Wow! Talk about LOTS of questions!
The top view of the outer shell can be seen in this wonderful drawing
First things first: Please post all your photos to the forum itself, instead of linking to off-site photos. It's one of the forum rules, actually... The reason is simply that off-site linked photos normally disappear after a while, because the linked site dies, gets move, goes away, changes structure, expires, etc. So people trying to follow your thread in the future won't be able to see what we are talking about, and it won't be any use to them.
4. CURRENT SETUP - After a lot of experimenting / repositioning, I settled with the speakers (Adam S3A) close to the FW, vertical, on top of the console desk. Adam Sub10 in the center, almost touching the wall.
There's some things right about that setup, and some wrong. One of the "wrong" parts is: " on top of the console desk". That will cause comb filtering and "roughness" in the mid range, artifacts in the lows and low-mids, as well as early reflections from the desk surface, plus possible vibration and early-early sound arriving at our ears
before the direct sound from the speakers themselves. Another issue us the "Adam Sub10 in the center". It is usually better to have the sub offset to the left or right, not on the center line, for many reasons. Also, the mix position seems to be too close to the front wall.
5. THE RESULTS are these:
I can't tell much from just those graphs. You are only showing a very small part of the spectrum there, seemingly with too much smoothing, and only for one single speaker, or for only both speakers at once (not clear from the graphs or the explanations). I would need to see the actual MDAT file,
You are also doing your tests way too loud (over 110 dB ?

).... either that, or you did not calibrate REW correctly.
I would suggest that you should first calibrate REW properly, using a hand-held sound level meter, at a level of 76 dBC on each of your three speakers separately, so that you will automatically get 86 dBC with all of them (in the low end). Do a full set of measurements like that, as follows
Left alone
Right alone
Sub alone
Left + sub
Right + sub
Left + Right
Left + Right + Sub
Each of those tests should be run full-spectrum, starting at 15 Hz and up to 22 kHz.
Upload the resulting MDAT file to Dropbox, and post the link (the file will be pretty big)
I think the results are quite good, except for the obviously longer decay below 50 Hz. I can live with that for now.
So you never plan to mix bass guitar in your room? No keyboards either? No large kicks tuned low? No EFX?
My main issue is a "FRAGILE" SWEET SPOT, and the main culprit is the RIGHT SPEAKER. ----- The left speaker is much more stable.
I have no idea what those graphs show. The graphs don't even line up! They use different scales. There's no indication of how anything was set up there at all. No use, I'm afraid.
things "fall apart" quite easily if I change some parameters
What "parameters"?
Reminder - the measurements were done with only the "shell" of the desk. If I put the wooden TOP SURFACE on the desk itself, everything goes crazy in terms of the FR. T
Not surprising. That's exactly what I would expect from such a setup. You should first of all set up your speaker / mix position geometry correctly, then run the full set of REW tests, as above. Only then can you start thinking about what type of desk to use, how big to make it, what angles to use, what type of treatment / were to put it, etc. Right now you are doing things backwards: Starting with a desk and trying to make the speakers work with it. That ain't gonna work!
This is because the sub helps, and I guess this positive effect is lessened when the sub is "closed off".
Or more likely because the sub is in the wrong place....
I have measurements of all of this, but I don't want to bombard you with 100 graphs
I don't need 1 hundred!

Just the set of seven, as above. And I don't need the graphs, either! I need the actual MDAT file.
Also, this dip does change a bit if I move the speaker, so I guess it's at least in part SBIR.
Not necessarily. The dip might not be "changing" at all: you might merely be looking at a different modal situation. There's no way to tell from a couple of FR graphs...
Also, any other speakers (not connected to the sub) exhibit these SBIRs even more, my sweet spot is fairly narrow, etc...
A sure sign that there is a problem with the geometry! First, set up the geometry correctly, and let's see how the response looks for that. Then we can worry about fine tuning that geometry. And only THEN can you think about what type of desk to build, and how to treat the room. See above.
The source of the 100 Hz issue is really hard for me to figure out
Probably floor bounce,or ceiling bounce. Typical of most small studios, or studios with geometry setup issues, or incorrect initial treatment. It might be SBIR, but there's no way to tell from a couple of FR graphs at the wrong resolution, with unknown calibration.
Maybe I'm going crazy, but it seems to me that adding absorption makes it worse, not better
Adding absorption WHERE makes WHAT worse? That's a big clue....
the discrepancy between the two speakers are most probably caused by the L R wall asymmetry.

Whoa!!!! Your WALLS are not symmetric???? Then you have MUCH bigger problems that speaker layout! You will need to take a few stpes back in construction here, and get your room symmetrical first. You cannot fix serious room asymmetry by fiddling with speaker positions. That's like trying to stop a speeding freight train by putting flower petals on the track...
But, considering the offending frequency is fairly high (100 Hz), I'm hoping there is a way to find it and kill it
You have a rather strange definition of "fairly high"!

In reality, 100 Hz, is right in the middle of the LOW frequency end of the spectrum. Its somewhere between where kicks drums / floor toms live and where snares / high rack toms live. It's right in the middle of the bass guitar range, and the low end of the keyboard. It's way below most female vocals, and the majority of male vocals: you can apply a low shelving filter below 100 Hz to most vocal tracks without noticing ane real difference at all. So yeah, it's low, for sure. Definitely not "fairly high"! And DEFINITLEY not easy to treat: the wavelength is around 3.5 meters...
1. Maybe someone more knowledgeable and with more experience than me could recognize this pattern, and pinpoint the possible "culprit"?
Yup. Geometry. Start with the room geometry: the front half of your room MUST by symmetrical. You have no choice. If it is not symmetrical, the you can't get a clean, accurate sound stage, You can't get a properly centered, correctly balanced stereo image. There will be no "phantom center". So first of all, get your room geometry right, what ever it takes. Then when that is right, set up your speakers and mix position in the theoretically optimum positions (which is NOT the usual-but-totally-wrong "equilateral triangle" you see all over the internet....), and measure like that. Then adjust / tweak the position, to perfection (using REW, NOT your ears). The start thinking about how to fit furniture around that arrangement, without interfering with it.
2. If the above is impossible, could you please advise me how to approach the testing?
See above: Fix the room geometry, set up the speaker/mix position geometry, calibrate REW correctly, then do the set of seven tests.
I know that "make the R and L walls symmetrical" is the best advice here, but this cannot be done so easily now.
Then I have some really bad news for you....: Your studio also cannot be made usable so easily....
You're the first acoustics person that described my room as small, I'm offended
It's only 5 m long. The wavelength for a 20 Hz tone is 17.2m. So yeah, as far as sound waves are concerned, it is small...

(Even worse, the height is only 4m! ...

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I followed the advice that for thicker traps lower GFR is advisable...
Not sure where you got that advice from ! Lower GFR is good for deep bass traps, but thickness isn't relate to GFR (well, it is for impedance, but that's a different story): The point is, you don't need to chose a lower GFR just because you want to make your trap thick. Rather, chose the GFR that is needed for the application, then make it thick enough to do the job.
MY SCs are 1,5 meters at their thickest. This is what the online calcs say
What "online calculators"? Did you check the impedance, or only the normal coefficient absorption?
If my listening position is at around 1,5 from the FW
... then it would be too close to the front wall!

That would put it roughly in the quarter wave peak for all first order modes, and the null for all second order modes...
Like I said, FIRST get your room geometry correct THEN worry about furniture and treatment.
Same as above, I'm a bit puzzled as you're the first person with this opinion. If my listening position is at around 1,5 from the FW, this puts me around 3,4 m from the diffuser. There and back, 6,8m => around 20 ms. I was under the impression this was OK.
Ask D'Antonio and Cox what they think about that!

If you really could get your head 3.4m from the diffuser, that would meet the first condition yes (minimum 3m), but firstly you can't, and secondly you'd then be limited to tuning your diffuser to a range where the wavelength of the lowest scattering frequency (which is one octave lower than the actual diffusion cut-off frequency) allows for at least three full wavelength before the wave reaches your head, or better still, 7 full wavelengths. ....
But that's all about the mix position: what about the couch at the back of the room? How far away will that be form the diffuser? Cna you get that one 3m way from the diffuser as well?
What's worrying me more is that the diffuser on the BW will reflect low frequencies => more SBIR.
Not if you build it right / locate it right...
The "mirror trick" makes sense for high frequencies, right?
Nope. All frequencies. They will all "bounce" off the wall when they hit it. Higher frequencies are more ray-like, and lower frequencies more "sphere-like", true, but there's no hard dividing line.
For the lows this absorption is not really an obstacle.
Really? Why?
It will help, but lows will still bend around it. Is this correct?
Nope! As long as the panels are reasonably large, and reasonable thick, with reasonably good, suitable absorption, then even there's pretty decent absorption down to low frequencies, especially for non-normally incident sound.
I'm thinking about my wonderful 100 Hz problem.
But I though you said that was "fairly high"?
But no, you won't be fixing that with absorption on your first reflection points. Because that's not what it is!
1. Why are resonant cavities bad (in my example - double windows and the ceiling), and then we go and make Helmholtz resonators and panel traps, which are basically resonant cavities / panels. Is the dampening the crucial factor here? Critical dampening vs. underdampening etc...
I'm not sure who "we" are in your example, but don't include me in that! I very seldom do Helmholtz resonators or panel traps... For several reasons.
Bu anyway, to answer your question: For those of "we" who do use them, Helmholtz resonators and panel traps are carefully designed, carefully tuned, and carefully located in the room to provide optimal treatment for a specific, well-identified issues, and they are correctly damped to absorb the problem optimally. Your windows and ceiling are randomly tuned, randomly located, not designed at all, and not damped... who knows WHAT they might be doing! For all you know, they could be amplifying a particular frequency that isn't even a problem, while NOT treating the frequencies that really are problems...
2. Can an "underdamped" oscillator make the resonant frequency LOUDER in a room, or just prolong its decay?
Both! very definitely. Have you ever played up and down the scale on a bass guitar, in an untreated room? Notice how some of the notes really BOOOOOM out, and ring long, while others don't? Those are notes that coincide with resonant frequencies in the room (likely modes). The exact same thing happens on a smaller scale with with any undamped resonant device. That's why many acoustical instruments have resonant cavities inside them, with ports to the outside world. If you take the rear shell of an acoustic guitar, it goes real quiet.... because there undamped resonant cavity that was amplifying the sound, is gone. The same happens if you stuff the cavity with fiberglass insulation.
Please ignore these questions if you don't feel extremely altruistic
Tonight, you got lucky! Now go out and buy a lottery ticket, before that luck runs out (and if you win, half is mine!

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- Stuart -