Ripped music? Purchased music?
Backups don't actually store your music. Purchased music (and also Matched or Uploaded music if you also subscribe to iTunes Match) is available "in the cloud" to be re-downloaded (along with Apps, Books, TV Programmes, and Films). Backups store device settings, app data, SMS, what apps you have and how they're arranged, etc. etc.
Was the music synced with iTunes on your computer?
Just re-sync. and copy it back over.
Did you have iTunes Match?
Just re-download it all.
