To add mass and reduce vibrations in the wall:
1- After installing additional vertical and horizontal studs, pack the space between all the lumber with sound absorbing insulation material. People have their preferences, one being Roxul Safe ’n’ Sound.
2- Then put up the sheetrock, and for a giant leap in vibration reduction, add a second layer of differing thickness (for a different resonant frequency profile. 3/4" and 1/2" is a good combination), with---most importantly---ASC (Acoustic Sciences Corp.) Wall Damp material between the layers. WD is a 1/16" thick viscoelastic material designed to absorb mechanical vibrations, and it’s effect is HUGE!
I have visited a listening room (that of Audiogon member folkfreak, in his Portland Oregon home) constructed with the complete ASC system (which includes materials that greatly reduce the transmission of vibrations through the building structure), and the walls were like stone. For those interested in isolation, folkfreak had his Magico loudspeakers sitting on Townshend Audio Seismic Podiums, a great product. The rest of his system was an EAR-Yoshino table with two arms and cartridges, a DCS Vivaldi digital stack, an ARC Reference pre (model 10 or 40, I don’t recall), and VTL power amps. Very, very nice.
Details on ASC Wall Damp are available on the company’s website. Very affordably priced, and very effective. Also great for DIY shelves, the WD placed between two layers of stiff material. Stiff materials often ring (ever rapped a piece of unsupported marble? Rings like a bell!), and WD makes them almost completely silent. As with walls, use different thicknesses for each layer, and even completely different materials. Stiff and quiet, every woman’s dream date. ;-)