Well, is that even a question? Ofcourse, music is allowed in Hinduism! In Fact, Hindu music is to a great extent influenced by Hinduism. All the different forms of Hindu music viz. Hindu classical, Bhajans, Kirtans, Ragas are based on Hinduism and its various aspects and mention Hindu mythology, Hindu teachings and more in one form or the other. The roots of Hindu classical musical can be tracked down to the Vedas and other religious scriptures.