Thanks for the replies.

I was thinking that it was the power supply, mainly since the volume knob doesn't affect the noise. I also noticed that the noise isn't always there; it usually comes on a little while after I've been playing the synth, after the thing has had some time to heat up.

I've heard that these Nova power supplies have reliability issues. Maybe I'll just open the thing up to see if there's anything obvious. I really wish I knew someone who had one so I could swap out; I hear those things are expensive!