Sing now, ye people of the Tower of Anor,
for the Realm of Sauron is ended for ever,
and the Dark Tower is thrown down.
Sing and rejoice, ye people of the Tower of Guard,
Minas Tirith was originally Minas Anor, “Tower of the Setting Sun.” This was in contrast to Minas Ithil, “Tower of the Rising Sun,” until it was conquered by Sauron and renamed Minas Morgul, “Tower of Black Sorcery.” Naturally, Anor was the more western of the two towers (hence “setting sun”). 
