This is something that's been rattling around my brain for some time now. I think we've discussed it a bit.
I *think* I know what's going on here. This is all very back of the envelope, but it's food for thought.
If you check out the positive compensation article on the Border Barrels site, you can see some measurements of the muzzle motion.
The relevant motion seems to be be a sine wave that peaks about 3 times per millisecond. So roughly 3000 Hz. I know this is a very different rifle - a rimfire - but the frequency is still significant because the overall results should be roughly similar for centerfire in terms of the impact barrel motion has on the target.
Now check out Varmint Al's analysis of mode shapes.
Notice that the the 3000 hz mode is well down into the mode shapes. It's a pretty complex shape. This isn't super relevant, except that it shows you just how tiny and weird the vibrations can get. Keep in mind that all of these modes are superimposed on top of each other to varying degrees. The exact frequencies will move around quite a bit, but this shows we're in the same ballpark which is nice to know. Some frequencies will be excited more than others, based on the forces involved. It's also worth noting that Harold Vaughn's experiments also found that it was higher frequency modes that mattered.
The third thing to note is that resonant frequency of a barrel is proportional to 1/L^2, where L is the barrel length. So it's pretty sensitive to length.
What's bothering me is that small changes should not impact that frequency very much - maybe half a Hz or so. It's a pretty small effect. None of this back of the envelope stuff is enough to quantify it. But it's not unreasonable to think it could just be a frequency change. Or maybe by shifting the frequency, it pushes it closer to the driving frequency and therefore changes the amplitude of that mode.
Now this is all very rough, and these numbers can vary widely, but I think it shows very generally how such small changes can have significant impact. The data available pretty consistently shows that higher modes in in the low single digit kHz range are what matter.
It's just one piece of the puzzle, and I'm not sure there's any immediate practical benefit to it. But I think it's interesting.