A little hair-splitting follows...
I agree that constant directivity is a desirable goal even at the lowest possible frequencies.
A definition for "constant directivity" would be
Source: AES "Metrics for Constant Directivity"
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Only Geddes Abbey or his other speakers is not a good example of constant directivity in my opinion. One could say that up to 1kHz there is still a "controlled directivity" if you look at the radiation as a whole.
The standard procedure to judge how good the "constant directivity" behaviour of a loudspeaker is, would be to normalise to the 0° frequency response and to consider whether the angular frequency responses are parallel to it.
Because of the extremely unsteady frequency response in the +-10 degree range, Geddes loudspeakers cannot be described with constant directivity. Even if one normalizes to the 22° listening angle proposed by Geddes, side lobes would show up. As a quick example Geddes Nathan normalized to 30°, with the 0° and 60° frequency response.
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A horn that works quite well (and far from optimal) with constant directivity would be the XT1464 from 18Sound. Above 10kHz the connection of the driver to the horn causes some problems - just ignore it (measurement 1m distance from horn mouth, 1/24 smoothing, normalized to 0°).
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directivity pattern with 1/3 smoothing
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This looks very much like CD!
How were the measurements taken? Standard measurements at a distance of 1m without a gate and with little or no smoothing would certainly look much "wilder" even with a horn system due to the room influences.
For +-45° the measurements show sound pressure fluctuations of just +-1.5dB in the frequency range 400-18000Hz and this with full room influences - how is that possible?
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