The original J.R.R. Tolkien novel "The Lord of the Rings" contained a number of songs, mostly sung by Hobbits, with fully fleshed out lyrics.  A few of these songs even made it into the Peter Jackson movie trilogy, *The Lord of the Rings*.

However, as far as I can tell, the actual notes and music to each song never appeared in any of the original books. 

Did the production crew for *The Lord of the Rings* make up their own music for these songs?  Or was there some reference in a book, letter or transcript to how the songs should be sung?