Triple Parity!

Try this.

Put the edge with the double parity in the up and front layer.

Do the following: r2 U2 r U2 r2 U2 r2 U2 r U2 r2

I got this off a Youtube video. It's very useful for a 7x7 cube too. Try this alg on a virtual (or real) 7x7 cube to see what it does.
 
That's a good 2 gen version of that parity alg, but I prefer this one just because it's a little faster (for me):

Edit: To solve the "triple parity" as you call it, solve two of the edges (I use E layer) so with the edges parallel vertically, I do (just the middle inner slice) E' R U R' F R' F' R E , then just do the OLL parity alg (r U2 (r) r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' ) for the last edge.
 
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