You can use 1x for the ridge, your rafters should be opposite each other.
It would seem you can get away with 2x6 for rafters going 16" O.C. You may
want a 2 x 8 for ridge for appearance reasons only, if the rafters/ridge
will be exposed. Otherwise I wouldn't go over 2 x 6 for the ridge.
Why 2x12, and why 2 of them?
If you need a structural ridge because there are no cross-ties, only a
structural engineer can answer that question for you.
In any other case a single 2x stock that fully supports ridge cut of the
rafters is fine.
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I'm probably way out of date, but when we were framing houses, a
2X10 made a swell ridge beam and if there were joists parallel to
the rafters, there was no call for collars. Think of the downward
force on the ridge beam: the force would be supported at each pair
of back-to-back rafters perfectly and if they were not
back-to-back exactly, the 2X thickness would still probably be
fine. The downward force would want to spread or flatten the
rafters, but that would be contained by the joists, or collars if
there were no joists (like a cathedral ceiling).
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