Having said this, and making it very clear that I do not advise anyone to connect a higher than rated impendence to any tube amp.
I don't know where that came from but it is the exact opposite of what is usually recommended for tube amps. Running a higher speaker impedance will only make the amp work a little harder. Running a LOWER impedance speaker can damage the amp. Running a 4 ohm amp like the Twin Reverb with an 8 ohm speaker load will not hurt a thing. It will work a little harder, may run slightly warmer, but should not cause any electronic failure. Running the same 4 ohm amp with a 2 ohm load has a good chance of frying a transformer or other serious damage. Solid state amps are more forgiving.
If you want to run an extension cabinet with the Twin Reverb, disconnect the internal speaker. If the cabinet is the same 4 ohm load, the speaker jacks are wired parallel, which results in a 2 ohm load if both are plugged in. Plug the extension cabinet into the main output jack, if it has two.
If it sounds quieter with the extension cabinet, at the same 4 ohm load, it's probably because the speakers in that cabinet are less efficient. More efficient speakers are louder at the same power level. If it were me, I would check the impedance of the cabinet with a multimeter to be sure it has the correct impedance. If anyone has ever tinkered with the wiring it might not be the same as labeled. Some speakers also just sound cleaner than others to begin with. Some guitar speakers are designed to break up a little easier, just for rock and roll players. Others, like the older EV speakers, had a reputation for being really clean. Don't know about the newer ones, I haven't kept up with them. Some I've seen listed in catalogs, like Celestion and Emminence, list some as being designed to break up faster and some cleaner, some "tuned" so to speak, for blues etc. I don't have my Sweetwater catalog handy to get a direct quote, connection is crappy right now so I won't do any serious searching...
Number of speakers has little if any impact. I can run my 6 watt Fender Champ through the Kustom 2x12 cabinet, 4 ohm so it's close enough to the right impedance of 3.2, and it makes no difference I can discern in volume or sound, except that the 2x12 cabinet is a fuller sound sound since it's moving a lot more air than one 8 inch speaker. Just for kicks I ran a small transistor radio through the speakers of a 2x12 combo amp once, worked just fine. I kept the Champ plugged into the 2x12 cabinet for at home practice for around a year before I moved back to Texas. Never had any problems with either. It only gets a little more bass, no other difference. I ran it through a 4x12 once at a guitar store, same thing. Number of speakers makes no difference, impedance is the main issue, and if the speakers are less efficient, they will not be quite as loud. More speakers will also produce more bass, they are moving a lot more air.
The common advice is never run a tube amp with no speaker load, which is always a good idea, that said, many newer tube amps are built so that it will not do any damage. I can't remember exactly, but I think it uses a grounded jack that will not allow any output signal unless a jack is plugged in. Make sure that jack is connected to a speaker load. That's why the main jack must be used for the extension cabinet. Otherwise it should shut the signal off.
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