. Among the many other examples, it is also possible to consider the treatment of the word ‘milioni’, which is repeated four times (bb. 129–39) in a vortex-like process of time expansions and contractions. This word is also the only one in the text to be broken up by rests, as a possible tragic reference to the many lives that the war had taken away (first soprano and second tenor, bb. 129–32). In the last sixteen bars (the proportional canon of bb. 142–57), the individual voices intone a word each. The only exception to this is the first soprano, the highest and most discernible voice, to which Nono assigns the only intelligible sentence of the whole work (‘le idee vinceranno [(our) ideas will triumph]’, bb. 146–50) choosing the most rhythmically incisive duration value (the semiquaver).

In the context of such a strict union between serial musical structure and verbal signification, even the punctuation of the text finds its own specific function. We have already mentioned the contrast created by the transition to the proportional canon built concurrently with the repetition of the word ‘muoio’ (that is to say, in close proximity to the period that separates the last two verses). Even more, the rotation method employed for pitches, durations, and intensities is also adapted to the structure of the text: rotations I–VIII correspond to the first sentence (rotations I–V to the first verse, and VI–VIII to the second); rotations IX–XV correspond to the second sentence; and four rotations of the tone series (XVI–XIX) correspond to the concluding proportional canon.

In the works that Nono composed after Il canto sospeso, it is on the terrain of vocality – and thus in conjunction with the presence of a verbal structure – that he continues to mould and experiment with new writing techniques involving systems of serial derivation. In particular, Nono’s development in the control of material, which can be glimpsed in his Cori di Didone (1958), would gradually lead him towards the new techniques that he adopted in his vocal works at the beginning of the following decade, such as Sarà dolce tacere, for eight solo voices on texts by Cesare Pavese (1960), and ‘Ha venido’. Canciones para Silvia, for soprano and chorus of six sopranos on texts by Antonio Machado (1960). Indeed, these two works open a new and more strictly post-serial phase in Nono’s production.

These are the last works in which Nono employed a numerical device (a square), though he also partially adopts a version of this device in Intolleranza 1960, the very last appearance of this technique in Nono’s work (see Reference De BenedictisDe Benedictis 2012). As had already happened in Varianti and in La terra e la compagna (both composed in 1957), the twelve figures included in the numeric scheme do not refer to any specific sound parameter in particular but rather work as abstract factors determining the distribution of musical material. As such, the square becomes a permutation matrix that acquires a precise function in the compositional process only if it is linked to (a) a tone series and (b) supplementary coordination devices (or ‘multi-parametric modules’, see Figure 10.8) regulating the single parameters.

Figure 10.8 Multi-parametric module prepared for Sarà dolce tacere

(used in the second section, bb. 26–67).

This complex compositional procedure (discussed in detail in Reference De Benedictis, Borio, Morelli and RizzardiDe Benedictis 2004) allowed Nono simultaneously to generate and coordinate sound complexes with varying density (gruppi, groups, as in the Figure 10.8) and rhythmic-harmonic stratification (durate and intervalli, durations and intervals). The simultaneity in the coordination of these three elements (groups, durations, and intervals) reveals how Nono’s research on sound became increasingly oriented towards a musical writing based on sound aggregates. In fact, a compositional technique based on ‘groups’ would entirely replace the previous ‘continuous sound’ method – the layering of multiple time lines that Nono had adopted in his Canti per 13 and later perfected in the second and ninth movements of Il canto sospeso (see Figure 10.7).

The basic features of the multi-parametric modules remain essentially unchanged from their first appearance at an early stage in La terra e la compagna up to their definitive version in Sarà dolce tacere and, later, in Intolleranza 1960. Conceived for vocal or choral works, these modules are once more developed in strict connection with the verbal material, and, with rare exceptions, they simultaneously coordinate always the same sound parameters. Their ideation and adoption reflect a change of paradigm in the use of serial techniques that is already emergent in Il canto sospeso. With these modules, the preselection of musical materials and their coordination shift from the macro- to the micro-formal level: these compositional procedures are not applied to the entire musical form of the work, but rather to the different parts that compose it, each organised in its specific context. First sketched out in Composizione per orchestra n. 2: Diario polacco ’58 (1959), this particular compositional procedure, based on the juxtaposition of sound events, attains its full form in Canti di vita e d’amore (1962), where constant variation and mobility of sound events become systematic in all its three sections.

The coordination of a tone series with the multi-parametric modules replaces the all-interval series and marks the gradual shift to a more explicitly generative compositional technique. In Sarà dolce tacere and ‘Ha venido’, Nono resumes organising his pitch series according to intervallic principles and opting (as he had done in the early 1950s) for a selection process based on expressive criteria. The use of the pitch series in these works also confirms Nono’s departure from a macro-formal compositional logic. In both these vocal compositions, no longer is a single pitch series used throughout the whole work; rather, the number of series corresponds to the number of portions of text being intoned. Nono also employs multiple series in the initial part of Intolleranza 1960 (as ‘character rows’ identifying every character in the opera), but he gradually abandons them as the work progresses. What makes these series different from the past is that each of the twelve pitches that compose them becomes potentially generative thanks to the coordination with the factors of the multi-parametric modules. As an example, if a pitch of the row is associated with a factor of the ‘groups’ line which equals ‘5’, then it should generate four more pitches according to an intervallic derivation determined by the same module in the ‘interval’ field; the corresponding factor in the ‘duration’ field will regulate the temporal flow. The understanding of the series as a motivic-thematic device is thus definitively abandoned: instead, the series becomes a generative device (a ‘matrix series’) based on the selection of specific intervals and adopted for the creation of harmonic fields (groups) of varying density.

The idea of the ‘group’ intended as a structural unit summing up and organising different parameters summarises the basic principles of Nono’s previous serial procedures, including the articulation techniques of sound complexes based on alternation and articulation of sound/non-sound partition. Since it is generated starting from a pitch of the ‘basic’ tone row and is defined in its internal components on the basis of the values prearranged in the multi-parametric modules, the group recapitulates all of the possibilities that Nono had previously envisioned for the series. The group (O in the example) can be retrograded (R), inverted (I, RI), stretched, or rendered ‘out of phase’ through the double ‘positive (note)/negative (rest)’ scansion of some sounds, and even ‘linearised’ (Figure 10.9, and see De Benedictis 2004, 216 –8). Furthermore, after it has been generated, the group is usually subject to several transformations in the subsequent editorial stages before reaching the final form in which it appears in the score, where it often appears to be completely concealed and impossible to analyse without the aid of the earlier sketches.

Figure 10.9 Representation of the various group types obtained from the transformation of an original group

The linearisation of the group (L) refers to the development of a line that should no longer be thought of as ‘melodic’, but rather as ‘harmonic’. This switch represents one of the most interesting aspects of Nono’s final serial phase. Nono adopted this serial procedure in the fourth and last section of Sarà dolce tacere (bb. 89ff.), and he later further developed it in ‘Ha venido’. Canciones para Silvia – where the presence of the solo soprano necessarily implies a horizontal dimension of pitches – and finally in Intolleranza 1960. Beginning from Canti di vita e d’amore – where the most refined application of the ‘harmonic line’, which is to say the linearisation of the group, is achieved in the central monody ‘Djamila Boupachá’ – this technique is gradually replaced by new systems for the selection of pitches.

In these two latter works, the very concept of ‘series’ begins to dissolve. In one of his notebooks from 1962, Nono wrote: ‘no more complete series’ (‘Q.10’, f. 3, Archivio Luigi Nono). Indeed, the interval is gradually made independent of the twelve-factor series and becomes the generative element underpinning the formation of all the pitch classes for each sound aggregate. The interval completely replaces the pitch parameter in the organisation of musical material and becomes one of the most important structural elements of this piece. It also works as a catalyst for Nono’s eventual departure from predetermination. In Canciones a Guiomar (1963), the compositional writing is oriented towards a stratification of sound events caused by the reading of more local systems that coordinate harmonic levels often of great initial complexity that are set up beginning from a nucleus of generative pitches. But by then, serialism had become less than a trace in a compositional process free from grids and systems and driven instead by acquired automatisms that would influence Nono until his last works in the 1980s.

That Igor Stravinsky would eventually be attracted to serialism is not surprising, given his conviction about the role of intervals in generating musical ideas. Reacting to those who criticised his adoption of the twelve-tone technique, Stravinsky once commented to Milton Babbitt, ‘There’s nothing to it; I’ve always composed with intervals.’ Babbitt later referred to this quote as ‘something of a witticism, but what it did show, much more than a witticism, was how profoundly this is an interval kind of sequence and not just a pitch-class syntax – fundamentally and centrally an interval syntax’ (Reference Babbitt, Dembski and StrausBabbitt 1987b: 20, 188 n. 12).

Stravinsky’s intrigue with intervallic patterns is significant in some of his earlier works – particularly in the treatment of the motivic networks that he established to support the narrative in passages of Firebird (1910) and Perséphone (1934). As I have written previously in Multiple Masks (Reference CarrCarr 2002), the abbreviated symmetrical form of the immortality motive from Perséphone is 4–9 [0167] in the Allen Forte pitch-class set taxonomy (its longer five-note form becomes 5–7 [01267]). By creating a symmetry among statements of the immortality motive in which the exact order of intervals is retained while producing twelve different pitch classes, Stravinsky may have unknowingly been anticipating his own serial technique in later years. He was also working – consciously or unconsciously – with a motivic technique similar to that which he previously established in the ‘Carillon’ section of Firebird, whose motive, 6–7 [012678], contains Perséphone’s immortality motive (both the five- and four-note versions) as a subset.

Cantata (1952) and Septet (1952–3)

In order to set the stage for a discussion of Stravinsky’s compositional process for In memoriam Dylan Thomas, his first composition to utilise serial technique exclusively, it is useful to establish the context for his choice of the text, and the influence or assistance of Robert Craft on Stravinsky’s path to serialism (Reference CraftCraft 1992: 33–51). It was on 8 March 1952 during a motor trip to Palmdale with Craft himself and Stravinsky’s second wife, Vera, that Stravinsky said ‘that he was afraid he could no longer compose and did not know what to do. For a moment he broke down and actually wept’ (Reference CraftCraft 1992: 38–9). Then, Stravinsky mentioned that the Schoenberg Suite op. 29 that he had observed a few weeks prior in rehearsal and performance made a ‘powerful impression’ on him. Webern’s Quartet op. 22 also happened to be on the programme. On hearing Stravinsky’s desire ‘to learn more’, Craft suggested that Stravinsky should re-orchestrate the String Quartet (referring to Concertino (1920)). Following this advice, Stravinsky completed the re-orchestration in 1952 as Concertino for 12 Instruments (Reference CraftCraft 1992: 39), which would be premiered on 11 November 1952 with Stravinsky conducting the Los Angeles Chamber Symphony Orchestra. This programme also included the premiere of Cantata (1951–2), significant because the compositional techniques used in Cantata predicted those of In memoriam Dylan Thomas.

In Figure 11.1, notice one of Stravinsky’s initial flirtations with serial procedures: overlapping entrances of the six-note prime (or basic) set and its variants (retrograde, inversion, and retrograde inversion) (cf. Reference MasonMason 1962). This forms the basis of what I will refer to as Stravinsky’s use of ‘serial variants’, as demonstrated on a sketch page (seen in Figure 11.2), labelled ‘cancricans’ [sic] (unless otherwise noted, all sketches discussed in this chapter, are housed in the Stravinsky Collection at the Paul Sacher Stiftung, Basel, for whose permission to reproduce them we are grateful). This technique is predictive of one discussed later found in In memoriam Dylan Thomas and can also be seen in Three Songs from William Shakespeare, for mezzo soprano, flute, clarinet, and viola, premiered on 8 March 1954 at the Monday Evening Concerts in Los Angeles, conducted by Craft.

Figure 11.1 Cantata, ‘Ricercar II’, overlapping sets

Figure 11.2 Cantata, sketch page showing serial variants

Some insights by Lawrence Morton about Cantata provide a reminder of the intricacies of Stravinsky’s use of the models of Bach as a basis for his own canonic structure of ‘Ricercar II’:

Morton also points out the structural delineations of the choral Prelude, Interlude, and Postlude in Cantata, all of which are strophic settings of the traditional ‘Lyke-Wake Dirge’, which describes the stations of the soul as it travels to purgatory. Little did Stravinsky or Morton know that the format for Cantata would resurface in his memorial for Dylan Thomas.

Septet (1952–3)

The ‘unity’ that prevails in Septet represents a continuation of Stravinsky’s approach to Cantata that is part of a new beginning of his compositional process. With this work, Stravinsky adopted Schoenberg’s idea of serialism on his own terms – Stravinsky did not make all notes equal in his adaptation of serialism as Schoenberg had done. In Paul Hume’s review of the premiere performance of Septet in the music room of Dumbarton Oaks (conducted by Stravinsky) on 24 January 1954, he refers to the ‘central germinal idea of the opening movement’ as generating the entire score (Reference HumeHume 1954). Stravinsky used baroque forms in Septet just as he had in Octet (1919–23), which was also included on the 1954 programme together with Histoire du soldat (1918). A manuscript page of the initial row table, used as the basis of Septet, was reproduced in Stravinsky in Pictures and Documents (Reference Stravinsky and CraftStravinsky and Craft 1978: plate 14). Serialism may have been so appealing to him because it enabled him to unify his melodic and harmonic ideas, just as he had endeavoured to do in Firebird.

In memoriam Dylan Thomas (1954)

When Stravinsky collaborated with literary figures, his musical settings often reflected the poetic form of the text as it did with André Gide’s for Perséphone. At other times, Stravinsky would take liberties with poetic metre of the libretti, such as Jean Cocteau’s for Oedipus Rex (1926–7) or W. H. Auden and Chester Kallman’s for The Rake’s Progress (1947–51) and one by Auden discussed later in this chapter, Elegy for J.F.K. (1964).

Another phase of Stravinsky’s approach to text setting would be in, as Robert Hatten described it, ‘his close musical approximations of both prosody and poetic form in his setting of Dylan Thomas’s villanelle, “Do not go gentle [into that good night]”, a poem that exists for its own music rather than as something written with musical setting in mind’ (personal correspondence, 24 May 2018). Craft recounts that Stravinsky began his setting of that villanelle in early March of the year following Thomas’s death. Stravinsky then completed the surrounding prelude and postlude later in March and in June, respectively. Perhaps he had meant to set the text as the entire piece, but then when he had scheduled the first performance for the new Monday Evening Concert series, Craft informed him that Heinrich Schütz’s Fili mi Absalom (for bass voice and four trombones) would also be on the programme. Likely inspired by the Schütz piece, Stravinsky then added the Dirge-canons for string quartet and trombones (Reference CraftCraft 1992: 58), and it is possible that the fact that Schütz studied with Giovanni Gabrieli may account for the antiphony between the trombones and string quartet that shows up during Stravinsky’s Dirge-canons. This is also strongly suggested by the opening rhythmic motive being the opening motive used in canzona (long – short – short), such as the one found in Canzona septimi toni for eight parts by Gabrieli from the collection Sacrae Symphoniae.

In total, there are eight pages of sketches for In memoriam, one of which contains a fragment that may have been Stravinsky’s earliest musical sketch for the work (cf. Reference CraftCraft 1992: 59). Looking at the top right corner of Figure 11.3, it is interesting to compare how Stravinsky chose the retrograde written in his own hand on the second line of the sketch before going to the top line for the pitches of ‘meteors’. These are specific pitches that Stravinsky would use in the published version for this line. Stravinsky labels these five notes as the theme. In the final published outcome, Stravinsky adds two pitches (B♭ to B) to the opening line of the text, therefore creating an overlap between two serial forms (I and R) of the theme.

Figure 11.3 In memoriam Dylan Thomas, diplomatic transcription of sketch page

The most fascinating aspect of these sketches is the evidence they provide for how Stravinsky was inspired by four-note patterns and used layering techniques to assemble cadential blocks from these patterns. As he was layering the serial variants, he introduced octave displacement and intervallic inversion for dramatic purposes, namely, by inverting an anticipated ascending minor second to a descending major seventh, and by displacing an ascending minor second to an ascending minor ninth. This compositional technique enabled Stravinsky to enhance the musical meaning of words, such as ‘dying of the light’ (D – ↑ D♭ – C – E♭ – E).

Another notable technique using the five-note series and its variants is the manner in which Stravinsky treated the intervals – a minor third, surrounded by two minor seconds that encompass a major third. He uses these intervals as an opportunity for further painting the text and typically has one of the two minor seconds change direction to produce a descending ‘sigh’ figure.

Canticum Sacrum ad honorem Sancti Marci nominis (1955) and Threni (1957–8)

Both premiered at successive Venice Biennale Festivals starting in 1956, Canticum and Threni share the distinction of being the first works in Stravinsky’s serial period to use biblical texts in Latin.

Stravinsky created a musical symmetry in Canticum that reflects the architectural design of Venice’s Basilica of Saint Mark, as well as a compositional process that juxtaposed that which was familiar to Stravinsky – eighteenth-century contrapuntal textures – with that which was still new to him – twentieth-century serial techniques. In fact, Canticum was the first of his works to contain a movement based entirely on a tone row. However, diatonic passages nevertheless remain present, as does evidence of the influence of Gregorian chant.

The setting of ‘Caritas’ in the third movement (bb. 116–29) serves as a microcosm of Stravinsky’s genius in combining contrapuntal models and dodecaphonic serial techniques. By using various forms of a twelve-tone row with the original (prime) form announced by the tenor on C♯ in b. 116, answered in the next bar by the trombone (prime, in augmentation) a semitone lower on C, the alto in the next bar on D (inversion), and two bars later, expanding even further upwards by semitone in the soprano line on D♯ (prime).

According to Craft, the idea of separating the entries of canonic voices by a semitone in this canon was likely influenced by a similar practice of separating canonic subjects in Webern’s Variations op. 30 (Reference CraftCraft 1956). Webern, however, initially limited these entrances by semitone to only two voices (opening measures: A, B♭, D♭, C and B♭, B♮, D, C♯), whereas Stravinsky adds not only a third but even a fourth, designing multiple entrances circling around C♯ (first down to C, then up to D, then further up to D♯). One has only to look at a transcription of a short musical sketch – possibly in Stravinsky’s hand – catalogued at the PSS. This sketch was acquired by the PSS from the Craft collection, and it was found with the orchestral score of the aforementioned Webern Variations. This suggests that Stravinsky studied the Webern score closely enough to jot down the serial variants. In fact, Craft writes that when Stravinsky was in Baden-Baden and ‘a recording of Webern’s orchestra Variations was played for him, he asked to hear it three times in succession and showed more enthusiasm than I had ever seen from him about any contemporary music’ (Reference CraftCraft 1992: 38).

What is even more remarkable is that the intervallic structure of the previously mentioned four-note motive in Webern’s Variations (A, B♭, D♭, C) coincides with the intervals produced by four of the five notes in the inversion of the theme in Stravinsky’s own analysis of In memoriam, which also resurfaces here in Canticum, as well as in Agon, and is pitch-specific with the Webern motive, then transposed up a semitone to B♭. Later in op. 30, Webern wrote several statements of this four-note motive on different pitches, starting in the Coda at b. 146, and it appears that Stravinsky circled some of these statements in his copy of the orchestral score.

Christina Thoresby, in her review of Canticum, wrote that Stravinsky was overheard telling a reporter after the premiere about the importance of mathematics in relation to the piece. Thoresby also noted that ‘after hearing it repeatedly at rehearsal and in performance it seemed to one listener to blend marvelously with the mathematics and metaphysics of the great Basilica’ (Reference ThoresbyThoresby 1956). Craft seems to all but confirm the influence of Webern in ‘A Concert for Saint Mark’ for The Score in December 1956, particularly in relation to ‘the structure of a canon such as the one in “Caritas” which ends like the last movement of Webern’s Opus 31, and which resembles a canon in the Webern Variations for Orchestra in that each entrance is at the semitone’ (Reference CraftCraft 1956).

Stravinsky also transcribed Bach’s organ work Canonic Variations on ‘Vom Himmel hoch da komm’ ich her’ (1956) for chorus and orchestra during this time. The performance forces are almost identical to those for Canticum, as it was conceived as a companion piece for the concert in which Canticum was premiered. The accompanying instrumental canons are of far greater interest than the choral element in this work, as the voices merely sing the unharmonised chorale melody.

Agon (1953–7)

A microcosm of Stravinsky’s metamorphosis from neoclassicism to serialism, Agon was begun in December 1953, but its composition was interrupted by both In memoriam and Canticum before it was eventually completed on 27 April 1957. Owing to the duality of Stravinsky’s compositional techniques at play in Agon, it remains the clearest lens through which to see his serial method develop. Roman Vlad highlights Stravinsky’s repeated use of the same six-note series from the second dance, ‘Double Pas-de-Quatre’ (for eight female dancers, approx. bb. 81–95) (Reference VladVlad 1978: 200). Stravinsky uses the hexachord in three successive transformations, each at different pitch levels, but all based on the same intervallic patterns, and all of which utilise the set 6z44 [012569]: the flutes in b. 81, the violin in b. 84 (inverted), and the flutes in b. 93 (retrograde inversion). Disregarding the actual appearance order of the intervals in the hexachord, these three statements are an excellent example of Stravinsky’s serial treatment of a hexachordal motive in the context of a neoclassical ballet. Following Vlad’s observations, the principal motives continue in the following section (‘Triple Pas-de-Quatre’, bb. 96–121) and are ‘presented mostly in their mirror’. Allen Forte continued to analyse Stravinsky’s explorations with serial transformations in the later sections as well, particularly ‘Bransle Simple’ (bb. 278–309) and ‘Bransle Gay’ (bb. 310–35).

Of special interest is the way that Stravinsky interchanges the minor ninth interval with its inversion in a short section (bb. 452–62) of the ‘Pas-de-Deux’ (complete from bb. 411–519). It is here that Stravinsky created a series involving twelve different pitches that he introduced through the sequential repetition of a given tetrachord. In addition, he created an imitative texture that enabled him to use one of his favourite baroque models as structural inspiration for his serial experimentation in Agon. Even more remarkable is the strong relationship that the intervallic design of the fugal subject has with the inverted thematic motive of In memoriam, completed during Agon’s fractured compositional period.

Threni: id est lamentationes Jeremiae prophetae (1957–8)

For this work, Stravinsky was inspired by Ernst Krenek’s setting of Lamentatio Jeremiae Prophetae [Lamentations of the Prophet Jeremiah], written in the early 1940s, but not published until much later in 1957:

Among the documents at the Stravinsky archive for this work, there is one page in Stravinsky’s hand that provides four forms of one twelve-tone series. In addition, there are sixty-six pages of sketches – some of which will be discussed below in relation to Stravinsky’s compositional process – and other examples that appear elsewhere in research published by David H. Smyth and Joseph N. Straus (Reference SmythSmyth 2000; Reference StrausStraus 2001 and Reference Adorno1999b).

In an article published in Melos, Vlad presented three of the four basic initial row forms, plus three transpositions (see Figure 11.4) (Reference VladVlad 1959: 36). For clarity, his original abbreviations appear (O, U, K, KU) along with their equivalents (P, I, R, RI, respectively). Stravinsky labels his integers using 1–12, instead of the more traditional 0–11, in both his initial row table and also when he is annotating specific passages in his musical sketches. Krenek and Vlad also used this approach, so consequently, this discussion of Threni will use the same 1–12 numbering system.

Figure 11.4 Vlad’s chart of various forms of Threni row

Vlad was invited to write the programme notes for the premiere, and both those and his later observations add a special dimension to the context of Stravinsky’s compositional process for Threni. For example, Vlad recounts that because two forms of the row (both a prime and inversion) appear simultaneously at the start of the piece, he asked Stravinsky which form constituted the original (or prime):

Figure 11.5 illustrates the two simultaneous forms of the row and the so-called ‘original’ in bb. 6–18, with row labels corresponding to Figure 11.4.

Figure 11.5 Threni condensed orchestral score, bb.

5–18. © 1958 by Boosey & Co. Ltd. All Rights Reserved. Reprinted by Permission.

One of the most fascinating examples of Stravinsky’s simultaneous statements of the row begins in b. 6 where P₁ is stated contrapuntally with I₁, with surrounding statements of R₁ in the first oboe and RI₇ (a tritone away) in the trombones, thus enabling R₁ and RI₇ to both start on F♯. By sharing the full statement of RI₇ among three trombones, Stravinsky achieves a pointillistic texture that is both reminiscent of baroque texture and lightly treading towards Klangfarbenmelodie. This is also the case with the last three notes of RI when they move from the first oboe to the clarinets (bb. 14–15, sounding G, G♯, D♯) and in the English horn (bb. 17–18, the last three notes of R₄, sounding E, F, C). These three-note cadential patterns help to unify the conclusion of this introductory section that ends in b. 18.

The technique also prefigures Stravinsky’s reordering of rows by the displacement of three-note patterns from the end to the beginning so that the order of pitches reads 10–12 followed by 1–9. This can be seen in the unbarred four-part vocal canon in b. 189 and is also noted in red pencil by Stravinsky on the corresponding sketch page for this section. Also found there is a rhythmic discrepancy – he doubles the durations from crotchets in the sketch to minims in the published score. Perhaps this was to make this unmetered section appear closer to the centuries-old settings of Latin masses, and also to emphasise the syllabic rhythm of the Latin text ‘Re/cor/da/re pau/per/ta/tis [remember poverty]’ (slashes indicate syllables).

Stravinsky also provides a helpful guide for the analysis of this phrase by writing ‘RI’ in a box next to the Bass I entrance. Above that on the sketch page, Stravinsky writes the canonic imitation of Bass I for Tenor I (RI₁₁). For the remaining voices of the canon in the published score, Stravinsky then uses RI₁₀ starting in the original order of 1–3 (D♯, E, A) for Basso II and imitated in Tenor II in the same original order (B♭, B, E). The interesting phenomenon is that the intervals of this (0,1,6) trichord are prominent throughout the various forms or variants of the row for Threni and resounds as the main musical idea for this work (Reference VladVlad 1978: 212).

Clare Hogan concludes:

In the 30 September 1958 European (Rome) edition of the of The New York Herald Tribune, Peter Dragadze wrote:

Movements for Piano and Orchestra (1958–9)

In a letter of 8 May 1958 addressed to Paul Fromm (of the Paul Fromm Music Foundation in Chicago), Robert Craft wrote:

While it is true that this meeting with Krenek coincides with the time that Stravinsky was working on Movements, it cannot be assumed that this was on the agenda during their meeting, though one sketch page contains an annotation in handwriting that seems to not be that of Stravinsky.

In December of that same year – when Stravinsky was in New York to conduct the city’s premiere of Threni – Stravinsky spoke with great enthusiasm to Milton Babbitt and Claudio Spies about his compositional process for Movements and showed them ‘all of his notes, alphanumerical as well as musical, pertaining to the Movements … and proceeded, as if to restore for himself and convey to us his original, unsullied (by actual, approximate performance) image of his creation, a creation that clearly meant crucially much to him’ (Reference Babbitt, Haimo and JohnsonBabbitt 1987a: 16).

The materials that Stravinsky showed to Babbitt and Spies during this meeting in New York are almost definitely among the numerous manuscripts and other documents at the Stravinsky Archive. Included in that collection are two pages of row tables, and fifty-four pages of sketches in Stravinsky’s hand, making it possible to observe Stravinsky’s early (if not earliest) examples of constructing rotational arrays based on hexachords created for Movements. Exactly where Stravinsky’s compositional process began for this work is difficult to say, though from some of his musical sketches, it is likely that he was thinking of a network of motivic ideas based on a series of intervals that provided him with the most possibilities, particularly those that included tritones.

The opening two bars of Movements are based on two hexachords at the top of the table, shown in Figure 11.6. Stravinsky disperses the pitches of the first hexachord among various instruments simultaneously – flute, trumpet, violins, and piano – whereas the pitches of the second hexachord are confined to the piano. The instrumentation of the first hexachord is suggestive of the artistic technique of pointillism (see Reference CarrCarr 2014: 144–5). The succession of intervals and pitches of hexachord O_β is the same as those of the inversion at β (I₃). Hexachords O_α and O_β share the same three tritones and would be categorised as 6–7: [012678]. More fascinating is the outcome of Stravinsky’s application of hexachordal rotation to O_β (hexachord 6–7, see Figure 11.7) that yields pitch specific replications under inversion (in different sequence) – evidence of the symmetry of the original intervallic profile of hexachord 6–7.

Figure 11.6 Movements, original (prime) row, split into hexachords α and β

Figure 11.7 Movements, diplomatic transcription of sketch page, annotated with rotation of hexachord 6–7

Stravinsky has left several musical sketches that help to explain his compositional process for Movements – one among them that shows Stravinsky’s experimentation with various transpositions of hexachord β – primarily in inversion of V that is labelled by Stravinsky as ‘Riv V’. He also uses other forms of this series, as he formulates his ideas for the section beginning at b. 27. It is possible to observe how he used compound intervals to enable pitches of a given motive to move between different instruments. Rather, it seems possible that Stravinsky was inspired by Webern, not only through an apparent close study of Webern’s transcription of the ‘Ricercar’ of Bach’s Musical Offering among Stravinsky’s notations at the Stravinsky archive, but also through his close association with Robert Craft.

In the sketch titled the ‘1st Interlude’ – the title did not carry over into the published score, though the music does as bb. 43–5 – Stravinsky indicated two hexachords: one of them the Retrograde of O_β (Riv. β on the sketch) and the other the Retrograde of the Inversion of O_α (Riv. Inv–α on the sketch), transposed down a minor third and reordered. Both the handwriting and authorship thereof are unclear; they may, in fact, be Krenek’s annotations on Stravinsky’s music.

Stravinsky’s next level of sketching for this ‘interlude’ adds barlines (though these are also changed in the published score) and instrumentation. Stravinsky’s handwritten numbers from the previous sketch mentioned above also remain. The outcome at the foreground level is linear, which could justify Stravinsky’s poetic licence to change the order of pitches in the hexachord – in fact, Massimiliano Locanto, in his analysis of this same sketch, justified the reordering of pitches on the basis of the vertical function of the intervals (ic5) (Reference LocantoLocanto 2009: 242). Stravinsky eventually returns to one of his traditional techniques – block form – in what is initially called ‘4th Interlude’ (bb. 137–40 in the published score). Whereas he freely moved the hexachords between instruments in the ‘1st Interlude’ in a Webern-esque fashion, he now restricts melodic hexachord statements to individual instruments.

Movements represents a turning point in Stravinsky’s serial compositional process. In a review of the world premiere in the New York Herald Tribune (11 January 1960), conducted by Stravinsky at Town Hall in New York City, Jay S. Harrison wrote:

A Sermon, a Narrative, and a Prayer (1960–1)

Whereas Threni was written using Latin texts from the Old Testament, the first two of the three movements of Sermon are from the New Testament and now in English: (1) a sermon from the epistles of St Paul; (2) the stoning of St Stephen (from the Acts of the Apostles); (3) a setting of poetry by Thomas Dekker. Given the uncertainties that occur in human life throughout history, particularly in times of war, disaster, and plague, the belief that humanity is saved by faith and hope becomes a source of consolation. Though it uses the Christian Bible as a lens, the spirit of universality is reflected throughout the piece.

In his article ‘Stravinsky’s New Work’, written in anticipation of the premiere of the work in Basel, with Paul Sacher conducting on 23 February 1962, Colin Mason put the piece in perspective with Stravinsky’s other works as follows:

The design of the twelve-note series for A Sermon is highly intervallic in nature, and one is immediately struck by Stravinsky’s abiding interest in the ordering of these intervals – in this case, the opening instrumental prelude (bb. 1–11) foreshadows the poetic meaning of the text that appears in the next section. Following the analytical insights of Colin Mason, the annotations on the score of this prelude indicate two statements of the twelve-note series by the bass flute, a segment of the row in retrograde inversion and then a statement of the retrograde by the bass clarinet. Looking further at the series apart from the score, there is evidence that Stravinsky reordered intervals to echo the intervallic patterns that he used elsewhere when he was negotiating similar patterns from In memoriam Dylan Thomas (Reference MasonMason 1961: 6). Other possibilities are that the influence of the motives in Webern’s Variations op. 30 and Agon were still reverberating in Stravinsky’s musical imagination.

In his book Stravinsky, Roman Vlad reminds us of comments that Stravinsky made in conversation with Craft, having to do with the connection between chromaticism and pathos. About this, Vlad writes, ‘The quality of pathos in the cantata is that of a work in which the ultimate experience of human life is distilled’ (Reference VladVlad 1978: 231).

Variations: Aldous Huxley in memoriam (1963–4)

Containing just 141 bars of music, Stravinsky’s Variations for orchestra lasts slightly over five minutes, yet contains a web of complex serial techniques. Without question, while endeavouring to incorporate his own voice into his compositional process for Variations, Stravinsky benefited from his associations with Krenek, Babbitt, and Spies, while downplaying the work of Schoenberg, Berg, and Webern.

Stravinsky’s approach to serialism in Variations strays from formulaic construction, incorporating short musical blocks that expand, following traditional variation technique. In at least one case, he even follows the model of a Bach fugue. Among his many manuscript pages for this piece, several larger ones are meticulously constructed and also heavily annotated in order to identify the occurrence of each row segment. It is not, however, readily apparent who wrote in the annotations to label the occurrences of the row forms in multiple colours in order to track the serial construction.

An exemplary point of baroque and twelve-tone juxtaposition involves his labelling of ‘fugato’ found on the manuscript page corresponding with b. 101. This is immediately preceded by a vertical hexachord distributed in the low strings, bassoons, trombones, and horns in bb. 99–100. Merely looking at these few bars, and indeed, virtually any part of the score, it appears that Stravinsky’s penchant for block form – hearkening back to the Rite of Spring – continues to play out in Variations, just as it will in his Introitus: T.S. Eliot in memoriam (1965).

Abraham and Isaac (1962–3) and Elegy for J.F.K. (1964)

Both of these works demonstrate Stravinsky’s penchant for versification and also happened to be programmed together at a performance on 6 December 1964 at Philharmonic Hall in New York City. The premiere of Abraham and Isaac, the text of which is in Hebrew, had been given six months prior (23 August) in Jerusalem, Israel, and Stravinsky’s preoccupation with syllabification was evident enough that even the review by Moshe Brilliant noted it, quoting Stravinsky as saying that he had ‘studied every syllable of the Hebrew text with the aid of scholars and composed the work accordingly’ and that ‘it could not be sung in any other language’ (Reference BrilliantBrilliant 1964).

Details of the collaboration for Elegy for J.F.K. can be examined in correspondence at the Paul Sacher Stiftung. With an explanation for the syllabic structure of his text, W. H. Auden wrote to Stravinsky and explained that he wrote the text in the poetic form of haiku, so that though the number of syllables in individual lines might vary, the total syllable count in each stanza would always remain at seventeen. It is debatable whether or not Auden’s specific use of haiku had an effect on Stravinsky’s compositional process for Elegy. His primitive ideas were written in a pocket-sized sketchbook that Craft said Stravinsky carried around in the last years of his life. It would appear that Stravinsky first set the last line of the first verse (‘The Heavens are silent’) to an oscillating two-note pattern that had occurred to him while on a flight from Los Angeles to Cleveland. He commented on this to a reporter from the New York Times, in an interview published on 6 December 1964, when asked about composing Elegy: ‘Melodic ideas came to me immediately, but the first phrase I was certain would never come unglued.’ Stravinsky considered those two oscillating notes as a ‘melodic-rhythmic stutter’. It is uncertain if he used scansion marks in his text analysis, as his setting of the text is, for the most part, straightforwardly syllabic.

Both works use serial techniques, though these are more pervasive in Abraham and Isaac. For this work, there exists a musical score partially annotated by Stravinsky himself, at the Paul Sacher Stiftung, demonstrating, for instance, his unique ordering of the notes for the hexachord in the first six measures, labelled 0_β and starting on the second note of the hexachordal series instead of the first. He signed this score on 3 March 1963. A primitive sketch for these opening measures shows Stravinsky’s early ideas for the pitch material – before he had made final decisions on metric and rhythmic aspects of these patterns. His ideas about intervallic patterns were almost final, even at this stage. There are, too, row tables in Stravinsky’s hand that become the basis of his experiments with vertical constructs to establish the work’s harmonic language. The most curious aspect of one of these formulations occurs in a ‘block sketch’ on a sketch page that may very well be in handwriting that is not Stravinsky’s, as they are written in the duration of semibreves and, perhaps more telling, appear to be written in ink. Stravinsky tended to use filled-in noteheads during sketching and usually did so in pencil, not in ink. The paradigm in the sketch clearly anticipates the material in bb. 229–39. In fact, Stravinsky encircled six block harmonies implied by the verticals from the sketch on his copy of the piano reduction of the score that he notated in part.

Stravinsky’s musical experimentation with serialism in the Elegy is less complex in terms of serial techniques when compared with Abraham and Isaac, although Stravinsky was attentive to the syllabification of Auden’s poem in the form of a haiku. The following fragments in Figure 11.8 show a transcription of the musical sketch for the opening line ‘When a just man dies’ for the sake of comparison with the published version. The fact that Stravinsky originally wrote without barlines might seem unusual until a comment Stravinsky made in the New York Times interview, mentioned above (p. 199), published the day of the New York City performance (6 December 1964):

Figure 11.8 Elegy for J.F.K., diplomatic transcription of sketch page

Introitus: T.S. Eliot in memoriam (1965)

Stravinsky’s use of block form as a compositional technique continued to evolve over the next two decades, and, when T. S. Eliot passed away in 1965, Stravinsky responded that same year by writing Introitus: T.S. Eliot in memoriam, a deeply expressive work of grief upon the loss of his friend, featuring once again a male chorus. This work is illustrative of Stravinsky’s use of serialism for expressive purposes; the combination of twelve-tone technique and the unusual instrumentation creates a heart-wrenching effect. Stravinsky writes that: ‘The only novelty in serial treatment is in chord structure – the chant is punctuated by fragments of a chordal dirge’ (Reference StravinskyStravinsky 1982: 66). This results in a texture that echoes the use of harmonic stasis as accompaniment to chant-like melodies. A performance of Introitus by the choir of Westminster Abbey was part of the ‘Homage to T.S. Eliot’ that took place at the Globe Theatre in London on 13 June 1965.

The first page of the sketch score, found at the Paul Sacher Stiftung, shows the evolution of his compositional process with sound blocks, the distinctive and regularly recurring ‘chordal dirge’ that is a trademark of the work. The combination of percussion instruments that Stravinsky used in Introitus serves as an evolutionary extension of the ritualistic profile that defines the Rite, while simultaneously reflecting the influence of the Rite on his process for an intensely personal epitaph.

Requiem Canticles (1965–6)

Requiem Canticles (1965–6) was commissioned by Princeton University in honour of a major benefactor in 1965, and Claudio Spies was instrumental in coordinating the details of the first performance at Princeton in 1966. Documents in the Claudio Spies collection at the Library of Congress confirm that he was in close communication with both Craft and Stravinsky concerning the serial analysis of the work, and he published a detailed analysis the following year, illuminating both the inter- and intra-symmetry of its nine sections.

It is notable that many of Stravinsky’s serial compositions are emotionally charged works. Though it was a serial composition, the chromatic beauty of Stravinsky’s interval-based writing is still plainly audible. Spies notes as much, saying that the ‘Lacrimosa’, of all the movements, is the ‘most meticulously and ingeniously organized’, and that it is ‘a paragon in this serene and deeply moving composition’ (Reference SpiesSpies 1967: 120–1). Stravinsky himself would pass away just five years after the premiere of Requiem Canticles. A performance of this work, conducted by Craft, at San Giovanni e Paolo in Venice before the composer’s body was taken to its final resting place at San Michele, made for a fitting musical epitaph. Requiem Canticles is written in the same Stravinskian language as his prior works, merely using a different vocabulary, tying together elements of all his stylistic periods and all of his characteristic instrumental and choral tendencies into a singular work of great brevity, yet packed with religious piety and intense emotion.