25 Boulez: Structures Recomposed In [19], Pierre Boulez describes a compositional strategy called analyse cr´eatri- ce, creative analysis, which is opposed to what he calls “sterile academic” anal- ysis in that the analytical results are used as germs to create new compositions. Before discussing Boulez’s ideas in detail, we should stress that his procedure transcends the purely analytical or compositional activities: He proposes a co- herent double activity that includes both analysis and composition. This means that our own discourse in this chapter will deal with both, analysis and com- position, the latter more specifically realized by use of the music composition software RUBATO! [75]. 25.1 Boulez’s Idea of a Creative Analysis Let us explain the practical consequences of Boulez’s strategy for the analyt- ical and compositional efforts1. Anne Boissi`ere [15] has given a concise sum- mary of Boulez’s ideas on creative analysis, which comprise these core items: The analysis focuses more on the limits of the given composition than on the historical adequacy. These limits open up what has not been said, what was omitted or overlooked by that composer. This hermeneutic work is not driven to deduce a new composition as a special case of what has been recognized (deduction), nor is it meant to help build the new composition by a passage from the particular to the general (induction). Referring to Gilbert Simondon’s philosophical reflections [106], the creative movement consists of the opening of a topological neighborhood of the given analysis within a space of analytical parameters. In such a space, analytical structures similar to the given one are selected and eventually used as germs for the construction of new compositions. This ‘horizontal’ movement is called “transduction” by Simondon. In this transduction process, what Boulez calls the composer’s gesture, is the movement toward the creation of new compositions, which share precisely 1 For a more philosophical discussion of this approach, we refer to [82, ch. 7]. G. Mazzola et al., Musical Creativity, 279 Computational Music Science, DOI 10.1007/978-3-642-24517-6 25, © Springer-Verlag Berlin Heidelberg 2011 280 25 Boulez: Structures Recomposed those analytical structures reflecting the given analysis. More concretely, we take the analysis of the given work and make a number of “small” value changes to the analytical parameters. For example, if we have exhibited a set of pitch inversion symmetries that govern the given work, we may extend that set and include also time inversion symmetries (retrograde). Or if we have recognized that the voices of the different instruments are derived by some systematic procedure, e.g. time expansions (dilations) plus transpositions from a leading voice, then we may add more instruments and apply the same procedure, e.g. further time expansions (dilations) plus transpositions to define these added voices. This creative gesture—building new works from the transgression of the analytical structure discovered in the given work—is what Boissi`ere calls a detonation.Itispreciselythisactofbreakingthegivenstructuresandstepping into unknown neighborhoods that characterizes Boulez’s concept of an open work. Boulez’s approach is visibly akin to our concept of creativity. Boulez’s creative analysis takes the given work as the critical concept in our theory and then inspects its walls with the analytical efforts. The open work is exactly this analytical search for walls where the given work might be limited. The creative act then would consist in the action of opening those walls and stepping to new compositional paths. To our knowledge, these ambitious claims have not been backed by con- crete examples: How should and would such a strategy work in detail? This is what we have accomplished in a formal (mathematical) setup and on the level of computer-aided composition and what we want to discuss in this chapter. In view of Boulez’s poetical text, such an enterprise cannot be more than a first proposal. But we believe that it could open a fruitful discourse on the role of creativity in the dialectic between analysis and composition. In this sense, our approach is not a thesis but a detailed experiment following Boulez’s ideas. It is, therefore, completely logical to pursue the trajectory to its completion: to the construction of a full-fledged composition2. Our choice of Boulez’s Structures is not random; it relates to the promi- nent role that this composition has played in the development of serialism. This is also confirmed by the fact that Gy¨orgy Ligeti has published a very careful analysis of Structures, part Ia. Ligeti’s investigation [67] is neutral and pre- cise, but it abounds with strong judgments on the work’s compositional and aesthetic qualities. Therefore, our experimental application of creative anal- ysis to Structures is not by chance. The very success (or failure) of the se- rial method has been related to this composition, which was not only one of Boulez’s sucesses, but also a turning point in his compositional development. 2 It should however be noted that such a creative analysis had been applied in the case of Beethoven’s op. 106 [71] before we knew about Boulez’s idea. The present approach is somewhat more dramatic, since we shall now apply Boulez’s idea to two of his own works, namely Structures [17, 18]. 25.1 Boulez’s Idea of a Creative Analysis 281 In view of Boulez’s principle of creative analysis, when applied to his composi- tional turning point in the Structures, one is immediately led to the question: Would it be possible to write a world of new music on the principle of serialism or was it just a radical experiment without much long-range effect? This is an important question when taking seriously the idea of creative analysis, and not only as a recipe for fabricating yet another work. And it is also an impor- tant question relating to a more systematic and demystifying understanding of musical creativity using analytical activity. In our case, the Structures, the Boulezian gesture of opening a work’s limits is a doubly critical and difficult one: On the one hand, it should help determine whether the huge calculations that led to the composition are worth being reused with aesthetic success. On the other hand, the method of seri- alism also marks the computational limits of humans to compose music. This latter fact will lead to the question of using music technology and in particular computers in a creative context. We must understand here how to integrate computational power into cre- ative works of music, and on what level of creation this can or should be done. Boulez’s Structures is an excellent testbed to learn this lesson. It teaches us that the control of laborious computational processes cannot be systematically delegated to very limited human calculation power and that there is a life be- yond strictly human composition. To paraphrase Schoenberg, “Somebody had to be Boulez.” Of course, computers are widely used by modern composers, but it is a common belief that creativity is separated from such procedures; it terminates when the big ideas are set. And computers are just doing the mean calculations. Apart from being classically wrong, we shall see that this is not realistic. In fact, no composer would contest the creative contribution of trying out a new composition on the piano—playing it on the keys and listening to its acoustical realization, which may give a strong feedback for the creative dynamics, even on the gestural level of one’s hands, as is testified by Ligeti and other composers, see [68]. We have to contradict Marshall McLuhan: The medium is not always the message. But it gives the message’s germ the necessary mold and resonance to grow into a full-fledged composition. Before delving into the technical details, we should address the question of whether not only computational computer power is necessary or advanta- geous for modern compositions, but also conceptual mathematical power. Isn’t musical composition anyway sufficiently controlled by plain combinatorial de- vices: permutations, recombinations, enumerations, and the like? The question is in some sense parallel to the question of whether it is sufficient to control a computer’s behavior on the level of binary chains, or machine language. Or else the question of whether it is not completely sufficient to perform a composition for piano by simply controlling the mechanical finger movements and forgetting about all those psycho-physicological ‘illusions’ such as gestures. The parallelism lies in the fact that all of these activities are shaped by high-level concepts that create the coherence of low-level tokens in order to 282 25 Boulez: Structures Recomposed express thoughts and not just juxtapose myriad atomic units. Of course can one write a computer program in machine language, but only after having un- derstood the high-level architecture of one’s ideas. The artistic performance of a complex composition only succeeds when it is shaped on the high mental level of powerful gestures. And the composition of computationally complex musical works needs comprehensive and structurally powerful concepts. Com- binatorics is just a machine language of mathematical thinking. We shall see in the following analysis that it was precisely Ligeti’s combinatorial limitation that hindered his understanding of the real yoga of Boulez’s creative construc- tions. You can do combinatorics, but only if you know what is the steering idea—much as you can write the single notes of Beethoven’s Hammerklavier Sonata if you know the high-level ideas. The mathematics deployed in the mod- ern mathematical music theory is precisely the tool for such an enterprise. It is not by chance that traditional music analysis is so poor for the composition of advanced music: Its conceptual power is far too weak for precise complex constructions, let alone for their computer-aided implementation.