2nd floor joist sizing

[TGS]

I'm building a version of the KC 1200 (Katrina Cottage) and I want the second floor joists and subfloor visible from below. Timbers are white pine. The span is 13'. Floor will be T&G 2x6 white pine. I like the look of heavy beams but I want it to be within reason. Based on your experiences, what size should my timbers be for the Joists? What spacing goes along with that joist size?

Thanks!

Martin

I should probably add that this is conventional framing and the beams will sit on top of a framed wall.