The crossovers are third order but not a typical alignment since they both EQ and filter at the same time. The crossover point is selected where the LF driver and the HF driver have the same polar pattern - 90° at about 900 Hz.

Now tell me, how did those Pi-7's image from the sweet spot? Anyway close to the Maggie's by chance? I am not as familiar with these high efficiency horn type speakers but, I am interested in the Pi-7 because I have a near perfect room for these. And, they are affordably priced.

How does one distinguish directionality from room modes?

If the room is small, room modes will dominate. There is no way to get around that I can see. The only way to get a clean measurement is in a very large room or open area with a corner. That is a textbook 1/8th space.

Tell how you measured this or if it is just speculation on your part.

Adam

Directionality, to me, implies that sound waves are free to propagate in any direction and a sources directionality defines the level of sound waves that propagate in an arbitrary but particular direction.

Room modes are quite different in that they can only propagate in a single specific direction. A sound wave that is exciting a mode does not travel freely but is fixed in the direction defined by the mode. To talk about the directionality of sound waves in the modal situation is a misnomer IMO. At a mode ALL sources, monpoles, dipoles, horns, whatever, have the exactly the same directionality. Does it make any sense to talk about directionality of the source in this case?

"If the room is small, room modes will dominate." True in ALL rooms at some frequency. The room modes dominate up at and somewhat past the Schroeder Frequency (if you don't know that term look it up). Above that ALL rooms act the same and modes are no longer relavent. This is fundamental room acoustics (See Kutruff "Room Acoustics" or my own texts).

I can get a clean measurement in any room, above a frequency defined by the first reflection. The smaller the room the higher the frequency. In fact, some recent studies have shown that it is possible to go much lower in frequency than this traditional limit implies, but that is another topic. But at no time can one use a corner for a "clean" measurement. 1/2 space is sometimes used but this too has its problems. The only really clean measurement is a gated free field one, which can be done, within limits, in any room.

Are you trying to learn something here or is this just a challenge? I will attempt to educate, but I will not accept a challenge.

I think this discussion went down an unproductive path from early on. No one questoned your assessment of room modes and their significance. I generally agree with your reasoning where that is concerned.

What I disagree with you about is the room corner, itself. You make assumptions about the room that I don't make. Where I see our difference is that you attach an arbitrary generalized room to the launch corner when you discuss it, and I consider the launch corner separetely. I see π/2 radiation and standing waves from radiator placement and room boundaries, but you only see an averaged and therefore generalized field of modal vibrations.

The room is a variable, so I don't think it is appropriate to lump it in, because that causes you to make generalized statements that aren't necessarily true. The size and shape of the room and the stiffness and absorbency of its boundaries determine how it acts. A very large room acts a lot differently than a small one does, as does one with angled ceilings, peculiar shapes or open areas. So I prefer to see the room modes as a separate matter from the radiating angle of the launch corner.