Nyal,
Let me know what you think
allow me some comments:
1. You refer to research by Welti and Geddes. I’m sure some readers would like to know more and read the technical papers themselves, so the bibliographic data would be quite handy.
Welti, “How many subwoofers are enough”, Audio Engineering Society preprint 5602 (2002)
Welti, “In-room low frequency optimization”, Audio Engineering Society preprint 5942 (2003)
Welti, “Low-frequency optimization using multiple subwoofers”, J. of the Audio Engineering Society 2006, p.347
Welti, “Optimal Configurations for Subwoofers in Rooms Considering Seat to Seat Variation and Low Frequency Efficiency”, Audio Engineering Society preprint 8748 (2012)
One other paper that is certainly most interesting in this context is
Fazenda et al., “Subjective preference of modal control in listening rooms “, J. of the Audio Engineering Society 2012, S.338
where different subwoofer configurations are compared for a single listening position using music as test signal.
2. In chapter 1 you refer to optimum room dimensions. The goal of the various optimization methods is to arrange all of the modes evenly on the frequency axis. Therefore, in order to experience the benefits of optimum ratios, all of the modes must be excited, simultaneously and at equal levels, and the listener must be able to perceive all of them, again simultaneously and at equal levels. This is possible only when source and listener are positioned in corners. As you say later in chapter 3, it makes a difference where you place of subs and seats, because the interaction with the modes is changing.
Since nobody will put the subs and himself into corners, which would actually be rather ridiculous, why optimize for an arrangement of subs and seats which nobody will ever use?
As for stacking modes on top of each other, listening tests have shown that rooms where 2 or even 3 dimensions are the same are not necessarily bad, simply because the result depends on where you put the subs and the seats.
As Floyd Toole has put it: “So it is not that the idea of optimum room ratios is wrong, it is simply that, as originally conceived, it is irrelevant in our business of sound reproduction.”
You have measured peak-to-dip variances of 15 dB+. To that Toole said in a conference paper back in 1990: „It has long been puzzling that music and speech can sound as natural as they do in rooms that are horrendously flawed by numerous resonances. The explanation seems to be that room modes are generally medium- to high-Q phenomena. In steady-state measurements, such as these, modes are very much in evidence. However, when excited by the sounds of speech and music, which are mostly transient or discontinuous events, they are not always as apparent to the ear as the measurements suggest.”
3. In the passage relating to room mode cancellation you say: “The effect of a subwoofer on the level of a room mode depends on where you put the subwoofer. If you put it in the center of the room at the null there would be minimal energy coupling between the subwoofer and the standing wave.”
Since you refer to “a room mode” the reader will think that the following is true for all room modes, which obviously is not the case, since only the odd-order modes have a null at the room center.
4. Quarter-wavelength cancellation from the wall behind the speakers: I did an experiment to see how this sounds, placed a small active speaker on a board with wheels, attached a string to the board, placed the board against the wall, played a 80 Hz sine tone, slowly pulled the board up to about 2 m distance from the wall, listened. On paper the cancellation should occur at about 1.07 m distance from the wall, but no, nothing, no cancellation, not even partially, nothing at all. Looks as if theory and practice are different worlds.
Klaus