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The theory of attempting to modify the barrel's natural whip such that you move the apex or vertex of the wave to just on/after the crown so that bullets exit at the literal same spot every single shot...I think this has merit...but don't see how it would help you (specifically with rimfire, where velocity is not as controlled).The adjustable muzzle weight tuners clearly worked in RF benchrest. Everyone serious in the game had one, and my testing showed a significant improvement once you found the right setting. This is on big, awkward, BR purpose-built game guns. They are pointlessly stupid in any kind of practical rifle. The one exception might be that rubber sex-toy-looking
LimbSaver Sharpshooter X-Ring Barrel Dampener
that you slide up and down the barrel, if you could find a spot that made a difference.
I don't recall hearing that tuners varied by range. The idea at the time I was in the game was that the muzzle whipped/vibrated from the shot, and the tuner moved the muzzle end to either an apex or vertex of that wave, where it was moving the least. And that reduced the variability in muzzle position at bullet's exit. But we shot at 50 yds, and sometimes also at 50 yds, and occasionally even at 50 yds. So there is that….
A stiffer barrel has less harmonics, and therefore less variation in harmonics. At least in my experience.Tune the whip is what I mention above...you want the whip - specifically so you can lob the slower rounds further and let the faster ones take on a straighter trajectory...thus they all end up around the same POI. The harmonics/whip is going to be relative to the round; the first pew moving 1040fps will not induce the exact same whip as the one moving 1060fps because they have different forces that they're applying on the barrel.