The speed of sound in air at sea level is about 1130 ft/sec.
Standing waves (between equivalent boundaries) only occur when (dimension = N/2 x wavelength) for any positive integer N.
And, of course, speed C = wavelength x frequency, so (wavelength = c / frequency)
Thus, dimension = N/2 x (c / frequency), and for the lowest frequency, N=1
Dimension = c / (2 x frequency)
which for c = 1130, c/2 = 565,
dimension = 565 / frequency, and frequency = 565 / dimension
Basic standing wave calculations can (and should) be applied to all room dimensions to identify the "normal" modes. Note that "normal" here is a geometric term meaning "perpendicular." Do a search for "Harman room mode calculator" and download the spreadsheet.
What you get looks like this:
Freq. | Adjacent mode spacing
37.7 | 12.0
51.4 | 13.7
70.6 | 19.3
75.3 | 4.7
77.0 | 1.7
102.7 | 25.7
113.0 | 10.3
128.4 | 15.4
141.3 | 12.8
150.7 | 9.4
154.1 | 3.4
179.8 | 25.7
188.3 | 8.6
205.5 | 17.1
"Freq." is a room mode, and there's a chart to help identify which dimensions are involved. "Adjacent Mode Spacing" is the "distance" in Hz to the next mode. Even spacing is the goal, but since wall placement's involved, it's not always adjsutable. Note that I have an issue at 70-75Hz, due to modes at 70.6, 75.3 and 77.0 - a 3rd harmonic in the longest dimension, 2nd harmonic across the room, and fundamental in the third - ceiling height.
All based on the formula frequency = 565 / dimension for the fundamental.
This is the theory. Practice will vary with the room construction and furnishings as well as dimensions.
- cinderblock walls reflect bass causing worse standing waves below grade than above
- normal above-grade construction using sticks and sheetrock can be very good for bass resonances, mainly due to leakage.
- slab foundations and second stories are like cinderblock walls compared with a basement or attic
- soundproofing reduces leakage, making standing waves worse
- open doorways allow leakage, and modify room resonances, driving them lower
- windows are leaky, making drapes over windows an adjustable broad band-type absorber.
And in your case, complex room geometry (L-shape open space within complex rectangular basement, alcove for screen, dividing walls to other rooms, adjacent room volume, staircase reinforcement of one wall, etc.) makes anything more than very basic calculations of questionable predictive value. However, I hope you see that there are a lot of aspects of your room that will scramble the resonance pattern, and perhaps give you a uniformly dense mode spacing that makes large spaces sound better than small.
But I also suspect that something to absorb some of the fundamental resonances may be in order. It doens't take much to test, and frequencies below 100Hz are far less affected by furnishings than above, so you don't need to test in a finished room. But test data is the only way to characterize the problem so countermeasures are appropriate to the problem.
As to the need for this, read through some of the multi-sub threads and you may notice that folks love to throw subs at room mode issues... issues they could treat and be done if low bass treatment were easy in a finished room - it's not. Thankfully, your room isn't finished!