Hi Walt,
I have to agree – unless you want to have a huge mouth there has to be a compromise.
I like what you have done with the X-tro - the other practical alternative is to fold it like KV2 or Funktion 1 or port it like the old JBL 4560.
Operating below 200 - 300Hz I would almost call it a bass horn, however it will probably have to operate in full space not half space like most subs, so the mouth, unless it’s a compromise will be quite large.
Here is an excerpt from an interview with Bruce Edgar that may be of interest ...
Bruce: Yes, those particular horns were made for me by Bill Firebaugh, the Well Tempered arm inventor. He's also been interested in horns. He showed the paper horns to me. I said, "I've got to have a pair of these." So he made up a pair of horns. They are a round Tractrix horn and a round exponential horn. You talk through them like megaphones. When you talk through the exponential horn, people can hear the coloration to your voice, which is a certain resonant quality that wasn't there before. You talk through a Tractrix horn and you don't hear it. It's completely open.
The explanation goes back to the difference between spherical and plane waves. When the plane waves travel down to the end of the mouth of the exponential horn, suddenly there's a bulge where they exit into space, and that bulge is essentially a discontinuity. So, you have reflections at the mouth, which travel back to the throat and set up a quarter-wavelength resonance condition. With the Tractrix horn, since the waves are spherical going through the horn, they exit the mouth with very few reflections. When I first started building Tractrix horns, I heard this immediately. They didn't have the same horn colorations I'd heard before. I said, "Well, I ought to build all my horns this way," so when I built a 70 Hertz Tractrix Bass Horn (Speaker Builder, 1983), I was in for a surprise. The problem is that the Tractrix is a short horn. If you take the equivalent Tractrix and equivalent exponential horns (same mouths, same throats, same flare rates), the Tractrix horn is shorter. At the low end, the response on any horn is limited by the throat reactance, which peaks at the flare frequency. The exponential horn is long enough that if you can put on a back chamber and resonate it with your loudspeaker at the flare frequency, you can partially cancel out that throat reactance. With a hyperbolic exponential horn, you can cancel it out exactly. With a Tractrix horn, you don't cancel it out at all, so the 70-Hertz horn rolled off at 100 Hertz. It sounded very good, but the problem is that the Tractrix horn response just does not extend to the flare point. There is no way that you can do it, so you have to live with the consequences. Well, for a midrange horn that's not too bad. The 300-Hertz horn that I make turns on at around 400 Hertz, and since its size is not huge, I can build a full-size 300-Hertz horn. It sounds very nice, but it won't turn on until 400 Hertz.
Peter