It's a matter of scale. Since the wavelengths of sound passing through basshorns are large, small features don't matter. That's why you don't need curved flares, exponential/hyperbolic flares can be approximated with a few straight segments. Same thing with mid/tweeter horns, but at a smaller scale. Ever notice the grains in ABS plastic tweeter flares? They're acoustically small compared to the wavelengths passing through the horn. Small features are like grains in film, which are too small to see. If you enlarge a photo enough, you'll see it has grains like pixels of a computer screen. They're just not visible at the scale the photo is used at. This is kind of the same thing with acoustics, if features are small compared to wavelength, they make no difference.

Compare the 12π Hornresp models with the measurements. Both are available at the link below. The model describes a perfect horn with a curved flare and a throat at the apex, just like the Hornresp schematic shows. The actual physical horn has four segments and the throat begins with a long thin apex and two square holes cut near it. Even so, the measurements tracked the models extremely well.

• 12π hornsub info (scroll down to the sections on development, construction and test results)