Do you have any MIDI devices? MIDI is an often overlooked source of ground loops.

The best test you could perform right now is to swap out your audio interface. Is there a friend or a music store you could borrow from?
 
 
You could even order one on line make the test and send it back if the hum remains. If it goes away then there you go,,, keep it.

stokedboss
If I remove the USB cable from the interface the sound goes away. However even if I plug it into say a port on my mac it comes back -- but ONLY when my PC is running. There has to be something inducing the noise from my PC but I don't know what.

Is this with the PC connected to the UPS? If so it might be that the UPS isolates the PC from nasties in the mains by using a switching unity gain power supply. They can sometimes kick all kinds of noise back into the mains, especially if they produce a very stepped “fake” sine wave output.

What’s the Mac? Laptop with psu in the cable or an iMac/Mac Pro with built in psu? If a laptop, is the noise there with the Mac disconnected from the mains and the PC on?

It’s not impossible that it’s the PC’s own psu that’s the culprit, or even something else on the same ring main - e.g. light dimmers, fridges, washing machines.....