Valued Constraint Satisfaction Problems Applied to Functional Harmony

Harmonization with four voices is a musical problem which is subject to hard constraints, which absolutely need to be ful- filled, as well as to soft constraints, which preferably hold, but are not mandatory. In this paper, we model this problem as a valued constraint satisfaction problem (VCSP): costs are assigned to pos- sible solutions based on the constraints they violate. We design an algorithm that finds a minimal-cost solution, thus solving the har- monization problem, and we present initial results obtained by this algorithm.