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Look at the whole system

To optimize a horn for efficiency, bandwidth, or whatever criteria, one should look at the whole system. The driver, rear chamber, front chamber, compression ratio, flare length, area and profile are all variables that can be modified for a specific goal.

See the Marshall Leach paper below:

"A procedure is presented for the design from specifications of moving-coil drivers for low-frequency horn-loaded loudspeakers. The method permits specification of the upper and lower system cutoff frequencies, the volume of the cavity behind the driver, the driver area, the horn throat area, and the desired system electrical impedance. From these specifications, the required Thiele-Small small-signal parameters and the electromechanical parameters of the driver are determined under the condition of a maximum-sensitivity constraint on the system. The procedure can be easily modified for a maximum-efficiency constraint."

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