• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

Pi Filter choke

What has that got to do with ringing bells, and MHz signals in presumably output stage anodes?

Well, it's just what I am reading: ripple current is a momentary function of capacitor size and applied voltage. As a result ripple current peaks typically range between four and six times the DC load current. That would be with a typical power supply, that does not hold 2700uF capacitance. The voltage arriving from the mains transformer when diodes are switched off might excite a resonance resulting in a damped train of oscillations in hundreds of kiloHertz (hence the 'bell' simile).
Regarding the current demand on the mains transformer with this a-typical 2700uF capacitance, core saturation might be occuring. When it does, it releases a leakage field of magnetic flux to induce currents in nearby circuitry. Sharper saturation (as might be expected from a toroid) produces a greater proportion of higher harmonics in the leakage field, extending to radio frequencies.
 
Yes I can appreciate how a seemingly excessive level of filter capacitance may look to have apocalyptic consequences. And poor design and construction choices may cause noticeable transients. But it isn't a given.

The capacitor charging pulses of most concern relate to the 940uF in post #1, not the 1.88mF (due to the choke), and for that particular configuration the peak initial surge secondary winding / diode current is only about 10A, so not excessive even for a 1N4007. And that pulse current has no relation to core saturation, as core saturation is related to primary voltage and frequency (not secondary current).

Perhaps you were reading about how that winding current pulse can interact with secondary winding leakage inductance, and sometimes lead to transients. Some have noticed that in the past - it doesn't have to be the situation.
 
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Well, because we do not know what to expect from someone's gear it seemed prudent to warn against a ringing power supply, what turned out to be no nonsense afterall. From your statement that core saturation is not related to secundary loading, you seem to say Jones is wrong at that point.