Major Nelson's latest podcast reveals the exclusive sound effects for Halo 4's Limited Edition Console - they can be heard at 1:09:44. Or you can simply play the youtube video below.
The first sound occurs every time the Xbox's power button is pressed. The second audio snippet will be heard every time the eject disc button is used. Both sounds were created by the audio team at 343 Industries and represent some kind of 'Promethean technology'.