Is teaching music forbidden, despite its medical and social benefits and its being a source of livelihood?

The science of music is not beneficial, and the effort and time spent on it require repentance and seeking forgiveness. The Ummah needs beneficial and fruitful sciences, not songs and melodies. The doors of lawful sustenance are many, and whoever fears Allah, He will make for him a way out and provide for him from where he does not expect.