Look into the wall construction products made by ASC. I have heard a room constructed with them, and the structure of the room---especially the walls---was the least resonant I have ever heard, by a considerable margin. Rapped with one’s knuckles, the sound produced was a mere "click", not the normal resonant "tonnnk". The walls were like rock!
The ASC system begins by isolating the first layer of sheet rock from the studs it is normally secured to. A layer of WallDamp is then applied to that layer of sheet rock, and another layer of sr is then put in place. The WallDamp material is a constrained layer adhesive, and put between two resonant surfaces like 4’ x 8’ pieces of sheet rock (which left undamped vibrate/resonate like a drumhead) it creates a remarkably non-resonant structure. It can also be used in the construction of double-layer shelves for equipment racks, and in double-walled loudspeaker enclosures.