My suggestion would be to buy some of the "egg-crate" foam mattress pads and tack them to the common wall. (Flat side to the wall.) If they're sufficiently affordable, do the entire room, including the ceiling if you've got upstairs neighbors. They really soak up the sound, and eliminate most all reverberations. You'll probably hear your own voice differently, because you'll only hear what actually comes out of your mouth, sans harmonic relections. A small project, really. Good luck.