On a day when it's bad, have a person below to listen while you walk around grabbing one stay at a time and sweating it a little or even shake it slowly to break any vibration. This might lead to one culprit.
I have never tuned to gauge settings, only to sailing performance, so my personal observation of humming I've witnessed as being caused by an overly-tight stay or two may not fit your case.
It's not completely impossible for an antenna installation to translate it's sound down an aluminum mast which, like a good horn, can both amplify and change the pitch.
G'luck
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