The strength of a loudspeaker designed to match DI at the crossover point is that the polar response is pretty uniform, not just the axial response. On this, you and I agree.

But in a system with a direct radiating midwoofer, you cannot control vertical directivity at all until the HF horn takes over, and even then, only at a fairly high frequency. I would rather limit vertical dispersion as much as possible, because that is a source of early reflections just as much as side wall bounce. I prefer to have the system match horizontal directivity or average DI while limiting vertical directivity.

As I see it, the DI matched two-way loudspeaker is a good solution, but like all good solutions, it has its compromises. It has no control of low frequency and midrange directivity. The system starts to become directional near the crossover point, which is pretty high in the midrange band. The whole vocal range and below has hemispherical radiation or greater.

The ideal would be to have controlled relatively narrow directivity throughout the audio spectrum. My personal preference would be that the pattern have an aspect ratio wider than it is tall, because this better utilizes the acoustic energy to cover the listening area. In an indoor environment, it also serves to reduce reflections from the ceiling and floor.

There are systems that can accomplish this, but they are larger than the typical DI matched two-way loudspeaker. The DI matched idea is a good one for making speakers of moderate size, since it helps make the transition between subsystems less abrupt and creates a more uniform reverberent field. But I don't think that widening the vertical pattern of the tweeter to match is productive.

The way that I make a two way is the ONLY way to get a matched DI through crossover. You seem to be implying that you can do this with a narrower vertical coverage which I don't believe is possible in a two driver system.

Further you say

"But in a system with a direct radiating midwoofer, you cannot control vertical directivity at all until the HF horn takes over"

Untrue, with a 15" woofer I get substantial directivity above about 500 Hz, well below where the waveguide comes in at about 1000 Hz and the two are perfectly matched in coverage.

"I prefer to have the system match horizontal directivity or average DI while limiting vertical directivity."

But I do both - matched DI in both Horizontal and Vertical AND matched directivity. You cannot do both with your approach. I can elliminate the floor and ceiling reflections with absorbers, which I do in my rooms, so this, which is your best point, is an easily resolved problem.

"It has no control of low frequency and midrange directivity."

Nothing can control low frequency directivity except complex, large solutions that are totally impractical in small listening rooms so I don't see your point here. And as I said I do get substantial directivity out of a 15" at 500 Hz - a DI > 6 dB as measured, and shown on my web site. I've already covered midrange directivity.

"The ideal would be to have controlled relatively narrow directivity throughout the audio spectrum."

I actually agree with this. BUT, there is a practical LF limit for which this can be done. I go as low as is practical given contraints on enclosure size. Give me a larger enclosure and I'll go lower with directivity control. You forgot the word "constant" applied to directivity though.

We don't see eye to eye on this, but you seem to be saying things that just aren't true. Show me a system that you have built that has the kind of directivity matching and narrow coverage control that I achieve AND show and that will go a long ways towards convincing me that you have a good point.

"Show me the data."

A DI matched two-way loudspeaker is a nice compromise solution that does provide some degree of uniformity through the crossover region, but that's about it. I prefer to limit vertical dispersion more than a DI matched loudspeaker with an axisymmetric horn will allow.

By the way, at 500Hz, with DI at 6dB, the radiation angle is still so wide that early reflections are significant in both the horiziontal and vertical axis. There's no way around that in a DI matched two-way loudspeaker system. Regardless, I still find DI matched two-way speakers to be a good compromise of size and performance. I just don't like using axisymmetric horns.

To which I agree, if doing this did not create more problems than it fixes.

"I prefer to limit vertical dispersion more than a DI matched loudspeaker with an axisymmetric horn will allow. "

I preferthe matched DI - weve been through this before.

"By the way, at 500Hz, with DI at 6dB, the radiation angle is still so wide that early reflections are significant in both the horiziontal and vertical axis."

True, but not very important, nor is there any alternative. To get a DI < 6 at 500 Hz would require a speaker much much larger, I mentioned this already. A non-axisymmetric horn does nothing to solve this problem. At 500 Hz our hearing and localization is not very sensitive to reflections - not at all like they are above 1000 Hz.

You also have not considered that a narrow vertical coverage requires a horn to be twice as wide as mine to control the vertival pattenr as well as mine. Thus for a given cabinet size at the crossover, the non-axisymmetric device does not actually work as well for pattern control as the axisymetric one.

If you actually measure the pattern that you get you will find that your narrow device will actually be wider than mine vertically at the crossover.

Your "solution", as I keep saying, sounds good on paper, but actually creates more problems that it solves. My solution while not theoretically ideal has a singular problem that is easily fixed in the room itself. Again, we don't agree on this point.

I like DI matched two-way speakers because they provide good performance in a relatively small package. But I also like the idea of using room corners, which constrains the radiation angle. The speakers need only be designed to sit snug in the apex so radiation is done within 1/4λ from the wall. This is one way to get directional control at lower frequencies from a relatively small horn. DI is set at 9dB, and is that at 500Hz and below. The only requirement is that the horns be designed with a 90° flare angle and be set within 1/4λ from the wall so that the lower frequencies use the wall angle as flare extensions, effectively forming a very large CD horn.

You've made this argument before and I still don't buy it. DI of a system in a room is not defined as DI is only applicable to free space. So using DI the way that you are is not reasonable. If we are talking about how speakers perform in real rooms thats fine, but then lets drop any DI discussions. If we are talking about DI then we have to assume that we are talking about a free field.

You room boundary extension concepts are grossly over-simplified and I continue to doubt that things work the way you hope they do.

Your dual axi-symmetric approach does work fine - agreed - if you can live with a cabinet that is now twice as wide. I made this point earlier too. You keep repeating your points as if you don't even read my rebuttal.

To wit see Beranek, Acoustics, sec XI. The DI is not defined for a "corner" it is only defined for a "source of sound".

The 9 dB comes from only defining the sound field for a 1/8 space and using full space as a reference - not very meaningful. ANY source in that space would thus have a minimum of 9 dB of DI, making the value meaningless. Even an omni-directional source would have a DI of 9 dB by this deffinition.

The 9 dB is simply an artifact of the boundary conditions in an unrealistic situation where there is only ONE corner. Klipsch actually built a chamber like this in Hope, but I know of no other. They did it because it was the only way to test corner horns.

When the sound source eminates from the apex of a set of radiating planes that meet to form a trihedral triangle, then the DI of the source is 9dB. This condition can be made by a large stand-alone horn, rows of bricks or a room's corner that forms the boundaries. Consider the ceiling and the radiating pattern is constrained even more.

Seems like I recall you had mentioned one of your horns had a rectangular radiating pattern. One of the reasons I brought it up is that a 90x40 horn is useful for matching the condition formed by the room's boundaries when sound radiates from the corner.

Anyway, it's been great to chat with you and I hope you and Lidia have a very merry Christmas.