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6BM8 has a plate impedance of 5600 @ 200 plate volts.Internal plate resistance is roughly 20K (see
sheet page 2).
Suggested External load resistance is, indeed, 5600. We *always* mis-match pentode power amps.
Actually the optimum external load is *nearly* V/I, where V is the supply voltage and I is the plate current. For 200V supply the suggestion is 35mA. 200V/0.035A = 5714, which is very-near 5600 (and probably works the same).
The transformer driving a reverb is *not* 22K, 15K, 5K, or whatever the nominal numbers are. The reverb tank input coil is highly inductive. An "8 Ohm" winding is maybe 2 Ohms at 100Hz, near 8 at 800Hz, near 40 ohms at 4KHz. When transformed, same trend: 22K only near 800Hz, lower at 100Hz, higher at 4KHz.
Nevertheless the tank will probably work well if you get near the 800hz ratings.
Remember V/I ~~= R.
If you have a 300V supply, and say 15K transformer, then the current "should" be 300V/15K= 20mA. Check: 300V*0.020A= 6 Watts, the BM8 is rated 7 Watts, it won't melt.
The 22K transformer might be fine at 300V and a mere 14mA.
300V and 5K implies 60mA, but 300V*0.060A is 18 Watts plate dissipation which is way too much for 'BM8. Which is why for ~~5K load they suggest 200V supply and fudge the "5K" up a bit higher.
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did not even have a reverb transformerReverb tank coils come in several impedances, notably 10 Ohms and 1K Ohms.
A tube is a several K-Ohm thing.
The K-Ohm tube loaded with 10 Ohms would sag horribly.
The K-Ohm tube loaded with 1K-Ohms would sag somewhat.
10 Ohms (4, 8) tanks *need* a transformer.
1K tanks can use a transformer or not. But there is no readily available 5K:1K transformer, certainly not the cheap-junk that we prefer for reverb (instead of $90 5K:600 studio iron). A 5K 10 Watt resistor is readily available and cheap, and will pass the tube's DC current yet shunt much of the signal current to a ~~1K tank.
You do have to ask if you need Big Power Tube reverb. A bazillion Fenders got away with a twin 12AT7 driving 15K-22K with just 5mA or 10mA current. You could run the 'BM8 at 10mA, just increase the cathode resistor a lot. 300V 10mA or 3 Watts in a 7 Watt tube does no harm. It seems like a waste of capacity, but there isn't a cheaper total-parts solution to get a small power tube and a gain-tube in one bottle.