Three Uses of Vuza Canons

THREE USES OF VUZA CANONS FABIEN LÉVY ECHNIQUE IS NOTHING MORE than a means of translating an aesthetic. It would be difficult to summarize the ‘aesthetic obsession’ which has given rise to my own compositional techniques for two reasons: firstly, this would make for a rather voluble tract; secondly, in the case of my recent works, insufficient time has elapsed to allow any degree of objectivity; indeed, even with my earliest works, I now have only oversimplified notions, and cannot always summarize these effectively. Let’s say, at the risk of over-simplifying, that my first works were attempts to reject overly-transparent analytical transformations of one or more ‘traditional’ musical parameters; they sought to combine, in a balanced manner, perceptual paradoxes and musical ‘inflections’ which could not be understood analytically.1 Meeting Italian mathematician Moreno Andreatta at IRCAM in 1998, and becoming familiar with his work on Vuza canons2 was therefore of significant consequence for me. Vuza canons (named after Romanian mathematician Dan Vuza) are rhythmically augmented canons which are said to be ‘perfect’ because the combination of multiple T 24 Perspectives of New Music voices engenders neither empty space nor superimposition. The implementation of each voice is perfectly complementary and thus expresses a perfect tessellation mathematically. A manual construction of these canons, of which there exists a finite number, is impossible; their creation calls upon the most complex algebraic theories. They were first calculated in the twentieth century by Vuza, and then more broadly studied and applied to digital algorithms by Moreno Andreatta. Perceptually, this type of canon proves paradoxical; an attentive listener will detect multiple entries of the same rhythmic motive, until, at such a time when all instances are present, a unique monodic line emerges. Three of my pieces to date make use of Vuza canons, each in accordance with its own aesthetic preoccupations. 1. VUZA CANONS AS PEDAGOGICAL TOOLS The transposition of a motive into different registers is a widespread pedagogical exercise, since it forces the student to explore extended techniques in different registers. In the last piece from Pour la classe [For class] from the cycle of pedagogical works Où niche l’hibou [Where the owl nests],3 this principle is applied in a ludic fashion with the use of Vuza canons (Example 1). Firstly, because of the use of these canons, motivic imitations are not superimposed upon one another; since each part is assigned its own distinct tessitura, the student can clearly hear his or her fellow performer reproduce a motive in a different register. Secondly, beyond the difficulties associated with transposing the motive, students are confronted with the challenge of maintaining the right tempo; errors in this regard will result in the undesirable superimposition of two voices. 2. WHEN VUZA CANONS PUSH THE LIMITS OF THE COMPUTER Vuza canons are implemented, albeit according to a different principle, in my project for computer, Soliloque sur [X, X, X et X], commentaire par un ordinateur d’un concert mal compris de lui [SOLILOQUY on X, X, X and X—a computer’s commentary on a concert it misunderstood ].4 This is not a ‘piece’ in the traditional sense; rather, it is a ‘meta-work’ generated in real-time by a computer using analyses and extracts from other pieces on the concert in which it is featured. In each instance, the result is different, not only because the final sonic– mosaic is composed of samples derived from other works in the concert program (as if the computer remembered the sonorities it just Three Uses of Vuza Canons 25 heard), but also because the work’s organization, or score, is composed based upon variables taken from the analysis of the just-recorded samples. As such, Soliloque cannot exist in a concert setting without other works. In early versions of the work, created using the now obsolete Mac OS9 and the program Supercollider, computational limitations placed dramatic constraints upon the potential complexity of this sonic– mosaic. Each elementary ‘cell’ consists of roughly three superimposed sounds, taken from the corpus of longer samples. Each sound is played EXAMPLE 1: POUR LA CLASSE (OPENING), EXCERPT FROM OÙ NICHE L’HIBOU, VERSION FOR TWO CLARINETS (2001, EDITIONS BILLAUDOT) 26...