We present two musical problems which are interesting examples of musical CPs. The first one deals with harp music from Nzakara people of Central African Republic, where canon structures have been discovered. The computation of such structures is a critical problem for constraint solvers in the sense that there are no exact solutions, the only possible way to solve the problem being to accept approximate solutions. The second problem deals with the analysis of Ligeti's textures. It is a kind of variation on the classical "choral harmonization problem" which is to some extent adapted to the atonal music of Ligeti. But unlike the choral harmonization problem where a great amount of solutions can be found, the Ligeti's problem is critical in the sense that it has only very few solutions. For both these real musical problems, we mainly use an adaptive solver belonging to the family of local search methods and developed at Ircam, which seems to be quite efficient.