Is Apollo the god of music?

Yes, he was the god of Music. And many more. He was the god of sports, herdsman, order, prophecies, laurel trees, mathematics, youth, reason, medicine, healing, truth, Archery, ravens, mice, poetry, bachelors, oracles, divination, and light. He was also the god of the sun, while his twin sister, Artemis, was the goddess of the moon.