Here is the answer to my actual question:
http://awc.org/codes-standards/calculators-software/spancalc
Edit: Sorry if I'm not on the same wavelengths as anyone else. I already know about insurance and inspectors, and that was not at all what I was asking about. I just wanted to know what length of wood would span a certain distance given various criteria. I would have expected an answer to that question, instead of all the "your a dumb homeowner who's going to get in trouble" type replies. I question the idea that there will be 50psf of weight from snow given the fact that it is an almost non-solid top, and saw no real attempt to answer my question, so I had to come up with this. It took me awhile to find, and I hope it helps others.
First answer! (On an old question.)
Could the side beams that run perpendicular to the house extend almost all the way to the house? That would provide an additional 3.5-4’ of coverage along the house side, where we typically place deck furniture.
I'm assuming you mean the rafters (that rest on the beam) would cantilever over the 17' beam by 4'? That will be fine, as there won't be any weight bearing on the rafters other than their own weight.
Are 4x4 posts sufficient for the pergola?
In my estimation, yes. Check out load tables to be sure (capacity varies by species, length, wet or dry conditions, etc.) They will look a bit spindly though.
Is the placement of those posts OK to carry/support the load to the structure below?
Should be fine, in fact, you could place the posts almost anywhere. Each post will be carrying less weight than the average American male.
Any other suggestions or questions I should consider?
Pergolas don't weigh that much, but they do catch a lot of wind so lateral load and rotation of the posts is a real concern. I understand you're bolting some the posts to the joists so that should solve that problem.
The 17' beam span will likely cause the 2x6 beams to sag. I'd recommend bumping up to 2x8 or 2x10.
By this point, you've probably built your pergola. How'd it turn out?
Best Answer
You can easily span 12' with a 2x12 for a pergola as long as your load is not crazy. What is going on top of the 2x12's? 2x2's? I would set my posts on 12' centers and cantilever 4' on each side. I would also sandwich a 2x12 on each side of the post. There actually is enough information in your question but there are many online beam span charts. Here is one. Hope it helps. Make sure there is no earth to wood contact on your posts and you will enjoy your pergola for decades. http://www.decks.com/deckbuilding/beam_span_chart_table