Assuming we are talking about a black powder gun and not a 50 bmg or other smokeless centerfire guns, a first question is it round or octagonal? A "traditional" muzzle loader or a more modern in-line?
For a traditional blackpowder muzzleloader, percussion or flintlock, a 13/16 .50 barrel is on the small side as most are 15/16 to 1"+. those guns usually start at 50gr black powder (or substitute equivalent by volume) up through 90gr on the small dia. side to 110 grains on the 1" guns.
Even further, it is generally accepted that US made steel is stronger than the cheaper steel used in spanish marked barrels.
Just my opinion, but if the 13/16 barrel is US marked I'd stay below about 70 grs max., 60 if it is spanish marked.
in-lines are constructed differently and each manufacturer specifies max loads typically 100gr or 150 gr. BP or substitute.
As you can see, we need to know more about what you are shooting to give more accurate guidance.
If any of this seems out of wack to any of you other BP shooters, please feel free to jump in and correct me.