I’ve seen issues with projectors running on one generator and my computers running on another. Apparently difference in grounds meant power was being pulled down display signal cables. Always run all kit from same generator. This might apply to sound too. Not sure different phases would cause this issue - it’s to do with grounding quality I understand.
Also, when using generators best work with a UPS too. Most UPS’s, if not all, will give you clean power isolated from dirty generators and of course save issues with power cuts.
Earths can make a difference as well, everything that you connect to should be on the same phase and the same earth, audio included, as an example, I had an installation, where the power was meant to have been like this, but turns out the trunking the cables were running through was on a different earth, a rack mount was touching the trunking, and when the sound was powered up, took out the sound card, 4 amps and 1 input on a deckling duo, an expensive mistake for the installers!
as for audio, an isolating transformer should separate the equipment electrically. You can get that as well for the video signals, but I suspect that those are more expensive, especially if you are running high resolutions.
u can avoid having glitches by switching on optic cables, also HDMI seems have better longrange performance then DVI. I have an issuse now, my datapath is capturing only crappy VGA now, cannot plug DVI or HDMI on it, same as SPARK DVI mixer lol… Suspecting that powersurge burned digital DVI pins or something…