2) If you tie the filament to the cathode resistor of the output tube, then the filament will be bouncing up and down with the signal, how does that help?
There are many sources of hum, and each one has its own cure independent of others. Not all appear in all amps. Electron emission from heater to cathode is one possibility, and elevating heaters fights that. That is separate from radiated hum from heater wires and other causes.
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