We can then deduce some proporties of the analysis from the cardinality of the set of solutions. If the initial score is a solution, it means of course that the analysis is valid. Furthermore, if there are many solutions, then there are many scores with the same anaylsis and the set of rules is probably not precise enough, or the analysis not really accurate. Of course, an evident way to model a score would be to state »the first note is a quarternote C3«, »the second note is a quarternote D«, etc. So the cardinality of the set of constraints measures in some way the pertinence of the analysis.

3.3 General features

We can see three categories of problems : >normal< (just a list of variables), permutations, cycles (where the variables have to be considered on a circle, which adds a modulo in the variables indexes). What’s more, apart from the problem on spectral chords, the variables are always homogenous, denotating the same kind of musical element. Concerning the constraints, most of them are defined locally (from the -th variable to the -th, sometimes -th), though we still have some global constraints, generally alldiff. All of this is summarized in table 2.

4 Resolution

4.1 Adaptive search

For the resolution of all these CSPs, we will use a general resolution method called Adaptive Search. This algorithm comes from Constraint Programming researches. Though it has not been initially designed for musical purposes, it applies particularly well in ou case. This algorithm has been proposed by Philippe Codognet (Codognet and Diaz, 2000), who tested it on classical CSPs like the -queens, magic square, number partitioning and arithmetic problems. It deals with problems in