A school that specializes in teaching students how to perform or compose music is called a conservatoire.
Use the noun conservatoire to describe a music school — you might also call it a conservatory. Some conservatoires focus exclusively on teaching music, while others combine music instruction with academics, drama, or dance. The word conservatoire is French, and it comes from the Latin root conservare, which means "to preserve." Originally, a conservatoire was a "hospital for foundlings in which musical education was given."