I'm glad that Roy confirms something I've been saying for years. Not that I'm speaking for him here.
1) Many horn shapes have radiation patterns which narrow as frequency goes up. Some of this is due to the geometry of the interior of the horn and some of it is mouth size. Mouth size or just a diaphragm does this simply because at high frequencies they are bigger antenna in terms of wavelength.
2) Olson's diagrams showed the narrowing but the diagrams seem to have been normalize to show on axis response to be constant. I think in reality there is gain on axis as frequency goes up.
3) Drivers used on horns have decreasing output as frequency goes up, just as Keele says. You see this when driver response on a plane wave tube is shown (about 3 kHz. But very often the response is shown on a horn with that increasing on axis gain..
4) You put 2 and 3 together and you get a type of equalization.
5) Constant directivity horns do not have as much change, as shown by Keele. Note that he had to equalize the driver to a constant output, and then the horn output was constant.
6) Horns like the K-400 keep the horizontal pattern fairly constant and the vertical pattern narrows. PWK called it controlled directivity. So it too has some gain on axis.
7) You see the 9 kHz "glitch" in the K-55. It may be diaphragm break up. It is about, say 15 dB down without the horn. But the horn has so much on axis gain it is can be heard. It may be that something similar is happening in the Jubilee. So it is necessary to eventually have a steep electrical filter.
8) The K-Horn is probably lossy at 400 Hz and above due to the second section where the path flips from horizontal to the vertical. However the real problem may be that final sections face away from the front axis and there is little gain at 400 Hz and above. If you look at the AES paper on the Jubilee, the design evolution is to have the final flares face more forward. Hence rising gain.
9) Keele calculates an increasing rate of roll off in the driver and you see this in midrange drivers on plane wave tubes. While a horn has some increasing gain, it can't keep up with it quite as much as the driver is rolling off. So at some point the overall response drops very quickly.
Gil
2) The drivers