This is very large. So a Klipsch corner horn can have a mouth size 8 times smaller than the flare frequency would indicate. As you reduce the mouth size, of course you also shorten the horn. This is apparently the case for almost all rear-loaded Lowther horns. Only the Carfrae when placed in a corner has an appropriately-sized mouth.
Every horn follows some type of expansion contour.
This is the type of curve between the throat and the mouth. The conical contour does not provide very good characteristics and is only used in extremely simple applications. The shortest curve is a Tractrix expansion. Note the flare at the end of the Tractrix contour. The Tractrix contour is very well suited to mid range and high frequencies.