This is a question with two answers. Obviously the purpose of absorption is to control reflections in the room. Reflections from flat surfaces are bad because they will be strong reflections and not broken up into different directions. And rooms commonly have large flat reflecting surfaces, commonly known as the walls, ceiling and floor! Worse still, these surfaces are usually parallel, which means that reflections can easily bounce back and forth between each pair of opposing walls, and between the ceiling and the floor.
So we have two bad features here - walls that are flat, and walls that are parallel. But it gets worse. What if the walls have hard surfaces too? What if the walls are covered only with bare plaster?
Now this really is bad, since all audio frequencies will bounce back and forth causing a particular effect known as flutter echo. The best place to experience flutter echo is outdoors between two parallel hard surfaces. Clap your hands and you will hear a sound not unlike twanging a ruler against the edge of a table (come on - you must have done that at school!). Once you have heard this in conditions that easily promote flutter echo, you will clearly hear it in rooms too. Needless to say, it's bad for recording, and it's bad for monitoring too.
So to combat flutter echo, you need absorption placed on the flat surfaces of the room.
Now, what about that other problem - excessive reflection of bass frequencies? It is always difficult to absorb bass, but it can be done with panel or membrane absorbers. You could distribute the absorption around the room, but if you didn't want to go to that much trouble or expense, where would you put low-frequency absorbers for best effect?
Well, without going into the science this time, it turns out that the worst kind of reflection, the 'standing wave' that prolongs the duration of reflections at certain frequencies, always causes a high-pressure region at the reflecting surface. Put another way, it is loudest near the wall. Also, standing waves will occur readily between pairs of parallel surfaces.
Now, if you can visualize standing waves bouncing back and forth between wall-to-wall, wall-to-wall and floor to ceiling, you just might be in a position to realize that these three pairs of surfaces intersect in the four corners of the room. So if you put absorption in a corner, it will be effective on all three standing waves, between the two wall-to-wall paths, and also the floor to ceiling path.
So this is exactly where your low-frequency absorption should go. Put it in the middle of a wall and it will only be effective for one of the standing wave paths. Put it in the corner and it will be effective for all three.
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