Note-against-note two-voice counterpoint by means of fuzzy logic

Abstract

In this study, we propose a fuzzy logic based approach for the ‘harmonization with constraints’ problem in music. After the mathematical modeling of the harmonization problem, the solution is carried out by means of proper fuzzy membership functions depending on the rules imposed by the music theory. To demonstrate the applicability of the proposed technique, particular problems of note-against-note two-voice counterpoint are considered. The method is flexible, adaptable and simple in terms of implementation. Moreover, from the constraint satisfaction perspective, the solutions generated by the method satisfy ‘arc-consistency’; which could not have been achieved by majority of the previous studies existing in the literature. The method also provides a gateway for the arranger/composer to incorporate his/her own stylistic preferences to the solution by simply adjusting the shapes of the membership functions. Additional features (such as providing variability in the final solutions at different executions) increase the power of the method in terms of creativity. This approach can be extended for the solution of more complicated problems in music such as orchestration, improvisation, and even composition.