There are a variety of horn flare profiles, from exponential to conical.

There is no one best horn shape. If you were to view the horn as a continuum from an organ pipe to a parabolic horn, each type has its own application. It is better to think of a horn as a resonant vessel that can reproduce a specific bandwidth with various degrees of dispersion and efficiency, sometimes self equalizing at the expense of directivity. In the low frequency region an organ pipe can reproduce a very narrow band of frequencies- sometimes only one ( like a flute). If you add more and more pipes, you can cover a multiple of frequencies, thus winding up with an organ. If you use an exponential horn, you get the best mix of bandwidth and efficiency, ever equalizing up as you go higher in frequency- at the expense of directivity.

The Tractrix offers good bandwidth, a very short horn ( less throat distortion) but also, narrows the directivity as you go higher in frequency because of beaming.

The Conical horn is a neutral horn which pretty well maintains the natural expansion of a radiator in air-with the least amount of modification imposed by the horn. They have to be long to work, and are the lowest in efficiency. The wavefront is always perpendicular to the sidewall of the horn, resulting in lowest 'horn' sound.

If you were to get a single widerange speaker ( say a JBL LE8t) and put any of these horns in close proximity to the LE8, you would see on a measurement curve, a 'suck out' range of frequencies caused by the shape of the horn. Kind of the inverse of an active horn. This is heard as the resonant 'signature' of a vessel. The Conical horn has the least effect of the various horn shapes.

This test (and just talking through the horn) would show the Conical horn of having the least coloration. The conical horn also has the most even dispersion pattern, at the expense of upper range efficiency.

You should note that the large multicell- a number of directional exponential horns tightly packed can also have very good dispersion- with good high end efficiency- at the expense of some mild coloration.

I am currently going into production with a 700Hz conical cast aluminum horn which will fit any driver up to 2" throat- from WE 555ww to a JBL 2440. This horn can be free standing, or built in, and is built in the style of the early Westrex/ large JBL acoustic lens horn. I love these old well made horns, and just wanted to offer the same quality today. Kind of a homage to the massive 537-500 ( or HL 88) used in the Westrex systems. More about this in the new year.

I had a wonderful time at Oswald's Mill, and was struck by the ingenuity, and passion that everyone in attendance has to the era of the mighty motion picture sound systems. Many of the amplifier designs sounded fabulous- a far cry from the goings on of today.

Thank you for letting me blow my own horn.

Bill