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There are many features that make music composition a challenging task for computer science. In this paper we investigate the suitability of using genetic algorithms and Kohonen musical grammar for task of music composition, and ability of these systems to cope with challenging aspects of music. Genetic algorithms are used as a tool to combine musical ideas which models the combination-theory of creativity. Kohonen musical grammar is used to extract the deterministic rules and structural patterns of music from an existing music to define the fitness function. These concepts have been applied to the generation of new melodic passages by considering pitch and duration properties of notes.