>>Can you recommend an article? I come across "acoustics" articles pretty often, but not ones that explain the hard math and how to do the calculations….
I'll look for something good. I learned what little I know from a Philips / DeForest "build your own speakers" book about 30 years ago which had a couple of really good chapters on room acoustics. I have not seen anything as comprehensive yet accessible since.
Here's what I remember. Speed of sound is about 1130 feet per second. For any given frequency, the wavelength is <speed of sound> / <frequency>. If the round-trip distance between the walls is 1 wavelength, or a multiple, you get a peak. If the round trip distance between the walls is 1/2 wavelength, or 3/2, or 5/2 etc..., you get a null (valley).
Let's look at your 13' dimension, or 26' round trip bouncing back and forth between the walls. One wavelength round trip gives you a peak -- 1130/26 is 43 Hz (43 hz signal has a 26 foot wavelength), so you should expect peaks at 43, 86, 129, 172 etc.
One-half wavelength (3/2, 5/2 etc..) gives you a null. If 26 feet is a half wavelength, then 52 feet is a full wavelength, corresponding to 22 hz. You should get nulls at 22 (1/2 wavelength), 66 (3/2), 110 (5/2), 154 (7/2).
OK, let's look at the chart. Yep, peaks around 43 and 86, and a hole around 66 Hz. Things rarely work out so cleanly, unless you have a square room
We need to do the same calculations for the 8.5 foot dimension but the 13 foot dimension will dominate since your room is square. The same concept can also be applied in a bunch of other ways as JohnK reminded me -- eg. if your speaker is 4 feet from a wall, or 8 feet round trip, you will get peaks at 141, 282, 423... and nulls at 70, 210, 350...
Even worse, if you have a reflection off wall, ceiling, floor then you're going to get peaks and nulls at frequencies where the difference in direct & reflecting path lengths is one or 1/2 wavelength.
Makes you want to just cower in the middle of the room with a big drink and good headphones, doesn't it ? The good news is that you only have to worry about a the lowest frequencies since at higher frequencies there are so many multiples that they all start to cancel each other out.
I have never played with bass traps, but from what reading I have done they sound like the best solution. Bass traps are basically custom-crafted big, flat boxes which absorb low frequencies to damp out the response peaks resulting from room modes. In theory they should be able to have some effect on the nulls (aka nodes) but nobody ever seems to talk about that.
Here's a first link to get you started. Google on "bass traps" and have fun. EQ will also work but with the drawbacks already mentioned -- you can't eq out a null, only a peak, and you need different eq for different locations in the room. Bass traps (in theory) treat the whole room.
http://www.realtraps.com/art_tuning.htm
Go get that drink now
