Just to clarify some folks have been using flash supressor and muzzle brake as if they were one and the same - which as far as I am aware is not correct. The flash supressor, well supresses flash, which unless you are shooting at night is really not an issues - especially with the 22LR. The muzzle break on the other hand is a device that diverts propellant gases thereby reducing perceived recoil, and muzzle rise.

Also while I am sure barrel harmonics exist - going back to my college physics I am pretty sure that in order to counter balance the harmonics you would need a very specific 'weight' which would vary depending on barrel length/weight/thickness/ammo and would not be something that would would be 'plug and play' between rifles.