> was thinking.. it has a 1:2 ratio
1:2 Voltage, 2:1 Current, Impedance is Voltage divided by current.
What Sluckey said.
> It's likely that the wire used in that transformer
Yeah.
For very low loss, the planned impedances would be similar to the original impedances.
If the 240V winding were intended for 16 ohm load, that would be 240V/16R= 15 Amperes, and 240V times 15 Amps is 3,600 Watts. So it seems a 3,600 Watt 240:120V could be used as a 16:4 transformer.
You surely don't have a 3,600W tranny, or want to lug such a lump around,
A 120V 120 Watts winding is clearly 1 Ampere, and the design load was 120 ohms. A ~~100VA tranny probably has 10% loss, much of this in the copper, which implies it has about 12 ohms of copper resistance. If you used it to feed a 4 ohm speaker, at-best you would get 25% power in speaker and 75% power in winding heat.
You could do the same with a 12R resistor between your 16R tap and your 4R speaker. And a helluvalot lighter.
You should check distortion. As a very rough guide, the audio AC should be less than a third of the rated power AC. "120V" winding, keep audio down to 40V or it will distort. (Power transformers DO distort in operation, but the crap reflect back to the big utility generator, not our teeny tubes.)
You should consider high frequency response. PT only claims 50Hz or 60Hz. In fact it "must work" to 400Hz so cap-input rectification works good, and it costs nothing to give that to you. If the primary and secondary are simply wound one over the other, 5KHz is not uncommon. If they are wound on separate bobbins, you may not pass 1KHz well.
> it would be a nice thing to have on the bench...
Find a good deal on a high-power 4/8/16 OT. It can have a blown-open or ripped-out primary, as long as the secondaries are good.