We study the synchronization of musical sequences by means of an operation deรฟned on รฟnite or inรฟnite words called superimposition. This operation can formalize basic musical structures such as melodic canons and serial counterpoint. In the case of circular canons, we introduce the superimposition of inรฟnite words, and we present an enumeration algorithm involving Lyndon words, which appear to be a useful tool for enumerating periodic musical structures. We also deรฟne the superimposition of รฟnite words, the superimposition of languages, and the iterated superimposition of a language, which is applied to the study of basic aspects of serial music. This leads to the study of closure properties of rational languages of รฟnite words under superimposition and iterated superimposition. The rationality of the transduction associated with the superimposition appears to be a powerful argument in the proof of these properties. Since the superimposition of รฟnite words is the max operation of a sup-semilattice, the last section addresses the link between the rationality of a sup-semilattice operation and the rationality of the order relation associated with it.