Requiem for a Tower
From Tolkien Gateway
Requiem for a Tower is the name for the up-beat song present in a trailer for The Lord of the Rings: The Two Towers. It is often associated with Peter Jackson's The Lord of the Rings: The Motion Picture Trilogy, but the track was neither composed for the films nor featured in them. It was the main theme for the 2000 film Requiem for a Dream. The piece of music is called Lux Aeterna and was composed by Clint Mansell.
For the trailer the song was re-orchestrated by The Ant Farm with three composers (Simone Benyacar, Dan Nielsen and Veigar Mairgersson), forty musicians and twenty choral voices.
A variation of the song would later be used in The Hunt for Gollum, accompanying a fight sequence.