snipedog wrote: Did you have a grounding problem in mind that might account for this anomaly James?
As mentioned earlier, if the system relies on grounding via the USB connection it might be worth trying a ground wire from the RME case to mains ground.
Do you use power line ethernet? That can create radiated noise although it is usually at RF rather than audio. Other RF systems which use pulses of signal (like DECT phones) can also cause problems that might initially sound like mains. Old fashioned fluorescent lights and old CRT monitors are another source of noise. I'd be very tempted to switch everything off and then gradually switch things on one by one until you find the source.
Have you tried any electric guitars with single coil pickups? Do they buzz?