In an apartment this is really difficult. If you can get the book "A compendium of materials for Noise Control" from the library check it out. It's out of print, but can be found at many universities. What you will find is that noise travels through the structure almost as much as the walls, particularly bass frequencies. Thus you need to isolate the area with either a large mass, or a broad airgap. The best is to use a combination of both. Sound isolation chambers essentially float a room within a room. Obviously, this is extreme and would not be appropriate in your circumstance, but what I'm getting at, is that there really is not a very good solution short of building another wall with an airgap between that wall and the existing wall. This is assuming that the frequencies are on the low end and penetrating through the structure. One interesting thing that could be done (to find out if I'm right about that--not knowing the construction I could very well be wrong). If your neighbors are patient enough, so an SPL plot accross the frequency spectrum inside your room and pretty loud 85 to 90 db--or close to the listening level that is bother some (assuming this won't damage any of your equipment), then plot this in the neighbors, you can see what the attenuation coefficients are for each frequency. If it's higher frequencies--which I doubt. Owens corning 705 fiber board mounted on the wall will help a great deal (it will deaden the room). If the fequencies are below 300 Hz--what I suspect. You would just about have to build a wall inside a wall.
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