How do these room dimensions look????

I am about ready to start on a new listening room that will intail making my garage/studio larger. I am limited in length and width to 19x15. I am planning to have a ceiling height of 10 feet sloping to 8 feet. The only dimensions I can play with is the 10 foot height (I could go to 11 or 12 feet sloping to 8). I know there are some good minds out there in Agone land regarding these issues......... any thoughts would be greatly appreciated.
To keep things simple for future reference as there are TONS of different combo's that are out there, one should try to use dimensions that do not share a common divisible factor. If you use dimensions that share a common denominator, you'll have bigger peaks at the point of room resonance rather. For instance, using one dimension of 8 foot and another of 12 foot, these will both divide evenly by a factor of 2 or 4. This would produce multiple points of reinforcement at those intervals. As such, you now have bigger peaks at those points than you would if you would have used dimensions that did not make use of a common divisible factor.

With that in mind, using something like 8 foot and 11 foot would work out better for your ceiling than 8 x 10 ( divides by 2 ) or the previously mentioned example of 8 x 12. If at all possible, using a higher ceiling would be better i.e. 9 x 11, etc...

If you were to use 10' as a figure for part of your ceiling, that would create a node in conjunction with the 15' dimension that you brought up. These are both divisible by 5, so i would avoid using that height anywhere in the room.

By staggering the room dimensions and avoiding evenly divisible figures, the room will not be quite as peaky. Rather than having several big peaks, which are harder to deal with, you'll have several smaller peaks that are spread out over a wider frequency range. Just keep in mind that ALL rooms are going to have multiple nodes ( points of reinforcement and cancellation ) in them no matter what you do, but starting off with something that isn't "running away" at any given frequency(s) puts you way ahead of the game.

Pick up some books on room acoustics by F. Alton Everest. After all, if you are starting from scratch, it is best to incorporate design principles NOW rather than later. Much cheaper and far more effective. Even with all of the reading that you do on the subject, contacting a good acoustician like Rives and having them help you out will will probably put you dollars ahead in the long run even though you might have to pay for that help initially. Sean
As Sean said you want to avaid piling up axial modes and use room dimensions that achieve as uniform of a distribution as is possible. There are a number of recommended proportions by various authorities that have been found to be favorable for Height/Width/Length:

Boner:H 1: W 1.26 :L 1.59

Sepmeyer: H 1: W 1.28 : L 1.54

Louden H 1 : W 1.4 : L 1.9

Volkmann H 1 : W 1.5 : L 2.5

Play with those proportions using your dimensions.
They are all fully discussed in the Master Handbook of Acoustics by F. Alton Everest, pgs 275-280. There are many other issues too and the Everest book is worthwhile for general theory and only a few bucks. It is very readable.

I remain
Your dimensions are fixed, well OK but you can stud out and install the dry wall with a 13 degree change from the front of the room to the back of the room. Do the trig, set up a chalk line and install your base plate and studs on the chalk line. With a sloped ceiling and walls with a taper front to back you will end up with almost no parallel surfaces, (front to back wall) and the front and back can be easily broken up with treatments.