I have hunted down Radio Moscow from several tube guitar amplifiers. There was a large number of short and medium wave transmitters in the megawatt class across the border.
Apparently the pick-up coil inductance and the cable stray capacitance formed a parallel resonant circuit that happened to resonate on one of the numerous high power transmitter. Often a quick fix was to use a different cable with different length, which apparently moved the resonance to a quilter place :-). Adding a resistor and capacitor to the input jack usually solved the problems completely.