In the field of music, good practice in the writing of harmony has been encapsulated in an extensive set of formal rules. It is a difficult and tedious mental task to check music for compliance. However, music so harmonized almost always sounds pleasing. In the present invention, a Harmonizer harmonizes a melody in accordance with the rules using an iterative technique of chord selection, permutation and submission to the rules until solutions are found. At difficulties, the Harmonizer can compromise preferences, in order to produce an optimum solution. The process is characterized by advances and retreats along the melody and is therefore suited to subsequent performance and not to real-time applications.