Page  317 ï~~MUSIC COMPOS CONSTRAINT SATISFA Russell 0) School of Computing Science Simon Fraser University Bumaby, BC V5A 1S6 Canada ABSTRACT: Recent attempts to develop exp have employed a rule-based approach, which w reliance on chronological backtracking as the c composition viewed constraint satisfi problem, the usefulness of the musical constrain all become manifest in the form of a constrain techniques can be exploited in an effort to redu efficient procedure for the generation of compos Marvin Minsky has said that "the problem of rm finding a structure that satisfies a lot of different con

Page  318 ï~~the variables' domains that can never appear in a so occurs, though not guaranteed to eliminate backtr search times [6]. As illustration, using our music exampl instantiating the variable i to the value 'E'. Since a than i, Tv can be removed from k's domain of pc deduce thatj must take the value 'C' in order that it must be different from f and lower than k, it has to t 'G' and the problem is solved. As this example ill one node to the next in the constraint graph, such reaching effects. Constraint propagation has been advocated and Levitt's method is based on value propagation wh computed from known ones in a spreadsheet-like problems such circuit design where the con; However, not all problems in music composition ca Instead, music composition can be readily vie of the notes (pitch, duration, etc.) that satisfy the Consider first species counterpoint. The task of ad model of a CSP. The variables are the notes of the

Page  319 ï~~Figure 2: a constraint graph for first species counterpoint o the cantus firmus and the cp are the counterpoint. the horizontal binary arcs police the melodic rules. The verti The tern quaternary constraints embody the forbidden parallel moti unary constraints that stop the composition from modulating