because the only load they carry is the dead load of their own weight or a slight dab of snow, the 2x8s will probably handle it, but proportioqantely they might look small. Since a pergola is decorative as much as it is functional, I would use 2x10s

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Off hand I'd agree with the 2x10 but 14'... plus it's cedar, that's got to be close, plus you need to apply the math on the elasticity when wet due to the exterior nature of the project. If you added a post no problem... 7' w/2-2x10 ... 14'... I don't know... even if the rafters are only 6' I wouldn't want to call it engineered to code.

But also I'd add that here in this county in CA they treat a pergola just like a roof so we still have to apply a 40# /sq ft live load I believe it's due to the fact someone is going to get up there, be it a painter, or the next owner stringing xmas lights or even someone might apply roofing, you now that corragated crappolla... so I'd check with you local buidling dept if you have any doubts.

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