Great suggestions so far -- I'll second the motion on reading Everest's book. Your limiting dimensional factor is your ceiling height* so I would not recommend making that any shorter than you need to do. Therefore, the raised floor might not be ideal (use carpets or rugs). There are different approaches to the ceiling. All of them would involve acoustical insulation between the joists. One option would be to use the doubled up drywall (per Tswhitsel) and hat channel construction with acoustical treatment of some type over it. Another option would be to hang acoustical tiles (the advantage of that is the direct physical contact to the joists is only though the wire). Do tons of homework or hire some professional help. But I wanted to reinforce how important it is to keep as much of that 9 foot acoustical height as possible. Good luck.
Footnote
* If you take golden ratio approach of the 1.618 factor (i.e., the width should be height times 1.618 and the length should be width times 1.618) a 9 foot ceiling would require a 14 foot six and three quarter inch width and a 23 foot six and three quarter inch length. The longer the length, the lower the wavelength the room can accommodate without creating a pressure zone (generally, pressure zones create inaccurately high bass -- you are, in essense, inside a speaker). A length of 23' 6 3/4" yield a pressure zone area below 16 Hz (3 times the wavelength of the rooms longest dimension): That's good. Where pressure zones end, standing wave areas begin. The standing wave frequency range for the 23+ foot length goes from 16 to 144 Hz. This is the strongest region of standing waves and will result in some dead spots and artificially boosted spots in the room (add at least an octave, maybe two to get to the overall range of influence). The longer the room, the better the sound (given the same ratios). The shorter the ceiling, the shorter the length should be. So keep your ceiling as tall as you can. The good news is that a 9 foot ceiling allows you to do the studs and double drywall on the walls as suggested by Tswhitsel (you should probably need to use 2x2 studs rather than 2x4 though).
The 1.618 ratio is not magic. The math can be found in Everst's book -- please read it. This stuff gets real complicated real fast. You also need to consider reflection times, etc. Send me an email and I'll respond with more info. Here is the scary part -- I'm not even close to being an expert even after doing tons of research. The good news is that even a little research will yield better results than doing nothing.
Look up "acoustical treatment" and "dedicated" on the forum search function to learn more about treatments, dedicated rooms and dedicated lines. Good luck.
Footnote
* If you take golden ratio approach of the 1.618 factor (i.e., the width should be height times 1.618 and the length should be width times 1.618) a 9 foot ceiling would require a 14 foot six and three quarter inch width and a 23 foot six and three quarter inch length. The longer the length, the lower the wavelength the room can accommodate without creating a pressure zone (generally, pressure zones create inaccurately high bass -- you are, in essense, inside a speaker). A length of 23' 6 3/4" yield a pressure zone area below 16 Hz (3 times the wavelength of the rooms longest dimension): That's good. Where pressure zones end, standing wave areas begin. The standing wave frequency range for the 23+ foot length goes from 16 to 144 Hz. This is the strongest region of standing waves and will result in some dead spots and artificially boosted spots in the room (add at least an octave, maybe two to get to the overall range of influence). The longer the room, the better the sound (given the same ratios). The shorter the ceiling, the shorter the length should be. So keep your ceiling as tall as you can. The good news is that a 9 foot ceiling allows you to do the studs and double drywall on the walls as suggested by Tswhitsel (you should probably need to use 2x2 studs rather than 2x4 though).
The 1.618 ratio is not magic. The math can be found in Everst's book -- please read it. This stuff gets real complicated real fast. You also need to consider reflection times, etc. Send me an email and I'll respond with more info. Here is the scary part -- I'm not even close to being an expert even after doing tons of research. The good news is that even a little research will yield better results than doing nothing.
Look up "acoustical treatment" and "dedicated" on the forum search function to learn more about treatments, dedicated rooms and dedicated lines. Good luck.