Start by insulating the space between the basement ceiling joists with a sound dampening insulation like owens corning quietzone fiberglass insulation.
Insulating floor joists in basement for sound.
Part of the problem with adding insulation for floor joists is securing such insulation between joists underneath the floor.
Make sure to use soundproof cocking to fill any holes or cracks.
The added layer of drywall plus the noise proofing sealant will improve the stc rating to between 41 and 45 depending on the flooring used on the above floor.
Make sure to use screws that are maximum 1 5 inches long as we do not want the screws to touch the joist.
Joist bays the open spaces between floor joists are prime hosts for insulation under specific circumstances.
The use of soundproofing caulking will improve the sound quality in the basement and reduce noise between the floors.
One thing a lot of people fail to do is to soundproof the basement stairs.
The idea that heat rises has prevented many builders in the past from insulating floors but adding insulation for floor joists can actually improve a home s energy efficiency as well as its insulating capabilities.
Next you might want to consider using a soundproofing drywall such as quietrock for the ceiling.
Hold the batts in place by stapling their paper faced vapor retarders to the lower edges of the joists.