As I understand the theory, it is about an annular strain that reflects back and forth from muzzle to breach, essentially a tiny bore diameter distortion that bounces back and forth. It may all be valid theory. The problem I see with it is that there are other vibration modes, such as longitudinal whip which when taken into consideration, we'd like the bullet to exit when the whip at the muzzle is at or very near an apex. Whether or not the annular vibration mode is going to harmonize with the longitudinal whip of barrel vibration is just entirely uncertain as I see it.
That line of thought has led me to wonder if there are "magic" barrel lengths that promote harmony between all the different modes of barrel vibration...but that's not something I'm ever going to try and figure out. Life is too short already and I've got a good bit of hunting to do. If the gun and load work well together, it's a GO and I'm outa here.
That's what the original theory was but I've read other ballistics theory books that claim that most ballisticians don't look at harmonics quite that way. In the book "Ammunition Demystified", by Jeff Siewert, the author claims that the harmonics are pretty much controlled by the mechanical properties of the barrel steel at the time of manufacture. Siewert, and others, say that the primary frequency of the barrel is the one to be concerned with. Regardless, I have never found a really good way to find the primary frequency of my barrels so I just use the OBT theory since it estimates the same thing and it works pretty well for me.
I follow Siewert's basic guide for a good load;
"...what we're really doing is looking for a powder that burns out completely while filling the case as close to 100% loading density as possible without exceeding the allowable pressure. Not coincidently, this propellent solution usually provides pretty close to the highest muzzle velocity that can be attained with the particular projectile-cartridge case combination."
With Quickload, I can create a list of powders that will match those parameters (100% fill, 100% burn in the barrel, and max pressure) and export it in to a spreadsheet, which allows me to filter the results down to one or two powder combinations very quickly.