It is sad when the most comprehensive info you can find on-line is in Wikipedia. However:

"rapid increase in pressure causes the barrel to vibrate at a certain natural frequency, much like a tuning fork. The point in time at which the bullet exits the barrel will determine the orientation of the muzzle relative to its rest position. Exiting near a peak or valley in the motion means the muzzle is relatively stationary, and shot dispersion will be minimized; exiting between a peak and valley means the muzzle is rapidly moving, and shot dispersion will be greater. There are two ways to address harmonics; reducing the amplitude with a stiffer barrel, or working with the natural frequency to minimize dispersion. Stiffness of a barrel is proportional to the fourth power of the diameter, and inversely proportional to the third power of the length. Because of this, short, thick barrels will vibrate with high frequency and low amplitude, and long, thin barrels will vibrate with a low frequency and high amplitude. Due to the impact of length, barrel harmonics are primarily a concern with rifles. By using the shortest and/or fattest barrel possible, the amplitude of the vibrations can be minimized to the point that they are irrelevant to accuracy."

So we can change pellets to change weight, skirt diameter, etc. and the resulting "timing." Just hoping like heck we find one that leaves the barrel in a peak or valley of the barrel "whip." Or, there are barrel shrouds, muzzle weights (no matter what name you give them) and vinyl tube overlays that have been recommended without any before-and-after group sizes posted in what I saw.

I guess I could add or remove more barrel clamps in the 2240 design, or, move them around on the gas tube to vary the "whip" until I find a sweet spot. Perhaps you are waiting for a question from me ha ha ha....

OK: Would not a free floating barrel just change the harmonic as opposed to a "bedded" or clamped barrel? It seems a clamped barrel would actually shorten the whip effect... Why would one be preferable to the other?

And, B: What has anyone done to affect harmonics that they could report here on the forum?