I just thought of something that could have some relation to this topic:
Take a horn with a driver, the driver produces a signal, the pressure wave will travel outwards more or less like a spherical wave front along the axis of the horn, think of the 2D waves in the surface of water when you throw a stone.
Eventually the wave will reach the mouth of the horn and leave it, when the wave hits the edge of the horn mouth, it will experience a discontinuity, this will produce a disturbance due to diffraction.
This disturbance will contain not only the frequencies of the original wave but also distortion; it will say higher harmonics of the signal. (This is a fact according to acoustics)
The edge of the horn mouth, will in case of a circular horn, function as a parasitic sound source shaped like a ring with the same diameter as the horn mouth and emitting a time delayed and distorted version of the original signal.
The time delay will depend on the path length from the driver to the horn mouth.
The large diameter of the parasitic sound source, as determined by the diameter of the horn mouth, will mean that the distorted and delayed emission will be extremely directive and concentrated in a narrow angle around the horn axis.
The directivity will depend on the frequency of the signal, interestingly the distortion due to its inherently higher frequency content will be more directive.
In case of traxtrix horns and like, with their large opening angels, this effect will be less pronounced than in something like conical horns, since the wave front in the horn will have detached itself more from the horn wall at the horn mouth, and will not see the discontinuity of the horn mouth as much.
Never the less, some effect will remain.
How can this be avoided?
1. Direct the horns away from listening position.
2. Cut the rim of the horn into a star shaped pattern.
This will smear out the diffraction of the wave front in the horn, in time and space, and maybe render it harmless.
3. Place triangular pads of felt of suitable size and thikness, at the horn wall at the perimeter but still inside the horn.
4. Use non circular horns so the wave front will not reach the horn mouth at the same time every where, same effect as 2.