Step 3: Soundproofing case study: walls
Searching on Craigslist, I found somebody who had ordered too many sheets of Quietrock 525 so I bought his leftovers for a third of the price. This is an excellent product but its cost can add up if you have to buy it new. It is much heavier than sheet rock and is layered with built-in damping. The sheets I got have the same sound rating as 8 stacked layers of regular sheet rock (but this isn't quite as good as it seems: 8 layers of sheet rock do NOT work 8 times better than a single layer...). We laminated the existing plaster partition next to our neighbor's kitchen with the Quietrock using Greenglue, and we have not heard a single pot bang since then.
On the opposite wall we tore down one side of the plaster partition, attached resilient channels to the studs and used isoclips, again, found for a fraction of the original cost via Craigslist, to float a new Quietrock partition. We were careful to leave a small gap between this partition and the other walls, the floor and the ceiling, which we later filled with acoustic caulk. If you make this system with store-bought materials it will get very expensive. If you aren't as lucky as I was finding deals, check out this instructable for a cheaper construction method.
Inside the wall we put a layer of Ultratouch, insulation made with recycled cotton fiber. You'll need to wear a respirator when you install this, but it is still much greener, healthier and more pleasant to work with than fiberglass. It won't itch. I also think it's better for sound, but that's just my subjective opinion, I haven't seen any studies. We were careful to leave an air gap and NOT to stuff the wall full. The purpose of the insulation is not directly soundproofing, rather sound absorption. We want to prevent the cavity inside the wall from acting like an echo chamber (which would amplify sounds the same way an acoustic guitar does). Using less insulation and leaving an air gap will soundproof better than stuffing the wall full.
The window wall looks out onto a relatively quiet courtyard so we did not soundproof the brick wall itself, but we did buy a soundproof window installed inside the window frame. Because closet was in the way we were not able to treat the back wall either. Since it's a brick wall it's got a pretty good sound rating, but unfortunately we can still hear when our neighbors open and close their front doors. That kind of impact sound is almost impossible to eliminate...