||Evolution is now considered not only powerful enough to bring about the biological entities as complex as humans and conciousness, but also useful in simulation to create algorithms and structures of higher levels of complexity than could easily be built by design. In the context of artistic domains, the process of human-machine interaction is analyzed as a good framework to explore creativity and to produce results that could not be obtained without this interaction. When evolutionary computation and other computational intelligence methodologies are involved, every attempt to improve aesthetic judgement we denote as ArTbitrariness, and is interpreted as an interactive iterative optimization process. ArTbitrariness is also suggested as an effective way to produce art through an efficient manipulation of information and a proper use of computational creativity to increase the complexity of the results without neglecting the aesthetic aspects [Moroni et al., 2000]. Our emphasis will be in an approach to interactive music composition. The problem of computer generation of musical material has received extensive attention and a subclass of the field of algorithmic composition includes those applications which use the computer as something in between an instrument, in which a user "plays" through the application's interface, and a compositional aid, which a user experiments with in order to generate stimulating and varying musical material. This approach was adopted in Vox Populi, a hybrid made up of an instrument and a compositional environment. Differently from other systems found in genetic algorithms or evolutionary computation, in which people have to listen to and judge the musical items, Vox Populi uses the computer and the mouse as real-time music controllers, acting as a new interactive computer-based musical instrument. The interface is designed to be flexible for the user to modify the music being generated. It explores evolutionary computation in the context of algorithmic composition and provides a graphical interface that allows to modify the tonal center and the voice range, changing the evolution of the music by using the mouse[Moroni et al., 1999]. A piece of music consists of several sets of musical material manipulated and exposed to the listener, for example pitches, harmonies, rhythms, timbres, etc. They are composed of a finite number of elements and basically, the aim of a composer is to organize those elements in an esthetic way. Modeling a piece as a dynamic system implies a view in which the composer draws trajectories or orbits using the elements of each set [Manzolli, 1991]. Nonlinear iterative mappings are associated with interface controls. In the next page two examples of nonlinear iterative mappings with their resulting musical pieces are shown.The mappings may give rise to attractors, defined as geometric figures that represent the set of stationary states of a non-linear dynamic system, or simply trajectories to which the system is attracted. The relevance of this approach goes beyond music applications per se. Computer music systems that are built on the basis of a solid theory can be coherently embedded into multimedia environments. The richness and specialty of the music domain are likely to initiate new thinking and ideas, which will have an impact on areas such as knowledge representation and planning, and on the design of visual formalisms and human-computer interfaces in general. Above and bellow, Vox Populi interface is depicted, showing two nonlinear iterative mappings with their resulting musical pieces. References [Manzolli, 1991] J. Manzolli. Harmonic Strange Attractors, CEM BULLETIN, Vol. 2, No. 2, 4 -- 7, 1991. [Moroni et al., 1999] Moroni, J. Manzolli, F. Von Zuben, R. Gudwin. Evolutionary Computation applied to Algorithmic Composition, Proceedings of CEC99 - IEEE International Conference on Evolutionary Computation, Washington D. C., p. 807 -- 811,1999. [Moroni et al., 2000] Moroni, A., Von Zuben, F. and Manzolli, J. ArTbitration, Las Vegas, USA: Proceedings of the 2000 Genetic and Evolutionary Computation Conference Workshop Program – GECCO, 143 -- 145, 2000.