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The filament power must be referenced to the DC in the tubes in some way, otherwise you get a lot of hum. The filaments are usually a centertapped 6.3VAC winding, with the CT grounded for the necessary reference. Other methods are low value pot (200-500 ohms) across the whole 6.3V with the wiper grounded, or two low value (100-200 ohm) resistors in series with the center grounded across an otherwise floating 6.3V. If the winding is not grounded and balanced around ground, it will cause hum. Measure the voltage from each side of the 6.3V to ground; it should be pretty much exactly half the AC voltage at either end. If it is unbalanced to ground, tweak the pot or change the resistors to get it to be. If you have grounded centertap style supply that is not centered on ground, this indicates a faulty power transformer.