I figured, "What the heck. I might as well throw it out there."
|Image from HERE|
Any reasonably diligent kid can get three notes while blowing across the top of a pop bottle. It may have been easier during the days of glass bottles but it can still be done with the common plastic ones.
Simplifed, the slug of air in the neck of the bottle (plus a hemisphere of air at each end of the neck) is the mass while the bulk modulus of the air in the body of the bottle determines the compliance. Increasing the size of the neck increases the mass. Increasing the size of the body increases the compliance. Since frequency is proportional to (1/(compliance*mass))^0.5, increasing either the size (length or width) of the neck or the volume of the body will result in decreasing frequency.
I messed around with a microphone and some sound analysis software and determined that at 70 degrees F and 900 feet of elevation a 30-30 casing has a primary resonant frequency of 1490Hz, a .308 Winchester has a primary resonant frequency of 1360Hz, a 30-06 casing has a primary resonant frequency of 1150Hz and a 300 Winchester Magnum has a primary resonant frequency of 1110Hz.
I was a bit surprised to see the frequency of the 30-06 so close to the .300 Win Magnum. Closer analysis indicates that it is probably due to the short neck of the .300 Win Magnum relative to the 30-06.
The final observation is that one simply cannot make the cases whistle if the primer hole is not closed off. It does not take much of a leak to poison the dynamics of Helmholtz resonator dynamics.