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Pellet type impacting horizontal component of POI

I guess the title says it. Can someone shed light on why there would be a horizontal component to POI shift when switching from one pellet type to another?

I see this quite often - consistent groups, identical everything (scope/zero/gun/rest/bench, settings, etc), and still, some pellet types print quite differently on the horizontal axis. Sometimes, the error is even reversed, i.e. pellet type A will consistently group to the right of POA, and pellet type B to the left.

Any thoughts on why that might happen?

Happy holidays to all ya turkey eaters and esp those of you who are lucky enough to be able to harvest their own. Cheers!

[edit: clarification]
 
In short, barrel harmonics can change the point of impact more than velocity change alone. All barrels vibrate when the arm is fired. The barrels can vibrate in any number of ways. There is a vertical component, and often a horizontal component as well. 

Each projectile will have a bit different time when it leaves the barrel, and can even influence the initial shock that starts the vibrations. 

This is the big reason, why two otherwise identical rifles will prefer different pellets. The ideal point where you want the pellet to leave is when the barrel is at its change of direction of vibration; it is when the muzzle of the barrel is nearly standing still. Sometimes this is not possible when the horizontal and vertical components are out of time with each other. 

I have a 6.5x55 Swedish Mauser that has this condition. I can get it to group either with a large vertical string (6+ MOA), and no appreciable horizontal spread (less than 1MOA), or the other way around. When I try to meet in the middle, I get a fairly round 3.5 MOA group. 
 
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Any sort of weight clamped to the outside of the barrel, will change the harmonics. The placement of the weight, the mass of the weight, are all unknown variables and are best found by trial and error, unless you have some interesting lab equipment that can actually measure all the vibrations with respect to time.

One of the first commercial successful applications of the variable weight was the Browning Boss system. It had a muzzle brake/weight that could be screwed in or out to change its mass location. 

You will see some guys have all sorts of o-rings, rubber grommets, and other things positioned about their barrels, to dampen these harmonics. Again, the placement of these is a trial and error sort of thing. Put a heavy snug fitting rubber grommet on the barrel, and move it around as you shoot groups to see what it does. Shrouded barrels are a bit more problematic with doing this, for what the barrel does without the shroud may not be what it does when it is installed.