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The current draw of a Bandmaster is too high for a 5Y3 to work reliably, even with the reduced power it will put out due to the greater voltage drop. It will be pushing it on the AC voltage rating as well.
There are three things you need to consider: current rating, voltage rating and filament current draw. You must not exceed any of these ratings for the valve when substituting. (Filament current draw matters to the amp not the valve, so should not be increased.)
For the common types:
5Y3 - 125mA, 350V, 2A
5U4 - 250mA, 450V, 3A (there are slight differences between the G, GA and GB but not enough to matter for this)
GZ34 - 250mA, 450V, 2A
So you can see it's always safe to substitute a GZ34 for either of the other two types, but in most cases not the other way round. The GZ34 has the lowest forward voltage drop and so the tightest sound. It will increase the HT voltage slightly too, so be sure the rest of the amp will be OK with that.
The 5V4 is a possible substitution - the ratings are 175mA, 375V, 2A. It's right on the limit but a pair of them run safely in my Trem-o-verb, so should just about be OK in the Bandmaster. It will give a slightly tighter sound than a 5U4 though, which is probably not what you want.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Might I just add that different rectifier valves have a different maximum capacitor value they can feed?
This also varies with other factors such as AC input to the anodes but for instance it is 64microfarads max (iirc) for the GZ34 which in practice means 47mfd(50mfd) .
FYI I have found the TAD GZ34 to be very rugged.
Hardly worth the mention but if you come across a very, very, very early A15 or A30 this needs to be checked and a mod done if a 100mfd is found as the res' cap.
Dave.
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Dave.