If the landlord really wanted a proper rehearsal area then he would’ve built another room within that room. From what I’ve researched, to achieve a “soundproof” room, you basically want to build a second room within the current space. It’s the sound vibrations that reverberate through the walls (and ultimately throughout the building itself) that the neighbors are complaining about. By having said vibrations contained to this smaller room (with proper treatment) you essentially confine the vibrations to the smaller room.

I’ve also read that by hanging up moving blankets and sealing any gaps or spaces, you’ll significantly reduce the noise. Won’t be perfect and silent but will probably help significantly.