Since most claims of "beaming" are supported by f = 2C/pi x D, the resulting "beaming frequency" (I am placing this in quotes intentionally" is about 700Hz for a 15" driver. In practice, the off axis response can often be an octave or more higher than this. The off axis response is generally taken as the -6dB point for ~constant power summing purposes when designing multi-driver cabinets (like a 215).
I used the Klippel example because that's one of the platforms that I use when developing or evaluating drivers, and how changes might impact the off axis response. I could have used LMS or AP, but much of the data I have is Klippel.
Using the Faital example, the -6dB point happens to be ~1kHz, but notice that the off axis rolloff slope parallels the slope of the on axis response starting at 1.5kHz rather than continuing at the earlier, steeper slope. This is a critical deviation from the predicted "purely piston" theory because of other factors such as cone material/shape and dust cap material/shape. These elements, just like whizzer cones, function as secondary radiators of higher frequencies. Otherwise, all 15" drivers would have exactly the same off axis rolloff (which obviously they do not).
This is exactly the principle behind the JBL D/K-130, with the aluminum dust cap bonded directly to the top of the bobbin, the aluminum dust cap serves as an effective secondary radiator which improves both on axis and off axis response. This is because the smaller dust cap effectively decreases the diameter of the radiating surface at higher frequencies. When the 15" diaphragm element and the smaller element are acoustically summed, the falling slope of the larger diaphragm is offset somewhat by the secondary radiator.
Here is an example of a 15" 2 way speaker system that is often used to determine summed polar response. I typically use between +/-30 degrees (60 degrees spread) or +/-45 degrees (90 degrees spread) depending on the application but you can see that this 15" driver is well within the -6dB point within this angle at 1kHz and actually ends up being close to 2kHz by the time the on axis and off axis patterns deviate.
My point is that blanket statements based purely on the simplistic theory don't necessarily apply when the entire picture and variables are included in the discussion.
