Update: I know this isn't the actually lullaby, and I really do know that, so please, if you going to leave a comment, just tell me that you like it instead of repeating that it's not the actually lullaby,
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Official Soundtrack For Twilight:
OFFICIAL track listings:

1. Muse — Supermassive Black Hole 
2. Paramore — Decode 
3. The Black Ghosts — Full Moon 
4. Linkin Park — Leave Out All The Rest 
5. MuteMath — Spotlight (Twilight Mix) 
6. Perry Farrell — Go All The Way (Into The Twilight) 
7. Collective Soul — Tremble For My Beloved 
8. Paramore — I Caught Myself 
9. Blue Foundation — Eyes On Fire 
10. Rob Pattinson — Never Think 
11. Iron & Wine — Flightless Bird, American Mouth 
12. Carter Burwell — Bella's Lullaby
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MP3 Download Link:
http://www.mediafire.com/download.php...

Sheet Music Link:
http://www.scribd.com/doc/3326406/Yir...
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Many people have read the Twilight series and have wonder what Edward's lullaby to Bella was. I hope this gives you a better understanding of the book and that you also like it. :)

Thank you everyone for you awesome comments. It means alot to me that you like it. Keep on adding some. I think its getting to the point were I can't respond to every comment. So just know I do look at everyone and if I feel I need to comment I will. Put keep that in mind. If you have any questions, or want to inform me on somthing, PLEASE send me a message. I defiantly will respond. Lastly, I do not own this song, it was created by Yiruma, and is call River Flows In You. Thank you so much, and enjoy! 
~Liz