This paper describes a compositional, extensible framework for music composition and a user study to systematically evaluate its core components. These components include a graph traversal-based chord sequence generator, a search-based melody generator and a pattern-based accompaniment generator. An important contribution of this paper is the melody generator which uses a novel evolutionary technique combining FI-2POP and multi-objective optimization. A participant-based evaluation overwhelmingly confirms that all current components of the framework combine effectively to create harmonious, pleasant and interesting compositions.