The comparison should be with a round barrel of the same weight.
...That is more to the point! I was trying to point out in my first post in this thread that "Removing" steel from a round barrel, cutting it to a triangle, or whatever shape, is an exercise in futility since the loss of steel will reduce the barrels stiffness and resistance to harmonic vibrations... That is not to say that one profile cannot create a stiffer barrel, given an equal quantity of steel in it's construction.
...As I said in my earlier post, many people seem to believe that milling flutes into a barrel will increase it's stiffness. That is not true, since the steel removed in the process reduces the strength and stiffness of the barrel. Fluting a round barrel does however increase it's cooling ability since it produces a greater surface area to exchange BTUs. A fluted barrel using a like quantity of the same steel as the round barrel certainly should increase stiffness over the round barrel. A triangle barrel would be stiffer in certain vectors of travel, while being more easily bent in others vectors of movement. The point being, that triangle barrels might prove to have a tendency of harmonic vibration that would be different than the equidistant vibrations normally seen in a round barrel.
.... Whether the triangle form will prove itself to be an accuracy improvement will be shown in time. I doubt it will prove itself more accurate than the round barrel, unless comparing triangle barrels of greater mass to a lighter round barrel.
