Why does pulling out main speakers from wall improve sound?

SBIR - Speaker boundary interference response.

As noted, perhaps not fully correct, but as the frequency drops for a dynamic speaker, the radiation become omni-directional. The wave reflecting off the front wall is reflected, with not a lot of attenuation, and then cancels the front wave of the speaker. The critical distance is 1/2 wavelength as that will be completely out of phase.

Ideally you want to be far enough from the front wall that the round trip distance is > 1/2 the wavelength of a fairly low frequency. Put another way, the distance is > 1/4 the longest wavelength. 3.5ft, and you just created a suck-out at 80Hz. Even at 5 feet, you are still hurting important bass frequencies, and this is not stuff easily corrected if at all with DSP.

Counter-intuitive, but the solution is to put the speakers closer to the front wall, and then treat the walls with absorption. Not those those trinkets I see in audiophile pictures that cover a small portion of the wall. You need to cover a good portion of the space behind the speaker, and the absorption need to work at a low enough frequency to prevent the SBIR cancellation. You will get boundary reinforcement by being close to the front wall, but this can be corrected with DSP.

+1 @tonywinga 

You are balancing boundary reinforcement (getting close to the walls), with SBIR (cancellation from front wall reflection), and room modes. @bigtwin , Focal appears to be attempting to at least balance some of that in their formula, but as you noted, it may result in unrealistic values for many listeners.

@sc2, it is a little more complicated than what you have indicated. The distance they gave you appears to be to be outside the 10msec critical early reflection time. That may add a low frequency bass suck out (~50Hz). For many, even with a dedicated listening room, that may be too far into the room.  That gets us back to the speakers being closer to the front wall, the front wall heavily treated for reflections, and using equalization to address boundary reinforcement. 

@jumia the floor is only a concern for boundary reinforcement. That can be fixed if needed by equalization (DSP). The front wall reflection comes back towards the listener (not the ceiling). It is critical.  The muddiness is usually a large suckout and some reinforcement around the wavelength = 4x distance to wall. Early reflections is there two but that's imaging not muddy. Muddy could be too much boundary reinforcement emphasizing bass too much.

Good video @yyzsantabarbara , it's my post from above but in easier to understand video form. They don't address how boundary reinforcement though and how to deal with it.

While responding to another post, I was reminded of the Dutch and Dutch 8C. They address the issue in a different way:

1) They use mainly acoustic methods to present an out-of-phase "midrange" signal at the sides, to cancel the midrange as it is "wrapping" around the cabinet. Quotes around midrange as it will be frequency controlled.  This would replace acoustic treatment with a traditional speaker.

2) They accept boundary reinforcement in bass frequencies and provide DSP correction, something that can be done with any speaker.