Insulation, Radiant and Vapor Barriers - Sound insulating adjoining ( neighbours ) walls

My house is semi detached, so I share a wall with my neighbor.

Back in the old days these walls were never insulated so although I am not looking for thermal insulation, I would like to have some kind of sound insulation.

I was thinking of nailing 2"x2" to the adjoining wall and then filling the cavities with white styrofoam sheets, they sell them I think 1'x8' sheets and then putting drywall on top.

Will this give me some sound insulation?? What are my options to sound insulate this wall without going actually framing a 2x4 wall and getting sound acoustic insulation?

My goal is to get better sound insulation by using the least amount of space.. My house is only 15 feet wide, losing another 4 1/2" to have it properly sound insulated is not something i want to do.

Your opinions and suggestions are greatly appreciated.

ya I guess you can go into that... it might not have as big effect as you might hope but adding some furring strips to your new wall after the white insulation board... but Im sure there is a board designed for sound proofing.. but then putting furring strips over that.. to create a tiny air gap.. which will help quiet sound more. Only problem is low frequency sounds are non directional and travels through solid mass.. so having an air gap will cut out those sounds

Try this:
http://www.certainteed.com/resources/Guide%20for%20Residential%20Sound%20Control.pdf

Be safe, GBAR