Hey, I've uploaded my clips of this. There's one which is normal, and another one which is a duet - I clipped and overlapped two bits and they fit together in harmony!
Correction
You people really should pay attention. Okay. Now I'm going to say what is already said in the Appendices of the ROTK Extended DVD. If you watch the section on music, you would know all this information.
This song was originally intended for the scene in which Arwen has the vision of her son. This scene was also intended for The Two Towers, but got pushed back because it slowed the story line down. When the scene got pushed back to ROTK, the song did too. When they began to focus on the scene as it went in to ROTK, they realized that to see Arwen and her vision and to hear her singing was just a little odd. So they wrote a new song for the scene sung by Renee Flemming.
Now they're stuck with a wonderful song and no where to put it. They realized it would work in the houses of healing because in a sense the same thing is occuring there too only with Eowyn. It also ties the two women together in their love for Aragorn. So you're looking at Eowyn and Aragorn, but hearing Arwen's voice. Pretty neat if you ask me.
No new information here, just what was given to us on the DVD. And I suggest that people get their information right before they post so they don't make fools of themselves. If I have gotten any of this wrong, please correct me as I haven't watched that particular section in a little while. But watch it first and you'll get the full story and reasoning of the people who actually made it, which really makes this a waste of time...