Why the teleposts? Can't you use double TGI's to cover the span without the need for the bracing? I am not engineering the home and don't know the load bearing issues but there is always a material solution to these things. If it adds a bit more cost you can justify it by the lack of the intrusion into the listening space and the cost savings in not correcting for them.
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You have many options for skipping the posts, but the basic room sizes are pretty much set for you. The posts won't really make much difference.
One thing that stood out in my mind was the 14"-8" x 21' option. You want to stay away from room sizes that are multiples of any given number. Seven is a common denominator for the dimensions you listed. You did not list a ceiling hieght so I assume you are going with an eight foot ceiling. Which is fine.
Given the options you listed I would suggest 12'-6" x 22'. I know that it is hard to get it into your mind that you will be building a smaller room, but it should sound better than the other combination of dimensions.
If you would like more info, check out Robert Harley's book "The Complete Guide to High-end Audio" or visit http://www.rivesaudio.com both of them have some very handy info for determining room size and sound quality. You should have Robert Harley's book anyway, just for the helpful info in it.
Thanks for the input guys. The ceiling would be around 7'4" after finishing. Unfortunately there is also ducting running parallel to the beam that will have to be "taken care of" but on the whole I guess it's a better situation than a lot of others have. I did check out Acoustics101 and intend to follow some of their construction recommendations when I build the room. Should be innaresting and fun.
As for your "telepost" concern (not sure what that is, ...maybe a support beam?), you'll have to decide that, and work that out.
As for room dimmensions, I strongly suggest using what world renound HT designer Russ Herschelmann uses in his theaters(designed Disney worlds IMAX theater, writes for HT mag, SGTHT mag, and AVinteriors on theater design, acoustics, engineering, tweaking, etc), He uses a modified 6% Bonnelo criterion. What he does is makes sure that room dimmensions are within 6% ratios of each other.(maybe 6-9% at most). What this does is garantee that room modes end up not doubling up or stacking up on each other, compounding problems, and allows for smoother bass modes in the room, rather than more pronounced ones. What you want to avoid(since you will have room modes no matter what) is double or tripple room modes that are stacked ontop of each other, which often happens with rooms that have boundaries and reasonant frequencies that are multiples of each other. So, in your room, Russ would take your fixed 7'4" ceiling, and then figure the width by doubling your width 7'4" x 2, which is 14'8", then add OR SUBTRACT 6% to that width (which is 15'6" or 13'9"). Then, for the length, you would multiply 7'4"(or 88") x's 3, which is 22', then add or subtract 6% or so(for a length of 23'4" or 20'8" or thereabouts!). What happens is, if you figure the room modes for these dimmensions, you'll notice they don't stack or "double up" on each other! This is what you want.
Anyway, you can figure room modes by looking it up on the net. Good luck, hope that helps.
E, thanks for the input. A telepost is a telescoping column used between the basement floor (with a foundation pad underneath) and a support beam above. In this case the beam is under the main interior support wall on the floor above. Kind of ironic that the width dimension that would work best for me is and exact double of the height. Mind you this is calculated before any wall board is on. I do have to strap and build out the exterior wall as it is only constructed of 2 x 3 with 24" OC. This is common in basements of new homes where I live. I may just have to build another wall in front of it completely to get the room dimension right. Heavier walls will help with resonance control so all's not lost.
This is a golden and rare opportunity. I recommend that you spend some of your budget on a consultation with a good acoustics firm or consultant. I have no stake in it, but I got a lot of good advice from ASC to tune the room I was working on, and I did not have the luxury of setting the dimensions, which is key. If I were you I would have them help me get the dimensions right and treat the surfaces. It is absolutely as important as the equipment you choose.