You DO need foam. Sealing you and your sound in a small hard box would be brutal. You can play to a 100-head club audience... if you played the same in a room with just one body (yours) of absorption, the sound level would be 100 times higher! So either your ears would bleed all over your drumheads, or you'd play softer, leaving you out of shape when you do play to 100 people.
But that's just for you. You also have Neighbors, who are either the landlords or are at least Senior Tenants who the landlord would listen to before The New Tenant.
The attic is the answer. This gives you an 8-foot "dead air space" between the drums and the Neighbors. You can't make that kind of isolation any other way. Even though heat/cooling is going to be a royal pain, you have to go upstairs.
You will probably still need a massive box, as confirmed by your informal sound survey. "A radio" is one thing, but the constant banging of a solo drummer will get on people's nerves even at low level.
2x6 joists in an unfinished un-windowed attic suggests 20 pounds per square foot design load (living rooms are often 40PSF, bedrooms sometimes 30PSF). If you brought ALL your friends to the attic, shoulder to shoulder, it is in serious danger of collapse. No Joke, it happened in this city last year. Big party on the second floor,
entire floor assembly dropped to the first floor. Fortunately nobody downstairs, and nobody seriously hurt. And I suspect this was an old cheap house build before building codes (possibly true balloon framing), and that it was one hell of a party. Unlikely, but don't let it happen to you.
Such floors are designed for Distributed Loads. Boxes of Xmas ornaments. People spaced fairly uniformly (at 20PSF, they have to be 3 feet apart). Don't have a heavy wall at mid-span of the joists. (A wall parallel to the joists may be self-supporting and may drop its endloads near enough to joist supports to not be a real issue.)
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I really REALLY recommend you purchase one of those Sound Proof rooms that come in sections
Wenger has them, has been selling them for 25+ years.
They are coy about the price, for obvious reason.... think $25K+ and up. Gasp! but you can hardly touch their performance (including door and ventilation leaks) for that price in permanent construction, you can't get ordinary labor to build a room this tight, and you can't move permament contruction to a new location. So Wenger sells quite a few of them; it is a good deal for serious musicians (and music schools).
>>By using three different thicknesses of drywall you will improve STC over using three equal thickness panels by substantial amount.
> I've never heard this before and I can't see right off how this matters as long as you have an equivalent mass.
It's a small detail. As Greg says: Each thickness has its own self-resonances; different thicknesses spread the resonances around. If you also use lots of construction glue to bond the layers into a single mass, you may as well use all the same size. In less-gluey work, it may make a small difference using several thicknesses; OTOH the price-break for buying a truckload all the same may allow more mass for the budget (assuming you are budget-limited and not weight-limited as in a 2x6 attic).
I do think the church basement is a good bet for your situation. Be nice to the priest/rabbi and to the sexton or other layperson who manages the place. Be sure the place is neater/cleaner when you leave than when you arrived. Put some of the energy that was going to haul drywall into your attic into paint or shelves or whatever handy-work the church needs done.
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I have my head as floppy as it can be.
Good plan.