FWIW, in one of the home renovation shows on HGTV they used "rock wool" as insulation in the ceiling of a basement apartment and managed to get a substantial reduction of sound transmission -- at least 50dB. (A 90dBA sound source on the main floor above was reduced to normal normal background levels -- about 40dBA as I recall.) There also used some kind of dense paint-on coating for the HVAC ductwork to drastically reduce its vibrational noises. Sorry, I don't recall what they called that.
Hopefully someone here can provide personal experiences with these types of products!