Where do you want to stop the sound from going? Are the upstairs occupants going to
complain? Do you have adjoining neighbours?
My first thought would be to remove
the plasterboard on the basement ceiling and add another set of staggered joists
supporting 2 or 3 layers of plasterboard as a new ceiling. If you are worried about
adjoining neighbours and need best performance, you would also need to build additional
walls and mount the new ceiling joists on the top of the new walls.
JRP Music - Audio Mastering and Restoration.