FWIW, everyone interested in barrel harmonics should watch this super slo mo Bryan Litz did of barre movement when fired. Only rearward movement not any up/down.... no visible harmonics.
Researchers have been measuring barrel vibrations since around at least 1901 and known of it long before that. Not sure what Brian wrote about involving that video but if it was to show muzzle deflection movement "harmonics" vibration that was less than ideal. With cantileved beam modeling the amount of barrel vertical movement is extremely small and fast oscilations. Consider how small of movement in the vertical plane it takes to raise POI @ 0.100" of say a 24" barrel using the bolt face as pivot point and muzzle the other point. To keep it simple make the bullet traj a straight line 100yds. It is quite small measured in the ten thousandths of an inch in muzzle vertical change using the bolt face as the pivot point.
Hereis a video using triggers for ignition to trigger accelerometer sensor and for bullet exit point ensuring delineation between pore and post exit movement but can easily be differentiated on the scope.
Barrel vertical deflection and vibration/harmonics really is not debateable. Its not theroy its fact. Its been measure with lab equip many times. The issue is accurate computer modeling of it to the degree that it could consistently model it for accurate positive compensation prediction. The issue is things like stock scopes etc also oscilate and there is not just a single oscillating force. But multiples that can both build on and counter each other etc.
Some historical references:
Barrel vibration harmonics was known long before these. The ref below were looking at finding ways to model, tune it, muzzle location @ bullet exit point i.e. positive compensation.
Some references:
Untersuchungen uber die Vibration des Gewehrlaufs. Abhandlungen d. math-phys. C1 D. Akedemie Der Wissenachaften, Vol. 69, page 747-775, Munchen, 1899
"The Vibration of Rifle-Barrels", Min. of Proc. of Inst. of Civ. Eng., Vol. 191, page 217-255, 1912-13 Francis Carnegie
"On Rifle Barrel Vibrations and their Effect on the Angle of Jump", R.D. Report No. 63, 1925 Woolwich Arsenal
"The Vibrations of Rifle Barrels", American Rifleman, January 1, page 17-32, 1927 Captain Philip P. Quale
"Vibrations of a Rifle Barrel", Journal of the Royal Technical College Glasgow, Vol. 4, Part 2, page 213-239, 1938 A.E. Martin and J. Muir
"Rifle Accuracy Facts", Pub. Precision Shooting Inc. Connecticut, 1998 Harold Vaughn
"Simulation of the Vibrational Response of a Rifle Barrel During Firing", Proceedings of the Advanced Simulation Technologies Conference, organized by the Society for Computer Simulation, page 66, April 5-9, 1998 Kevin N. Schwinkendorf and Steven P. Roblye
The Vibrations of a Barrel Tuned for Positive Compensation Nov 2015
is a good brief summary of these past work and the more recent research done. 22LR makes for easy testing used there.
This is another paper that has good descriotions of the type of testing that was done
