Green 788, I went to the link you posted and read it as well as Chris Long's article. Very interesting. Very noticable was all the theory, formulas, numbers, et al. Like virtually all that's in pring about barrel harmonics, there's no mention of any actual tests made to measure barrel movement when fired.
The only person I know of who has recently measured barrel whip or vibration during firing is a resident mechanical engineer at the US Olympic Training Center. His measurements were made with accelerometers close to the muzzle (not attached 'cause that would change the barrel's resonant frequency) that measured the muzzle movement from when the trigger released the sear to bullet exit. Here's some stuff he learned.
Rifle barrels have a fundamental frequency that's low; typically 40 to 80 Hz. The high frequency one hears when they tap a barrel is a harmonic (around the 20th to 30th) of the fundamental.
When fired, there is only one whip of the barrel that causes bullets to exit at different points. That whip is about one cycle of the barrels's fundamental frequency. It's much like taking a garden hose that's laid out straight, then grabbing one end end to whip it and you see the single wave go down the hose.
The high frequencys noted at the muzzle were insignificant in changing the direction bullets go.
A given barrel alone will have its own resonant frequency. Fit it to a receiver and the barreled action's resonant frequency will be different than the barrel alone. Mount a scope on that barreled action and things will change again. Then bolt that scoped barreled action in a stock and changes will happen again.
Many years ago (1930's?), one of the US military arsenals did some tests using spark photographs of the muzzles of two bolt action rifles; a Springfield M1903A3 and a British SMLE. The objective was to find out why the SMLE shot smaller groups at long range than short range while the reverse was true with the M1903A3. 'Twas discovered that the M1903A3 .30-06 ammo had a lower muzzle velocity spread and its bullets were leaving the barrel at about the same place in the barrel's vertical whip. Short range accuracy with the M1903A3 was pretty good but at long range it fell off quite a bit. The SMLE was a different story, however. The greater muzzle velocity spread of the .303 ammo didn't cause larger groups at longer ranges. Instead, the faster .303 bullets were leaving the barrel when its whip made the muzzle point at a lesser elevation angle and the slower bullets left when the barrel whip put the muzzle axis at a greater elevation angle. Slower bullets were launched at a greater angle than faster ones; their trajectories came together for best accuracy at 800 - 900 yards. No wonder the SMLE was a favorite for long range work.