When loudspeakers are placed close to walls, the delay between the direct and reflected sound waves affects not only the perceived timbre (due to room gain and comb filtering) but also the degree to which believable phantom stereo images are created. If reflected sound waves arrive too soon after the direct sound, they generate spurious directional cues that spoil the stereo-imaging magician’s trick.
Some people go to great lengths to absorb room reflections with acoustic absorbers and diffusers, but the evidence  suggests this probably isn’t a good idea. These products have inherently uneven frequency response; their presence can drastically alter the timbre of the reflected sound, and it’s harder for the ear/brain to ignore reflections if their spectral content is different from the direct sound.
The precedence effect can be an effective remedy for the effect of room reflections on stereo imaging. To the extent that the reflected sound is a sufficiently delayed copy of the direct sound, with similar spectral and temporal content, the ear/brain system will take its directional cues only from the direct sound. The reflected sound gets filtered out psycho-acoustically. To make this work we need loudspeakers with frequency-independent polar response (i.e. “constant directivity”) and we need to place them far enough from reflecting surfaces.
Ideally we need to delay the arrival of lateral reflections at the listening position by (at least) about 6ms relative to the direct sound. So the path length for the direct and reflected sounds must differ by at least 2m (7ft). This is hard to achieve in even a largish room, as shown in the images below. Linkwitz’s rule-of-thumb placement is >4 ft from the wall behind the loudspeakers and >2 ft from side walls, with speaker separation >8 ft. It turns out this isn’t quite enough.
For any rectangular room with a symmetric 8ft equilateral arrangement of listener and loudspeakers, the speakers need to be at least 1.4m (4.5ft) from the side walls and 1.1m (3.6ft) from the front wall, if the first reflections from these walls are to be delayed by 6ms. The listener also has to be at least 1.1m (3.6ft) from the back wall to delay reflections from that wall. The derivation of these figures is an exercise high school geometry, the gory details of which I’ve put in this little paper.
Analysis: My Listening Room #1
Here’s an analysis of how the first-reflection delay varies with speaker placement in my main listening room:
The green triangle is the listening position. Black contours indicate, for any given speaker placement, the resulting delay in arrival of the first lateral reflection at the indicated listening position. To achieve ≥6ms delay the speakers must be in the shaded region. Red contours indicate speaker placements that give exactly 6ms delay for reflection from a particular wall. The dashed lines are a guide: a pair of speakers placed symmetrically on these lines will form an equilateral triangle with the listening position. The green circles are where the speakers would be in the case of an 8ft equilateral arrangement. As you can see, this placement delays the first reflection (which comes from the side wall) by only about 4.5ms, although the front wall reflection gets 6ms delay. My Plutos and LX521 still sound impressive when placed this way, but I’m guessing from this that they could sound better.
In the room above (which is about 15’×19′) with equilateral positioning, the furthest I can separate the speakers, without decreasing the arrival time delay below 6ms, is 1.9m (6.5ft). This requires that the speakers be placed 1.3m (4.4ft) from the side walls — quite a bit more than Linkwitz’s rule of thumb. Clearly, even in this largish room speaker placement is a compromise.
Analysis: My Listening Room #2
My other listening room is long and narrow (22’×12′) and even more challenging for speaker placement:
I need to sit at least 1.1m from the back wall, partly to delay reflections from that wall, but also to keep the bass from booming. Here I’m only getting 2ms delay for the front wall reflection. To get 6ms reflection delay for this wall the speakers need to be at least 1.1m (3.7ft) from the wall, which allows for an equilateral separation of only 1.6m (5.4ft).
I’ve tried setting the room up like this too:
This shows that the side wall reflections are delayed by only 2ms or so. In this orientation it’s almost impossible to delay the side wall reflections enough. To achieve 6ms delay with equilateral placement, the greatest speaker separation I can use here is 1.1m (3.6ft). This is very much near-field and a bit claustrophobic. I’ve listened to my Plutos this way, but dipole speakers are out of the question. The previous orientation definitely has better imaging.
Siegfried Linkwitz’s Listening Room
Linkwitz has published details of his listening room setup in this AES convention paper and elsewhere. Here’s my first-reflection-delay analysis of his setup:
It appears he’s only getting about 4.5ms delay for side wall reflections. This is probably OK for dipole radiation, which greatly attenuates the sound directed at the side walls, but it does fall short of Linkwitz’s own recommendations. I’m willing to bet his room would sound better oriented like this:
This arrangement gives almost 7ms delay to the front wall reflection, a bit more for the rear wall, and about 15ms for the left wall. The listener is 1.3m from the rear wall. The “right wall” is actually open, so this arrangement sacrifices symmetry, but with the left wall so far away I doubt that this matters as much as the gains in reflection delay.
The Smallest Room Where This Can Work
Q: What is the smallest room where one can separate the speakers by 8ft (equilaterally) and still delay lateral first reflections by 6ms?
A: About 5.2m (17ft) wide by 4.3m (14ft) deep. You can read the details in this paper.
Here’s the analysis for that hypothetical room:
Moving any of the room boundaries closer to the listener will put one of the reflections at less than 6ms delay. In this configuration all four first reflections arrive at the same time — perhaps not a good idea — but in a slightly larger room it would be possible to place things to stagger the reflection arrivals.
 Floyd Toole, “Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms”, Focal Press, 2008.