The horn shape is tuned to emphasize bass. Because bass frequencies have a very long wavelength, the size of the horn needs to be large to cover low frequencies. A straight horn would be very long, so bass horns are usually folded to fit into a smaller space. The ideal shape for a horn is a round cross section. However, the tractrix contour has often been used with sucess for rear-loaded bass horns in Lowther speakers.
Rectangular horns are the most common.
See my Horn Speaker page for more details. Most of the Lowther factory speakers are rectangular horns. These speakers have parallel walls, so the width of the rectangle is fixed. Multiple folds might also be a problem, a couple of speakers have only one fold. Lowther factory designs.