Most barrelmakers use 3 tapers when making a swamped barrel, from the breech to a waist, the waist being flat, then a taper from the waist to the muzzle. I think they use the same principle when making an octagon to round- a single taper to the wedding ring. On some originals this is not a single taper but more a curve.
I'm considering growing a pair, as they say, and working over an octagon to round barrel on a grinding wheel just as they did back in the day, when starting with a forged barrel. Round the bottom 3 flats of the octagon to round section as many of them were, eliminate the wedding band on the bottom 3 flats, etc. The barrel would be easier to inlet and a bit lighter as well.