Which of the ancient Greek gods represented the classical music school?

It's the muse. There are nine gods in Greek mythology who are in charge of music. "Muse" is the general name of nine ancient literary goddesses in charge of art and science in Greek mythology. They represent myths and legends expressed through traditional music and dance, that is, poems handed down from the times. They are the daughters of nine hair bands born to Zeus, the king of gods, and Mnemosyne, the goddess of memory of Titan.