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Computational creativity using artificial intelligence and computational intelligence has received increasing attention. Automatic music composition is a blooming field in computational creativity; especially, automatic accompaniment has gained some promising results. However, most of the automatic accompaniment systems based on evolutionary computation require human feedback as evaluation criterion, which is vulnerable to the fatigue and decreased sensitivity after long-time listening. This study adopts music theory as the basis of evaluation criterion for accompaniment to address this issue. Specifically, we develop a genetic algorithm (GA) to generate polyphonic accompaniment, in which the fitness function consists of several evaluation rules based on music theory. Three accompaniments, i.e., main, bass, and chord accompaniments are considered in the study. Experimental results show that, given a dominant melody, the proposed method can effectively generate multiple scores to form polyphonic accompaniment.