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Quick list of concepts:
You'd like to have the drum room framing decoupled from the original structure.
If there's no drywall already, you can add new stud walls 1" away from original. Can be 24" OC studs to conserve materials.
Ceiling is trickier, due to slope. But same decoupled, separate framing concept.
Add R13 fiberglass to new walls.
Add double 5/8" drywall on inside.
The floor is the bugger. Don't add a floating floor, assuming the ceiling under the drum room is drywalled. Instead, consider adding a layer of soundboard and double OSB (damped), or just add damped OSB directly to the existing subfloor.
You would do well building the inner walls on this new floor
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