Whatever you decide to do (or by now you might have done it already haha), it is worth doing research beforehand, as the same materials combined in different ways can give very different results. My starting point was this book: Home Recording Studio: Build It Like the Pros: Rod Gervais: 9781435457171: Amazon.com: Books . The author of that book at least used to be active on a forum, I think recording.org or something.
As I remember, mass, decoupling, and damping are the most important principles. In the type of construction I did, the mass is the drywall, the decoupling is the Genie Clips, and the damping is the Green Glue. The ceiling also doesn't touch the walls - you leave a small gap and fill it with a dense acoustic caulk also made by the Green Glue company. Basically the idea is to have heavy things that "float" off of their supporting structures.
I don't know if anything I've said will be useful, but have fun with your project and I hope it goes well. 🙂 What I'm talking about may very well be overkill for just a saxophone... The book I linked to has the exact specs on attenuation of many different constructions, so you could find the one that would suit your goals and limitations.
I'm still in my research-and-getting-off-my-ass-phase to do something about it 🙂
