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Crossover question

this may seem like a dumb question, but here goes:

If a crossover is rated at 8 ohms, do the drivers hooked up to it have to be 8 ohms as well?

Let's say I have a 15" 4 ohm speaker that I want to put in a cabinet with a 6" midrange rated at 8 ohms, and use a crossover with them rated at 8 ohms. Is that feasible?
 
No, you can't use a crossover which expects an 8 ohm woofer section with a 4 ohm driver, without some aberrant behavior (ranging from shifting the frequency to melting something).

You're stuck rolling your own and it will behave as a 4 ohm box for the most part (with rising resistance up top IIRC, but since almost all of the power is to the woofer, it'll be the load most important to amplifiers).