This article introduces a genetic algorithm based system intended for automated generating of a realistic rhythmic (drum set) accompaniment. Present systems do not insist on the natural music criteria and realistic (human-like) result. They generate a rhythmic accompaniment regardless to the other instruments used. The fitness operators are mostly based on manual evaluation by user. The system described in this paper uses automatic fitness evaluator and prefers some of the natural music criteria. Accompaniment is generated with regard to a harmonic-accompaniment instrument (HAI).