#1
I just bought a 1960a cab from the 80's. It's rated at 16 ohms. I'm running a mesa single recto head into it. It has one 8 ohm cab output and two 4 ohm outputs. Can I plug it in through the 8 ohm output? Thanks.
-Fender American Deluxe Jazz Bass
-Tech 21 Sansamp RBI
-Mesa Powerhouse 212
-Fender Bassman 410
-Tons of other bass/guitar gear

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#3
Having the cabinet more than the head will reduce the power the cabinet recieves, but will actually increase the efficiency of your head unit. This isn't bad but doesn't really help you either. Best solution here would be to find another 16ohm cab and connect it in parallel with the one you already have.
#4
i have a peavey penta cab that can run at 16 ohms but i kinda was going to sell it. When you say it dosn't help me either, what exactly do you mean?
-Fender American Deluxe Jazz Bass
-Tech 21 Sansamp RBI
-Mesa Powerhouse 212
-Fender Bassman 410
-Tons of other bass/guitar gear

FAST MELODIC PUNK! CHECK OUT MY BAND!
therowleyestate.bandcamp.com
#5
Ideally you want to match impedence of your cab with your head unit. It has to do with whats called the thevenin resistance of your amplifier (some technical electrical engineering stuff). Basically when you match the load resistance to what your head appears to have internally you gain the maximum amount of power out. This reduces the efficiency of the amplifier but for a guitar amp it doesn't matter.
That being said, having the speaker load lower than the amplifier (i.e. running a 4ohm cabinet out of an 8 ohm unit) will cause a "loading effect" which puts a great deal of strain on the amplifier which could break it. this is why you never run a head without speakers.