THE BIGBANG RUBETTE: GESTURAL MUSIC COMPOSITION WITH RUBATO COMPOSER Florian Thalmann University of Bern Institute of Computer Science and Applied Mathematics Guerino Mazzola University of Minnesota School of Music and University of Zurich Institut f ¨ ur Informatik ABSTRACT Inspired by the gestural aspect and the immediacy of hu- man improvisation, the music composition software RU- BATO COMPOSER [1] has been extended with realtime functionality. Its complex mathematical operations can now be applied using simple mouse gestures to create or transform compositions. The corresponding results are visualized from different perspectives anytime during a transformation, which encourages a more spontaneous and explorative way of composing. 1. INTRODUCTION Musical composition is situated between spontaneous hu- man improvisation and algorithmic, computer-aided com- position that is detached from human interventions. The former stresses gestural immediacy and feedback from the sounding realm, whereas the latter delegates the transfor- mation of abstract rules into sounds to a computational dataflow. The delay experience between rules of composition and the resulting product is well known in serialism, for exam- ple, in the huge man-made calculations of Pierre Boulez for his famous structures pour deux pianos [2, 3]. Seri- alists needed a huge amount of time for calculation and hardly knew how their results were going to be. As al- ready criticized by Iannis Xenakis [4] and Gy¨ orgy Ligeti [5], the resulting compositions were too complex to be an- alyzed by human ears during audition and therefore seemed arbitrarily structured. It is certainly not an ideal situation for any composer to delegate his or her thoughts to a complex external pro- cess, be it purely mathematical or computer-aided. The ideal would be to have all sorts of complex calculation processes, but to be able to assist to each component with- out delay and without being separated from the ongoing process stages. This is not only a desire of immediacy, but also of transparency. The result of every compositional operation should not only be observable after its applica- tion but also foreseeable. More intuitively speaking, one would like to compose gesturally like in free jazz, with the extension that these gestures can also be interactions with “visible” algorithmic processes. In this paper we propose a music composition tool, which visualizes complex mathematical operations on mu- sical objects and makes them accessible through simple gestures. 1.1. Facts about Geometric Composition Strategies Gesture theory in music has mainly been driven by in- strumental interactions [6] and less by gestures dealing with abstract compositional strategies. The latter was ad- dressed in a rather abtract if not metaphorical spirit by Boulez in [7], we discuss this approach in [8]. In this paper, we want to make these ideas more concrete in the case of geometric composition strategies. Is it possible to implement such devices in a gestural way as proposed above? To this end, let us recapitulate the general framework of geometric composition techniques. One is given a set C of notes (part of the prelilminary composition to be transformed) in a module M . Such a module is typi- cally the n-dimensional real vector space R n . A trans- formation then is an affine invertible map F = T t ◦ L, where T t (x)= t + x is the translation by t ∈ R n , and L ∈ GL(n, R) is a linear map. We want to calculate the F -image F (C) of C. As it is hopeless to handle a general n-dimensional transformation directly by intuitive gestures, we decom- pose the map F into intuitively more accessible factors. The first theorem used to do so states that any F may be written as a concatenation F = F 1 ◦ F 2 ◦ ...F k of trans- formations F i , which, each, involve only one or two of the n dimensions and leave the others unchanged. The second theorem tells us that we may choose the F i to be one of the following five musical standard operations: (1) translations T t (in music: translation for pitch transposi- tion or da capo in time), (2) reflections Ref l at a line l (in music: inversion, retrograde or parameter exchange), (3) rotations Rot c,α by angle α around the center c (in music: retrograde inversion (rotation by 180 degrees), or general rotations as proposed by Maurizio Kagel or Her- bert Eimert), (4) dilations Dil c,λ,μ from center c by hori- zontal factor λ> 0 and vertical factor μ> 0 (in music: dilations in time for augmentations), (5) shearings Sh l,α along the line l and by angle α (inmusic: shearing in time