Originally from trhe Greek "mousikos" meaning pertaining to a Muse or the Muses, goddeses of the arts. Like a lot of Ancient Greek ideas, this was adopted by the Romans and absorbed into Latin culture and language.
We get our words "to muse" (to think about possibly in an artistic way), "museum" (a repository for the arts, especialy historical artefacts), and "musette" )a sort of folksy small bagpipe musical instrument) from the same root.