couple of things
most of the old frames I've looked at use a m&t that is 1/4 the size of the timber, so in a 12x12 I would expect a 3" tenon, the most common size barn timber around me is 10x10, most often with 2 1/2" tenons.
The other thing is that I disagree that a 4x6 is a timber. It needs to be 5" thick before it is a timber. Just a technical point.