Actually, Tal, it used to be quite obscure, but there is a fair bit of research now. It's my field of interest, and I've written a lot about it, since it is a topic that fascinates me. I'm currently collaborating on a book with a heart surgeon who firmly believes that music and creativity has positive benefits for heart health, and she has a number of examples from her practice. Once I get my life sorted and back on track I hope to pursue more research in that area and learn more about the psychological effects, i.e. release of oxytocin.
I recently came across an interesting topic of binaural beats, and the concept of entrainment. The example used is two tuning forks that start to vibrate at the same frequency when they come near. Our brain waves vibrate at lower frequencies when we are relaxed. Binaural beats use the idea that by listening to a particular frequency, our brain waves will become entrained to it, which causes chemical changes and promotes relaxation. There are a few charlatans out there who try to market the concept, but it has an interesting scientific base.
As ooDad says, Music therapy provides ample evidence of the power of music to treat a whole range of issues, including pain management. When my mom was in hospice for the final few days before she died, the music therapist came by. My sister and one of my daughters were there, and we all harmonized on Blackbird. I have to say that for those few minutes all the pain was gone from that room.