I'm not sure you need "tribute". It was such a lovely piece that it literally cured my sprained wrist while listening to it. A tribute means an act or item made to respect and admire something else. I'm not sure that was the intended meaning in your sentence unless the music you are listening to was written to respect something else. Possibly written in the same style, but not the original. If that is the case, then "The tribute to the lovely piece literally cured my sprained wrist while listening to it."