I would start by pulling and then reinserting all of the tubes and cables connected to the amp (including the power cord on both ends).
Doing so will help clean the contacts they are making.
Do so when the amp and source gear is off/cold.
Sounds like a transformer hum, as newbie mentioned, which can hopefully be remedied by this simple exercise.
Doesn't read as being a loose transformer needing tightened down (from your description) but I wouldn't rule that out completely.
DeKay