I wouldn't bother. Just get some acoustical panels for your corners and you'll be fine. Furniture helps too.
I would build in soffits, soffit traps, corner traps, and use a Rives PARC. Those room ratios are going to give you serious bass problems and you will probably need to electrically correct, but don't do only that. Try to reduce the problem as much as reasonably possible first.
If it was easy for me to convert one of my rooms to one of the recommended golden-ratio sizes, I'd do it in a heartbeat. Nothing, and I mean NOTHING beats great room acoustics. If you have a great room, even mid-fi gear can sound glorious.
The alternative of spending a lot of money on bass traps and expensive equalizers and getting worse results does not make sense to me, provided that you have the ability to easily alter your room dimensions to a size that will support relatively linear bass response. Most folks know that's the hardest area to get right.
I have seen a few different ratios. I am not sure which is best. The one I am looking at now comes from the book by Robert Harley; The complete guide to high end audio, he states that the ideal length and width of a room with an 8' ceiling is 15.2' x 11.2'
I have seen other ratios as well. Anyone have more info on this?
For what it's worth, when I built my music room I carefully researched ratios. Even went so far as doubling the sheetrock and incorporating sound channels. Still, my room tends to interact a little too much with my system.
I keep thinking about when they spent millions designing Avery Fisher Hall to be "acoustically perfect" only to end up with a muddy mess of sound.
Then there are rooms that should sound like crap, yet end up golden.
Go for proper system, listener and acoustic panel placement, you'll probably be just as happy.
One thing to watch out for as Ouput555 has discovered (the hard way), doubling sheet rock makes for a rigid wall. It helps with sound isolation, obviously, but the more rigid the wall the greater the peaks and nulls in the low frequency. If you do change the dimensions of the room, my advice would be to fur out and use single layer sheetrock with standard bat insulation behind. The 1/2 inches sheet rock is semi-transparent to low frequencies and acts as a capacitor to some degree--thereby reducing the bass problems.
doubling sheet rock makes for a rigid wall
Good point. A leaky room is far better in bass response than concrete walls. Concrete basements rarely sound as good as wood frame walls and wood floors. The only people who suffer from a leaky room are the others in the house and potentially the neighbours!