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A tractrix and a exponential horn was compared in a AES paper sometime 1950-1970, I dont remember when exactly.

The two round and straight  horns where made with the same theoretical cut off frequency, something like 100Hz, they had the same mouth and throat diameter, hence the exponential horn was somewhat longer.

The measurements was made under open sky on a roof top.

The results in the low frequencies towards the cutt off  was clearly in favor of the exponential horn, it had a rather smooth and civilized roll off, while the tractrix was rather uneven and ragged, the usefull range was extended maybe a octave lower.

Tractrix is nice, but it is only a reasonable connection between one space angel and a small area and 180 degrees and another larger area, the theoretical basis is based on geometry and some charming but faulty asumptions on wave propagation.

A much more sound shape is the oblate spheroid horn invented by Earl Geddes.

It is actually possible to get comercial horns with something I think is an near oblate spheroid shape and a nice 180 degree termination at German ebay under the name ”Jabo”

The price is really reasonable.

The manufacturer ironically calls them ”Kugelwellenhorner” witch is German lingo for Tractrix horn.

Regarding the shape of dazzies horn: I can only see a decorative reson to make it round, I dont believe that round is better than rectangular in this range, in fact a rectangular shape will make a much better coupling to the room boundaries possible and extend the useful range 1-2 octaves lower, depending if dazzie can place it against a floor (or ceiling) and a wall.

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