Okay, without getting too much into the amps themselves which can tolerate different ranges for "matched" sets, or seperate bias, etc., when you are matching tubes with your Hickok or other Mutual Conductance tester, what is an acceptable perchantage/tolerance for you to consider being "matched"?
Vintage amps were generally designed with a +/-20% factor but I believe that may be a little wide for tube matching. There's the drift factor to figure in too along with a good, useful life.
First off, it is not possible to accurately match power tubes for plate or cathode current with any Hickok (or all but a small handful of other specialized units) tube tester. The voltage applied during testing is simply too low for it to be a meaningful exercise. It also lacks the current capability needed for large power tube testing.
Second, there may have been components with 20% tolerances, but that doesn't necessarily apply to the tubes. It was quite common to run tubes at or near their dissipation limits - and a 20% error would have caused a lot of tube fatalities.
And lastly, I believe current draw would be more critical than mu but at what range?
Your Hickok does not measure mu! It measures transconductance (Gm) - and that's not the same as mu because there is a 3rd number involved, Rp (plate resistance).
Here's the formula for mu:
Mu= Gm x Rp
Tubes not well matched for mu may (or may not, depending on a lot of things) affect sound quality/tone - but
mismatched Gm is not a "mission critical" issue! Mismatched Gm will not cause amp damage.
On the other hand tubes not well matched for cathode current can cause a number of problems, including premature wear and/or damage to a tube; if circumstances are right it can also damage the amp itself.
Take the scenario of a quad of 25 watt dissipation rated tubes - 3 are relatively well matched for cathode current, but the 4th is 25% higher than the others (this is not at all uncommon). Assume the plate and screen voltages are 450 volts.
Under the conditions in the amp the three "matched" tubes all pass 50 ma. So these tubes must dissipate 450 volts x .05 amps (50 ma), or 22.5 watts of heat. For a 25 watt rated tube that'll generally be okay. But the 4th tube of the set passes 25% more, 62.5 ma. 62.5 ma x 450 volts is 28.1 watts, and this tube is in trouble.
As that tube gets hotter it liberates more "gas" molecules from the tube internals. As more gas molecules are liberated the tube current will tend to increase. As the tube current increases the tube temperature increases - which increases the amount of outgassing. The increase in outgassing causes an increase in current which causes an increase in heat which causes more outgassing... well, you can see where this is headed. If and when the tube has its meltdown it may well take out other parts in the circuit.
While this is off topic a bit I hope it'll be helpful. There are a zillion posts here about red plating tubes, and
poor tube current matching is often the cause - just the scenario I described above is what happens.
If you have a mechanism to apply realistic voltages to the tubes then you can current match - and I use a standard not in %, but in pure numbers of + or - 1.5 ma. That's tight enough that even if they drift some (despite burn-in and all the other things done to minimize it) the tubes should still work well together. I will occasionally make an exception if circumstances allow, but in general the standard I use has worked VERY well.
My standard for Gm is 10% - although I strive for 5% whenever possible. I also test for Gm when the tube is blazing hot off the match rig. There are some tubes that have a reduced Gm as the tube gets hotter - for one, the SED 6550C tubes tend to have significantly lower Gm (10% - 15%) when hot than when when operating just in the tube tester.
Yes, you can use your amp to match tubes as tcdriver described, but be careful! In addition to the potential for damage from a runaway tube, it's hard on the tube sockets - and since there is some variation in the circuit the results aren't generally as accurate as putting the tubes in carefully controlled environment.