Sorry if that was confusing, but I'll try again.... You mentioned that your Atari's whine changes depending on what channel it is set to. My guess is that it's something in the RF modulator that is oscillating or vibrating at a harmonic of the TV signal, but in the audible range. The tubes I mentioned don't have anything to do with your console or TV, I was just offering a reference as to similar behavior that I have observed in the vintage electronic equipment I collect.
Best way to figure it out would be to listen carefully, possibly with the cover off and see if you can pinpoint exactly where the sound is coming from.