Music and song were very important in elvish culture. Through it the elves preserved their history, their legends. A song could be also a weapon, an intrument of power as Luthien Tinuviel proved i her face to face with the Dark Lord Morgoth Bauglir.
That is why it's interpretation by the fans of Tolkien's mithology is so interesting.
While perusing through the net I found athe folowing article about one author of Elvish music.

"With the tsunami of Elvish lore and Tolkien-madness descending upon us with the recent release of the first installment of the Lord of the Rings film it might be a congenial time to consider a brilliant and bewitching composition inspired by the don's fancy (as Robert Graves ever so snidely called it).

In 1977 Allan Rae composed the five movement suite entitled Mirror of Galadriel. There have been innumerable works (mostly death metal songs) and compositions inspired by J R R Tolkien's epic fantasy novel, but attempts at serious classical realizations frequently fall short. For some reason there is a peculiarly strong urge to a New-Age style emptiness.

In song settings it is often an issue of the sentimentality inherent in the original text (Bilbo's 'songs' are trite, as they ought to be for the mostly simple Hobbit), while the Elvish songs miss something in translation from Sindarin or Quenya. Only roaring electric guitars in orcish songs seem to work well. The magic that Tolkien weaves in the vision of Galadriel, of the Ents, of the hidden danger of Isengard and the murderous horror of Mordor seem to elude classical composers...."

To read the rest go to this link:
http://www.mvdaily.com/articles/2002/01/rae1.htm