As to the modes, that's another story. You have to go through room ratios
Let's consider first what happens along the length of a room when the air inside is excited by sound from the loudspeakers. A room's resonant frequencies are determined by the distance between the room's wall. The farthest apart the walls are, the lower the resonant frequency. Specifically, the lowest resonant frequency called the fundamental resonance, occurs within the room's length equals the half wavelength of sound. Put another way, a resonant mode will occur when the sound's wavelength is twice the length of the room. Other resonant modes occur at twice this frequency, three times this frequency, and so on. Whenever the length of the room is a multiple of half of the sound wavelength, a resonant mode will occur.
Here's an example and how to determine your room resonant modes based on your room's length, width, and height. The formula is F1 = 1130/2L. F1 is the first resonant mode, 1130 is the speed of sound in air (in feet per second), and 2L is two times the room's length (in feet). If the room is 21' long, its first resonant mode (F1) will be 27Hz (1130/2 x 21).
We know that the next mode will occur when the wavelength equals the room's length, at 54Hz (2 x F1), then again at the next multiple of half a wavelength ( 1- 1/2 wavelengths) at 81Hz (3 x F1), again at 108Hz (4 x F1), and so forth. Again, it is only necessary to consider room modes up to 300Hz.
The room's height and width will also create their own resonant modes. If we have an 8' ceiling, the resonant modes will occur at 71Hz (1130/2x8), 141Hz , 212Hz, and so on. If the width is 13', the resonant modes modes will be at 43Hz (1130/ 2 x 13), 87Hz, 130Hz, 174Hz, 217Hz, 261Hz, etc. We end up with a chart that look like this:
Mode Length Width Height
21' 8' 13'
F1 27Hz 71Hz 43Hz
F2 54Hz 141Hz 87Hz
F3 81Hz 212Hz 130Hz
F4 108Hz 282Hz 174Hz
F5 135Hz 353Hz 217Hz
F6 162Hz 260Hz
F7 189Hz 304Hz
Interpreting the resonance modes; Let's say for room distance, L24', W16', H8'; Length mode (F3) at 72Hz, coincides with the second mode width (F2) 70Hz and the first height mode (F1) 71Hz, these combine modes, will pile-up creating a huge peak in the response at this frequency. This undesirable situation occurs because the room's length, width, and height are multiples of each other. Expect a thick, peaky, and very colored bass reproduction.
We can minimize the frequency-response peaks and dips caused by room resonance modes by choosing a room ( this isn't always possible unless you build a room from scratch, or convert a garage or basement into a listening/monitoring/studio room) with dimensional ratios that more evenly spread the resonant modes over the low-frequency band. This gives you a head start in getting great sound from your system.