So yeah, I'm also a musician and I do transcriptions by ear in my spare time—mostly from film music. Recently I've been trying to limit my my transcriptions to strictly what I can pick up by ear and relying on as little outside information as possible.
Anywho, this is The Passing of the Elves (or Elvish Lament) from The Fellowship of the Ring—only appears in the Extended Edition.
Sheet music (PDF) can be found HERE.
Audio track (via YouTube) can be found HERE.
Pretty self-explanatory. Was surprised to learn that Howard Shore did not write this; a group called Plan 9 did all the "cultural" music in the Lord of the Rings films.
Anyone who cares can let me know if they disagree with anything I heard. I'm not at all sure if the two male voices are even in this piece, but I'm pretty sure I heard someone singing in that octave.