Music score analysis is an ongoing issue for musicologists. Discovering frequent musical motifs with variants is needed in order to make critical study of music scores and investigate compositions styles. We introduce a mining algorithm, called CSMA for Constrained String Mining Algorithm), to meet this need considering symbol-based representation of music scores. This algorithm, through motif length and maximal gap constraints, is able to find identical motifs present in a single string or a set of strings. It is embedded into a complete data mining process aiming at finding variants of musical motif. Experiments, carried out on several datasets, showed that CSMA is efficient as string mining algorithm applied on one string or a set of strings.