Wood is a poor sound insulator because it is neither dense (like rock) nor pliable (like foam). If anyone used it to insulate the floors for SOUND, then they were really backwards. Because of its physical properties, wood transmits sound waves through it, especially low frequencies. Thus, the ideal wall between apartment units has two independent, unattached wood frames standing next to each other, with the studs staggered from each other so that sound does not tranfer through the wood from one apartment to another.
Ironically enough, dead air space in a wall or a ceiling often serves a tremendous purpose in sound insulation because it interrupts the transfer of the low-end vibrations: namely, when the bass physically "shakes" physical objects. In other words, sandwiching dead air space between two solid surfaces provides better insulation than those two surfaces pressed together.
If the space between your ceiling and the floor above you is all solid material, then removing some of that material and replacing the ceiling would work well. If you have the room, you might also consider a drop-down ceiling to create that dead air space between what now is your ceiling and what was your ceiling. The tiles used for drop down ceilings, although ugly, are called "acoustical tiles" because they also absorb sound.
You can also consider replacing that superfluous wood (if it really is superfluous and not serving a structural need you have not figured out, yet) with actual sound insulation. Instead of transmitting sounds waves through a solid wood substance, insulation deadens and absorbs the waves analogous to the way a spring absorbs physical shock.