Here is why I come to this forum...
I am and have been an advocate for accurate, full bandwidth playback of modern soundtracks and music in HT. For years the experts, accredited or self-appointed making no difference in a forum where new-comers are just looking for options, howled and jeered over the very idea of playback of anything <20 Hz. The arguers were as grossly incorrect as they were prolific. "The content <20 Hz is unintended noise", "You can't hear those frequencies anyway", "The equal loudness curves dictate that you would need 140dB <'x' Hz", "No subwoofer can play that low with enough authority cleanly", "You'd need a nuclear power plant for mains and you'll have to rob a bank", "Room gain is dependent upon how sealed the room is", "Room gain begins at a frequency whose wavelength is 2* the rooms longest dimension", "Rooms >2000 ft^3 will have little, if any room gain", etc., etc.
Most of this has been dispelled over the past decade but some of it persists, like the discussion in this thread re; room gain. What it is, how it works is still largely a mystery to the average enthusiast because of the mysterious explanations by people who have never experienced <20 Hz reproduction.
Here is what brought your paper to the thread, from a post by LTD:
Originally Posted by LTD02
todd welti also refers to the zone below the first mode as the "pressure zone".* again though, same result, so use whichever term you like.
I quoted the pressure zone mentioned in the paper:
The pressure zone response of the room. This is non-modal response of the room, i.e. the room acts as a 2nd order low-pass filter at low frequencies. The low pass characteristic can be seen below about 8 Hz in the above plot.
(That's ^^^ where the 8 Hz came from)
LTD claims, among other strange things on the subject, that the "pressure zone" acts as a 2nd order shelf boost <L2, but the paper seems to contradict that, so not sure in what context he cited your paper.
Regarding the other comments:
The bottom line with the grid drawing of little heads in a 6' x 6' square space, it's just incorrectly presented. The reader should not have to re-read and re-draw to get the correct context. I appreciate the actual procedure now, but it took you to explain it. Illustrations are used in lieu of or to support explanations. If drawn correctly, a discussion as to what the drawing represents would not be necessary.
Like so, for example:
For the record, we both know that no HT will have folding chairs for seating, squeezing listeners at 2' O.C., but, I do appreciate the time you took to lay it out for me. Over the past 12 years, this is the first time in dozens of posts that referenced the paper that anyone took the time to explain the grid details so that they made sense.
I agree that concentration on any single mode is not wise. I haven't said otherwise. I just feel that the floor-to-ceiling mode, which exists in every room, is as important as any other parallel surfaces, yet is completely ignored by the professionals. The ceiling is also potentially an additional boundary of purely constructive reflections through the typical 80 Hz crossover region when the point source is the correct distance from it. This is not trivial.
The floor-to-ceiling mode is also far more universal than other modes because most rooms have a ceiling height of 8' (70 Hz) or 9' (62 Hz) and are both in the crossover region, vs other boundaries which are infinitely different from room to room and outside of the typical crossover region. If you ignore stacking, it will depend on where you sit in the room, as your measurements show. You're actually off by a couple of inches in your stated ceiling height, IMO. Move your marker up a couple of Hz. I can't move my primary seat and planar placement options have no effect.
Finally, stacking offers the most output in the least area of floor space, which is a checklist item that's usually at or near the top of the list. Most people here build overkill systems for headroom at the extreme low end and to handle whatever software the industry throws at them. When it comes to <20 Hz, displacement is king and that means multiple drivers. It's an unavoidable requirement of the recipe. In most rooms, placing 30 or so liters of displacement in proper sized enclosures around the room, on the floor, is not an option.
So, I advocate multiple drivers for bandwidth, not smoothing response or any other reason. Because most people don't or conventional wisdom ignores, these are not reasons to not explore the possibilities and present the data.
I see that Kreisel's new stuff is made to stack, the alignment is sealed, the drivers are dual opposed, etc., so some industry folk are either paying attention or just finally getting around to dealing with the same reality we've evolved to of how to separately place the required 8 or more drivers.
To my knowledge, sheetrock and doors do not absorb anything <40 Hz, the BW of interest. The pressure waves are either reflected off a rooms boundary back into the room or they're lost through the boundary to outside the room or somewhere in between those two. Drapes, traps, sofas, etc., have no absorption authority over low frequency soundwaves.
If your test room was constructed of sheetrock and a flimsy door, where it concerns subwoofer frequencies, it was not a live room. Live or the opposite, where low frequencies are concerned, has everything to do with TL and little if anything to do with absorption.
This is the essence of room gain. It's the result of wave interference that is progressively more constructive vs destructive as wavelength increases, minus boundary TL and including modal influences <30-40 Hz with the final arbiter being signal chain roll off at the extreme low end.
I don't expect most people to wade through what I write or have written, much less give a hoot. But, some do and these are the basic facts of the matter. When people post that multiple sub locations = smoother response, they need to do a lot of qualifying for that statement to be true. Because, of course, every room is different and placement options vary in each room. When people post that sound waves turn into liquid below L2 as in an infinitely rigid cylinder of infinite length, or whatever the Star Trek parallel universe theory of room gain is on paper, they should be ready to present actual data and a reasonable explanation of what the he!! they're talking about.
I was going from (ancient) memory, but I looked up the actual quote in the paper:
Due to several factors, including a sizable rear projection television located at the front center of the room, and a limited number of available subwoofers, the configurations are slightly different than those modeled in Investigation 4.
It's no big deal, it just illustrates the point I tried to make; that real rooms will skew the results of a simulated empty room of rounded-off dimensions.
I appreciate the time you've spent here, and… can you please tell us more about the software program you wrote?