One of the finest discussions I've ever seen of music and Middle-earth is by our own
Aiwendil. A revised version of this paper will, I believe, be in
Estelyn's forthcoming book on Music in Middle-earth, but for now here's the early version:
A Speculative History of Music of Arda.
A really superb analysis! It taught me much about music in general as well as about Middle-earth. I can't speak highly enough of Aiwendil's thought.