My god, Stuart, I can't thank you enough for for putting so much effort to explain the physics behind the facts,

You are very welcome! That's what we are here for...
Well, I wanted to avoid that, since I realized that it wouldn't be an acceptable method by you or the rest moderators.
Cell phone "sound level meters" are not accurate, and I sure wouldn't want to use one for actually room tuning, but for a rough initial calibration, they are OK. As long as you update the calibration later, with a decent "REAL" sound level meter, that's fine. The issues in a typical empty room will be way, way larger than the small difference between a cell-phone app and a real meter.
my main monitors are the hs5's, and though it's a wonderful speaker for its price, and very useful when mixing, it definitely isn't the flattest responding monitor in the planet.
Right!

At 5", it also doesn't go down very low. About 70Hz, I reckon. So it wouldn't be a lot of use for tracking or mixing instruments with a lot of bass content (drums, bass, electric guitar, keyboards, etc.)
This line confused me a bit, because if GFR is proportional to the air flow and inversely proportional to the pressure applied, then it means that when its rate is high, the gas (air) penetrates more easily. To my small mind this comes in contrary with the term acoustic impedance which is the opposite (to my judgement). Obviously I am mistaking something here, could you please help me with this? To put it in a simple question:
OK, I didn't state that very clearly, and perhaps gave you the wrong impression: Gas flow resistivity is defined as the change in pressure (or pressure drop, if you prefer) across the sample, divided by the flow rate. It's the same as electrical resistance basically: The pressure drop is equivalent to the voltage drop, and the flow rate is equivalent to the current:
R = Δp / qv
where:
Δp = air pressure difference (pascals)
qv = volumetric airflow rate (m3/s)
For an electrical circuit that is the same as classic Ohm0s law: R = V/I There's a lot of parallels between electronics and acoustics.
This was the problem for me when I browsed the thesis (link) Ι posted in my first post, which claims that when density raises, then absorption lowers.
Which is true, for a certain range of values which is different for each material. Don't get confused with resistance and impedance, though; if you know electronics, you know that they are not the same thing...
Ok, now that starts to clear things in my mind quite a bit. I made a graph to show you the way I get it.
That's basically it, sort of, maybe...

I wish it were as clear-cut as a standard bell-curve, but it's a little more complex.... I'll get to that later.
Correct, I meant 0.08m, or 8 cm, or 80mm. Please forgive me because I am rushing sometimes when typing... ^_^

You and me both...
Well, if you notice in the sketch of my room, there is an ADAM sub7 subwoofer placed next to my PC tower. Truth is I barely even use it. If I remember correctly it goes as low as 35Hz, so I am not expecting my room to be allowing these large wavelengths to sound right, (or to even sound at all). Currently, if I was able to get a bit smooth response down to 100 Hz I would be quite happy. I am not expecting any miracles to happen.
If you treat the room correctly, it can sound very "right". However, do understand that the goal for a control room is not to make it sound "good"! It is to make it sound FLAT. And flat actually doesn't sound so good to many people... It sounds... welll... err... Flat! No hissing highs, no roaring lows, no exciting mids... just all things at the same level. In fact, if you put average Joe Public in a room with perfectly flat response, give him a graphic equalizer and tell him to make it sound "nice", you'd probably end up with the classic "smiley face" curve set on the EQ controls: Boosting the highs and lows, cutting the mids. Flat doesn't blow your socks of: But flat is what you need for accurate mixing. Flat allows you to hear what each instrument REALLY sounds like, and what your mix REALLY sounds like. It tells you the truth, whole truth, and nothing but the truth. I've had some people be a bit disappointment at first with their new rooms tuned flat, because it doesn't impress the hell out of anyone... until they start using the room, and suddenly appreciate that they can now hear things in their tracks and mixes that they never even knew were there. Then they "get it", and start loving "flat".
Actually, I don't normally tune rooms perfectly flat, because it's just a bit too lifeless (and part of the reason why true LEDE rooms are not liked, and no longer built by serious designers). Rather, I apply a "house curve" to the frequency response, which does put a slight lift in the bass (but still way less that "Joe Public" would do), then roll it off very gently from the mids all the way through the high end. There's a couple of curves that can be used here, but the point is the same: make it a little more interesting, a little more like a typical small domestic speaker would sound like.
So, back to your place: If you have a couple of decent mains and a good sub, you can get your room sounding quite decent, close enough to "flat with a house curve" that it can be very usable as a control room.
Don't short-change yourself on what can be done in your room! It won't be Studio Three or Blackbird, of course, but it doesn't have to be bad!
now that really makes me really concerned, because if I build the panels and the room sounds too dull, then I will have to take them apart to modify them,
Nope! Not if you build them right. Build them as a simple self-supporting frame filled with insulation, and test like that BEFORE you put the final finish fabric on. If you need to return some of the highs to the room, then add the plastic, perhaps in broad strips, or maybe even thin wood panels. Then when you have it right, THAT's when you put the final finish fabric on, to cover up all of the "ugly".
Just one more question, have you ever encountered any problem with REW in terms of frequency shifting of graphs? I set a range of, say 65 to 20000 hz and the plot shows from around 70 to 20000 hz.
It's probably not a frequency shift at all, but rather the way you are viewing the data. If you apply smoothing or filters, then you reduce the resolution, so REW cannot show you data lower than a certain point, because it AVERAGED that data into a smoother curve.
Besides: why are you only starting at 65 Hz? And why are you only ending at 20 kHz? Did you read the instructions on how to use REW to take measurements? I think you need to read this:
http://www.johnlsayers.com/phpBB2/viewt ... =3&t=21122 .
I measured at 75 dbspl.
Yup... you DEFINITELY need to read those instructions!
but I didn't want to stretch my speakers on this.
Ummmm if your studio mains can't sustain 80 dBC each, then there's a SERIOUS problem! Yamaha doesn't publish the SPL specs for the HS5's, but I'll bet they can push 100 dBC without sweating too much.
The same reason applies for choosing a range starting from 55hz and upward. I just don't want to end up with blown woofers in my hands, I hope you understand.
I think you are the one who is not understanding!

How would you blow the woofer on a speaker by sending it normal music frequencies? Have you ever listened to music on those that has a bass guitar? Or drums? Or keyboards? Or electric guitars? All of those put out substantial energy below 70 Hz.... If you didn't "blow" your speakers by listening to that music, why would you "blow" them now by letting REW do the exact same thing?
Made you are misunderstanding the specs of your speakers: When it says that the frequency response -3 dB at 74 Hz, or -10dB at 54 Hz, that does NOT mean that YOU have to turn the level down by 10 dB for tones under 54 Hz! It just means that when you play any sounds on those speakers, they will just produce all the 54 Hz tones at a level that is 10 dB lower than the rest of the tones they can produces, or for 74 Hz tones the level will be 3 dB lower. That's all it means. It does NOT mean that you will blow the speakers if you play music that has a bass guitar in it, that goes down to 35 Hz. Or keyboards with tones at 60 Hz. It just means that the sound level put out by the speaker for that part of the spectrum will be lower than for the mid-range of the spectrum.
Besides, as I mentioned previously, I am not expecting to be able to get lower frequencies playing smoothly in such a small room.

Why not? What does the size of the room have to do with the ability of your speakers to produce low frequency sound? There is no relationship. Can you hear low frequencies when you play music in your car? The interior of your car is FAR smaller than the interior of your room. Can you hear low frequencies when you listen to music in headphones? Sure you can! But the "room" between the headphone speakers and your ears is minute, compared to the size of your room. Can you hear bass guitar and drums when you listen on your iPhone ear-buds? Of course you can! Yet the room between the ear bud driver and your ear drum is miniscule: fractions of a cubic inch.
There is NO relationship at all between the size of a room, and the ability to produce and hear low frequency sounds. None at all.
You seem to be confusing the issue entirely here: Room acoustics is NOT about the ability to hear any frequency in your room! Rather, it is about using treatment in the room to deal with issues that would "color" the sound put out by your speakers, by adding extra stuff to it, or taking some things away from it. That's all. Your room, left to itself, will indeed color the sound: it will increase or decrease the levels of some frequencies, an it will increase or decrease the length of time that those frequencies tend to "bounce around the room" after the speaker stops playing them. Acoustic treatment is ONLY about that: getting those "coloration" things under control, so that you can hear exactly what comes out of the speaker, without it being changed by the room in any way.
The measurement file can be found here :
Unfortunately, those files are not much use, since you didn't follow the instructions. You ran the tests at a level that is ten times too low, and you cut off the frequency range that we need to see, so the data you provide does not show ANY of the modal activity of the room at all.
Think of it this way: You go to the doctor because you have a huge injury to your leg, and you tell him to fix it... but when he says that you need to roll up your trousers and take off the temporary bandage you wrapped around it, you refuse! You tell him "NO! I can't do that, because it might look bad, and it might hurt, and the bandage might get damaged...." Do you think the doctor is going to be able to do anything at all to fix your leg, if you won't even show him what is wrong with it?

Do you think an acoustician will be able to fix your room, if you refuse to even show us what is wrong with it?
You have a decent sub: Hook it up properly, connect your HS5's, set the sub cross over to about 90 Hz, and do the REW tests like that, as the instructions direct. In this case, do a set of SEVEN tests: S--, L--, R--, LR-, LS-, RS-, LRS- Where "L" = left speaker on, "R" = right speaker on, "S" = sub on.
In the case I won't be able to find this particular density product, should I go for 40 or 50 for these 1st reflection panels? (Probably it wouldn't make that much of a difference, but I thought I might ask before choosing.)
Either of those would be fine, but do realize that you are showing two charts with two entirely different products: one is fiberglass, the other is mineral wool...
I am thinking about 10cm thick insulation with a gap of equally 10cm.
For first reflection points, that would be fine. 10cm of OC-703 would be great.
As for the bass traps, I wasn't thinking about building any, but now I am reconsidering it, trying to find a way to accomplish that without attaching it on the corner walls. Do you think this could be possible?.
You WILL need bass traps in there: that goes without saying. I don't even need to see valid REW data to tell you that: It's a small room, so it will need bass trapping. However, you are probably already getting some bass trapping from the things in the room... that helps, but it likely doesn't go far enough.
Since you don't want anything attached to your walls, build a self-supporting wood frame and put the insulation in there. Search for information on how to make a "Superchunk" style bass trap using OC-703. That's a very effective bass trap.
how could I deal with that foundation column in the front right corner? Should I build the trap around it? Would such a trap still be effective?
Yes. And yes. Yes build around it, and yes it will work.
Also, I can't think of any way to build an effective trap over the dresser on the rear right corner. It's a narrow niche of 49cm x 58cm. Is there a point on building a trap in there?
Any trap is better than no trap! Fill that entire gap as best you can with insulation.
Here, there are products with roughly double density rates than the ones you proposed (mineralwool or fiberglass respectively) that have a significantly better absorption coefficient. I hope you are not getting me wrong, I don't doubt the validity of your proposals by no means ! I am aware - from the 3 years I've been around this great forum - that you have huge experience on these stuff , and most likely (if not definitely) there is something I am missing here, but I am only trying to understand why those denser products seem to be more effective in low mid range.
As I mentioned in the first post, it is a lot more complex than just plain density. There's the issue of the size of the fibers that make up the insulation panel, how closely they are packed, how "straight" or "crooked" the air path is through those fibers (technically know as "tortuosity"), how flexible the fibers are, how much they are compressed in manufacture, the binder used to hold them together, the type off facing on the panel, whether or not the fibers run mostly in a certain direction, or are arranged randomly, the direction that sound moves through the panel, etc. It's nowhere near as easy as just looking at density.
There's also the issue of how those numbers where derived, and what they actually mean: when you see that 703 has a coefficient of 1.24 at 500 Hz, that does NOT mean that it absorbs 124% of all sound at 500 Hz.! Clearly, that is not possible. You have to understand that the test method used to derive those numbers only considers the frontal area of the panel, not the edges, and there are a number of strange and wonderful acoustic things that happen around edges and corners, so the TOTAL absorption of the panel can, indeed, by higher than just the absorption that happens through the front face. Some people don't get this, even some people who should know better, and they either say that the numbers are wrong, invalid, irrelevant, no use, etc., or they try to tell you that the panel really does absorb more energy than you throw at it...

go figure!
As with most things in acoustics, if you want to get down to understanding exactl how things work, and exactly what the numbers mean, it's going to take a while and a bit of research on your part to get there. But if you just want to use the panels to fix the problems in your room, it really isn't necessary.
So, getting back to the point: Don't try to judge absorption characteristics of a product based only on density. As you can see form the graphs, the relationship is not linear, not constant, different for each type of insulation, and different for each manufacturer. If you use density alone, you'll be even more confused when you start looking at closed-cell foams, open-cell acoustic foam, melamine foam, and even metal foam....
Lastly, I am currently in the research on those plastic sheeting issue you mentioned. There is some info on the site, but if you think there is a particular topic that I shouldn't overlook in my research I would love you to cite it here.
There's a set of equations for foils, that gives you a very rough idea of what frequencies it will reflect, and which ones it will pass through:
F = 90 / m
F = The frequency at which the foil transmits 80% of the sound
m = The surface Mass of the foil in kg/m2
THEREFORE:
F*m=90
m=90/f
That defines the point where foil of any given surface density will be 20% reflective (80% transparent) to sound (allowing 80% of that frequency through to the other side, reflecting back 20%, or coefficient of reflection = 0.2). The curve rises to about 99% reflective above that (1% transparent), at about 6 dB/octave, and falls off to practically 0% reflective (99% transparent) below that, at the same rate.
However, once again, take that with a grain of salt. Different foils react differently, if you stretch it taught or leave it lose has a HUGE effect, leaving an air gap between that and the insulation (or not) has an effect, etc., etc. It's just a guideline to get you to the right general type of foil, then you can play around to fine-tune it to your needs, if you need to.
- Stuart -