With respect to a rectangular horn mouth, is there a ratio of width vs. height after which the horn's performance begins to suffer noticeably? I'm thinking conical midbass, here.

Assuming a constant flare angle, the frequency where pattern control is no longer set by wall angle is determined by mouth size. If the mouth is axisymmetric, then the frequency where this happens is the same in the vertical and horizontal plane. If, on the other hand, the horn is wider than tall, then the horn will act as a diffraction slot that widens the flare in the vertical plane before it begins to do this in the horizontal plane.

• Pattern from single slit diffraction

DM

Look at the two radiation patterns below.

See how the one on the left makes a radial pattern and the one on the right makes more of a focused beam? That's because the one on the left is what results when wavelength is large compared with the width of the slot. This is what happens at low frequency, when the horn mouth is much too small. In that case, the flare wall angle does nothing, and the mouth acts as a diffraction slot. The one on the right is closer to the transition frequency, where the horn still directs the radiation angle. As the horn transitions from being large enough to control the pattern and too small so that the mouth acts as a diffraction slot, you'll see the pattern below. Notice that there are nodes of energy separated by nulls in between.

You can see how the pattern changes with respect to wavelength in the applet below:

• Single slit diffraction applet

Could the vertical diffraction effect from a rectangular mouth (narrow height compared to lower cutoff) create obvious comb-filtering problems in a vertical line array of like horns? Would anyone really notice, even if they danced the "Pogo"?

Again, all horns that are arrayed will have potential combing. If they're spaced further than 1/4λ apart, they'll not sum as a single sound source and will act something like double-slit interference. If the horns are axisymmetrical, then they will behave the same in the vertical and horizontal planes. If not, they will act differently in each plane. That may or may not make arraying more difficult, depensing on what kind of array you need and what frequencies are required.

Usually, a sound engineer strives for single sound source summing. But that is not always the case. In some cases, it is desirable to have dense interference, in order to smooth the sound field. For example, if sound sources (or reflections) cannot possibly be maintained within 1/4λ, then nulls will form in certain places. One way to correct for that is to add sound sources that increase energy in nulls formed by interaction betwen other sound sources. Ironically, multiple sound sources spaced apart cause nulls to form, but adding a few more can average the sound field. This is called dense interference and it is a very useful technique.

• Horn Arrays

Whatever happened to the more relaxed, full-wavelength coupling criteria of the V-DOSC? Does it only apply to direct radiators arranged and spaced a la Christian Heil? Back then, the thinking seemed to be that direct radiators were meant for coupling and horns were meant for segregation when coupling was no longer feasible.

As for patent infringement, I don't mean to be disrespectful but the Unity horn is not unique in design principle at all. It is multi-driver horn arrangement with drivers offset down the throat, intended to sum properly within the horn, approximating physical offset with electrical phase. There are other implementations of this design approach that preceded the Unity, however, the patent office apparently found some aspects of Danley's implementation to be unique enough to grant a patent on it.

This does not mean that any loudspeaker that limits spacing between drivers to 1/4λ spacing between sound sources is infringing on the Unity patent. Most speakers have this as their goal. I think the Unity patent covers the specific implemention of placing midranges and woofers staggered down the horn wall with a crossover that attempts to stagger phase to match the physical offset. It doesn't cover coaxial horns, not tight pack arrays, not speakers with crossovers designed to provide proper summing, not horn speakers with drivers offset from the apex of the horn.

I'm not entirely clear what arguments were made to set apart the Unity from the earlier Renkus-Heinz CoEntrant design that preceded it. It's not something I've been interested in. But I want to reassure you that you can find many ways of building a speaker that keeps spacing to a minimum without infringing on the Unity patent.