Hi the Eugene, and welcome to the forum!
Adding to what Greg already said:
I want to build a small booth for tracking vocals mainly but also smaller solo instruments and amps too (not big enough for drum kit). The room will mainly be used for mixing and production of electronic music.
OK, so this is going to be a three-room studio: a control room, plus a vocal booth, plus an iso booth. Is that correct?
The rest of the shared warehouse is full of rehearsal rooms, other recording studios, (visual) art studios, photography studios and even furniture storage and design. Directly either side of me is a photography studio and furniture storage/design. The rehearsal rooms are the loudest obviously - but they have been designed and built well and are not too noisy.
How loud? You will need to measure that, since the most basic part of studio design commences with good isolation. So you will need a sound level meter (not expensive: maybe US$ 100 or so for a good one), set it ti "C" weighting and "Slow" response, then stand in your room while the other places are all making noise, and measure the level in your room. Walk around, and measure at several places. Then go back and measure again at some other time, when there is nobody else around, and it is really quiet. Then make a third measurement at any place you feel like, where you judge that it is very, very quiet: silent enough to be able to mix accurately, even on very soft, gentle tracks. Report those three measurements here, and we'll help you figure out how much isolation you need. Everything else in your entire studio build follows on from that point. The isolation need defines the largest possible size and probably also the shape of your rooms, so you do need to have that in place first.
and want to build ASAP.
I'm sure you do, but that would be a big, BIG mistake. This is not what you want to hear, I'm certain, but it is the plain, solid, harsh truth: you won't be able to build anything for many weeks, likely months. The single most important thing you will need to do (after figuring out your isolation number), is to spend the time to design your entire studio properly, in every single aspect, before you even buy a single 2x4, sheet of drywall, or bag of nails. You have to design it fully, completely, entirely, including the structural part, the layout, the geometry, the sight lines, the traffic paths, the positions of doors and windows, which way the doors open, what they might bump into when they do open, the locations of the speakers and the mix position and the client couch, the acoustic treatment in each room, the HVAC system, the electrical system, the sealing, and a thousand other things. If you aren't already experienced in construction, then you'll need to spend time learning how to lay out your framing, what size framing to use at each point, how to place king studs, jack studs, and cripple studs around doors and windows, where to put noggins, what load and deflection you want for your ceiling, what type of wood you need and how big it must be to safely span the distances across your rooms with the load you will be hanging from it, HVAC flow rates, flow velocities, static pressure, sensible heat load, latent heat load, BTU ratings, etc. etc. If you aren't already experienced with acoustics, you'll have to learn all about that too, involving things such as Mass Law, MSM equations, baffle step response, coefficients of absorption, coefficients of diffusion, edge diffraction, reflections at different frequencies, modal response, SBIR, power balance, and a thousand other things. Once you know all of that, then you can actually sit down and start designing the studio. We strongly recommend using the SketchUp design software, which you will also have to learn (if you don't already know it). And once the design is entirely complete, in all aspects, THEN you can call up your carpenter and get him started.
Building a studio is 90% design, 10% actual construction. If you look around on the forum, you'll find several threads with "horror stories" of people who started building their studios before they were designed properly, and then had to tear it down again and start over (or just give up in some cases).
Realistically, if you don't already know all of the above, then it will likely take you 3 to six months to learn it, then another 3 to 6 months to actually design the place. So if you want to do all of that yourself, plan on about a year before you'll be ready to build. If you decide to hire a designer to design the place for you, then still plan on about 3 to 6 months before you can start building, realistically.
I'm sure you did not want to hear that, but I imagine that the reason you came to the forum and posted your thread, asking for help, is because you trust us to give you good advice! So that's the very best advice I can give you: don't start building until you are ready, with a complete design in front of you.
I'm getting a sound meter from a friend in the next few days to test the noise.
Excellent! But you might want to get your own, as you will nee it regularly during the build, and afterwards, for room tuning. The cost of a good sound level meter is a miniscule tiny fraction of what the build is going to cost, so it's worth getting your own.
Obviously trying to do it as cheap as possible
Do your best to estimate what you think this will cost you, at the absolute maximum. Multiply that by a random number between 2 and 10. Add in a "fudge factor" of somewhere between 120% and 500%. Adjust by a safety margin of about 1.5 to 5.73. Open any newspaper to the financial pages, point at any number on that page randomly, and add that number to your total. Dived that by a small fraction between 0.2 and 0.4. Call your local Pizza Hut and ask for a quote of a thousand pizzas, and add that. Also call your local brewery and ask for a quote of a hundreds cases of their best beer. Add that too. Finally, add in another hundred bucks for the cost of the sound level meter, and that's it! You have your total real cost!
Simple!
OK, point being: building a studio is always going to cost more than you think. There's many aspects that you don't even realize you need to quote yet, and you wont' know until you get there. For example, you are going to use dozens of boxes of caulk to seal everything, and I'm sure you didn't consider that yet. HVAC is always a big expense (yes, you absolutely do need it). Heavy-duty door hinges, door seals, door closers can all add up. etc. etc. Not trying to scare you: just bringing a dose of reality to the table!
and not expecting 100% perfect results.
You should be! You are planning to spend many thousands of dollars here, so it would be wise to expect that it will get you the best possible results that fit the budget!
I want a booth which is isolated from outside noise
Implies lots of mass, implies heavy building materials, and the structure to hold it up, and a lot of sealing, and HVAC so the artists can stay alive and comfortable inside, and thick, heavy glass for the windows, and thick heavy doors, which in turn implies heavy duty hinges, and a heavy duty door closer, plus lighting, plus audio snake, video screen connection, Internet connection, electrical power, all of which must breach the isolation barrier without trashing your isolation....
and a control room that is relatively flat for mixing.
"flat" in what sense? Most people think of "flat frequency response" as being the most important goal to aim for in a control room, but they are wrong. It's important, yes, but flat time-domain response, and flat phase response are far, far more important. I can build you a room that has flat frequency response but sounds terrible and would be no use at all for mixing. And I can build you another room that has very much "un-flat" frequency response yet is really good for mixing. It's good to have flat frequency response if you can get it, but it's not the most important measurement.
If you want your room to be good for mixing, then it must meet the criteria and specifications for a "critical listening room", as laid out in chapters 7 and 8 of the ITU BS.1116-3 document. Here's a link to a room that meets and exceeds those specs:
http://www.johnlsayers.com/phpBB2/viewt ... =2&t=20471 And here's another,
http://www.johnlsayers.com/phpBB2/viewt ... =2&t=21368 . That one is in progress right now, in the process of final tuning. It won't be able to get quite as good as the other one, because of the small size of the room, but we'll get it close.
The room is 6.98m long x 3.77m wide.
That would be decent if it was just a control room, all by itself. As you'll see in BS.1116.3, the minimum recommended size for a control room is 20 m2 floor area: yours is 26m2, which would be nice for a control room. But putting a control room AND a vocal booth AND an iso booth in that space is cutting it very fine!
I'm hoping I can build 4 walls into the room with wood studs, double layer 16mm Fyrcheck Gyprock (green glue in-between) and insulation
Correct, but you are forgetting the ceiling! You need a new ceiling up there, on top of your walls, to complete the isolation shell. And your existing ceiling is going to need some major work to make it usable for good isolation.
Those walls will take up at least 15cm thick, so your final floor area would be (6.98 -0.3) x (3.77 - 0.3) = 6.68 x 3.47 = 23 m2 roughly. So you lost 3m2 to the isolation walls...
Then build the booth into one end of the room approx 1.2m deep x the full width of room
That won't work. You need to isolate the booth all by itself, not have it as part of the control room. If you try to have them together, your isolation is limited by Mass Law. Not very good. So you would need another 2 x 0.15 m to account for those isolation walls, meaning that your control room can be a maximum of 6.68 - 1.2 - 0.3 long. = 5.18 long x 3.47 wide = 17.97 m2. Borderline, and you don't yet have an iso booth!
For the ceiling I'm hoping to start at the 3m height at the edge of the vocal booth and follow the angle up of the existing roof for the 1.2m of the booth, then angle down to meet the other end at 3m.
It's possible, yes, but it complicates treatment considerably when you have a room that gets narrower towards the back, especially for bass frequencies.
I don't want to go soffit mounting speakers -
I though you said that you wanted the room to be as flat as possible for mixing? So why do you not want to do the single most important, most effective thing that will help to get your room flat?
make dimensions good so as to avoid as many standing waves/nodes as possible
That would be the exact WRONG thing to do, and is impossible anyway. This is a common misconception, so let me explain: Room ratios is a whole major subject in studio design. It works like this: The walls of your studio create natural resonances in the air space between them, inside the room. (This is totally different from the MSM resonance of the walls themselves: this is all about what happens INSIDE the ROOM, not what happens inside the walls. Two totally different things.)
So you have resonant waves inside the room. We call those "standing waves" or "room modes". Those "modes" (resonances) occur at very specific frequencies that are directly related to the distances between the walls. They are called "standing waves" because they appear to be stationary inside the room: they are not REALLY stationary, since the energy is still moving through the room. But the pressure peaks and nulls always fall at the exact same points in the room each time the wave energy passes, so the "wave" seems to be fixed, static, and unmoving inside the room. If you play a pure tone that happens to be at the exact frequency of one of the "modes", then you can physically walk around inside the room and experience the "standing" nature of the wave: you will hear that tone grossly exaggerated at some points in the room, greatly amplified, while at other points it will sound normal, and at yet other points it will practically disappear: you won't be able to hear it at all, or you hear it but greatly attenuated, very soft.
The peaks and nulls fall at different places in the room for different frequencies. So the spot in the room where one mode was deafening might turn out to be the null for a different node.
Conversely, if you have a mode (standing wave) that forms at a specific frequency, then playing at a slightly different frequency might show no mode at all: for example, if a tone of exactly 73 Hz creates a standing wave that is clearly identifiable as you walk around the room, with major nulls and peaks, then a tone of 76 Hz might show no modes at all: it sounds the same at all points in the room. Because there are no natural resonances, no "room modes" associated with that frequency.
That's the problem. A BIG problem.
Of course, you
don't want that to happen in a control room, because it implies that you would hear different things at different places in the room, for any give song! At some places in the room, some bass notes would be overwhelming, while at other places the same notes would be muted. As you can imagine, if you happen to have your mix position (your ears) located at such a point in the room, you'd never be able to mix anything well, as you would not be hearing what the music REALLY sounds like: you would be hearing the way the room "colors" that sound instead. As you subconsciously compensate for the room modes while you are mixing, you could end up with a song that sounds great in that room at the mix position: the best ever! But it would sound terrible when you played it at any other location, such as in your car, on your iPhone, in your house, on the radio, at a club, in a church, etc. Your mix would not "translate".
And you also don't want major modal issues in a tracking room, for similar reasons: As an instrument plays up and down the scale, some notes will sound louder than others, and will "ring" longer. The instrument won't sound even and balanced.
OK, so now I have painted the scary-ugly "modes are terrible monsters that eat your mixes" picture. Now lets look at that a bit more in depth, to get the
real picture, and understand why they look bad, but aren't so bad in reality.
So let's go back to thinking about those room modes (also called "eigenmodes" sometimes): remember I said that they occur at very specific frequencies, and they are very narrow? This implies that if you played an E on your bass guitar, it might trigger a massive modal resonance, but then you play either a D or an F and there is no mode, so they sound normal. Clearly, that's a bad situation. But what if there was a room mode at every single frequency? What if there was one mode for E, a different mode for D and yet another one for F? In that case, there would be no problem, since all notes would still sound the same! Each note would trigger its own mode, and things would be happy again. If there were modes for every single frequency on the spectrum, and they all sounded the same, then you could mix in there with no problems!
And that's exactly what happens at higher frequencies. Just not at low frequencies. Because of "wavelength"...
It works like this: remember I said that modes are related to the distance between walls? It's a very simple relationship. Remember I said the waves are "standing" because the peaks and nulls occur at the same spot in the room? In simple terms, for every frequency where a wave fits in exactly between two walls, then there will be a standing wave. And also for exactly
twice that frequency, since two wavelengths of that note will now fit. And the same for
three times that frequency, since three full waves will now fit in between the same walls. Etc. All the way up the scale.
So if you have a room mode at 98 Hz in your room, then you will also have modes at 196 Hz (double), 294 (triple), 392 (x4), 490(x5), 588(x6), 686(x7) etc., all the way up. If the very next mode in your room happened to be at 131 Hz, then there would also be modes at 262 Hz(x2), 393(x3), 524(x4), 655(x5), etc.
That's terrible, right? There must be
thousands of modes at higher frequencies!!! That must be awful!
Actually, no. That's a GOOD thing. You
WANT lots of modes, for the reasons I gave above: If you have many modes for each note on the scale, then the room sounds the same for ALL notes, which is what you want. It's
good, not bad.
But now let's use a bit of math and common sense here, to see what the real problem is.
If your room has a mode at 98Hz, and the next mode is at 131 Hz, that's a difference of 32%! 98 Hz is a "G2". So you have a mode for "G2". but your very next mode is a "C3" at 131Hz. That's five notes higher on the scale: your modes completely skip over G2#, A2, A2#, and B2. No modes for them! So those four notes in the middle sound perfectly normal in your room, but the G2 and C3 are loud and long.
However, move up a couple of octaves: ...
There's a harmonic of your 98Hz mode at 588 Hz, and there's a harmonic of your 131 Hz mode at 524 Hz. 524 Hz is C5 on the musical scale, and 588 Hz is a D5. They are only two notes apart! Not five, as before.
Go up a bit more, and we have one mode at 655 and another at 686. 655 is an E5, and 686 is an F5. they are adjacent notes. Nothing in between! We have what we want: a mode for every note.
The further up you go, the closer the spacing is. In fact, as you move up the scale even higher, you find
several modes for each note. Wonderful!
So at high frequencies, there is no problem: plenty of modes to go around and keep the music sounding good.
The problem is at low frequencies, where the modes are few and far between.
The reason there are few modes at low frequencies is very simple: wavelengths are very long compared to the size of the room. At 20 Hz (the lower limit of the audible spectrum, and also E0 on the organ keyboard), the wavelength is over 56 feet (17m)! So your room would have to be 56 feet long (17 meters long) in order to have a mode for 20 Hz.
Actually, I've been simplifying a bit: it turns out that what matters is not the
full wave, but the
half wave: the full wave has to exactly fit into the "there and back" distance between the walls, so the distance between the walls needs to be
half of that: the half-wavelength. So to get a mode for 20 Hz, your room needs to be 56 / 2 = 28 feet long (8.5M) . Obviously, most home studios do not have modes at 20 Hz, because there's no way you can fit a 28 foot (eight meter) control room into most houses!
So clearly, the longest available distance defines your lowest mode. If we take a hypothetical dimensions as an example (typical of a very small home studio), and say the length of the control room is 13 feet (4m), the width is 10 feet (3m), and the height is 8 feet. (2.5M) So the lowest mode you could possibly have in that room, would be at about 43 Hz (fits into 13 feet or 4M perfectly). That's an "F1" on your bass guitar.
The next highest mode that you room could support is the one related to the next dimension of the room: In this case, that would be width, at 10 feet / 3M. That works out to 56.5 Hz. That's an "A1#" on your bass guitar. Five entire notes up the scale.
And your third major mode would be the one related to the height of the room, which is 8 feet /2.5M, and that works out to 71 Hz, or C2# on the bass guitar. Another four entire notes up the scale.
There are NO other fundamental modes in that room. So as you play every note going up the scale on your bass guitar (or keyboard), you get huge massive ringing at F, A# and C#, while all the other notes sound normal. As you play up the scale, it goes "tink.tink.tink.BOOOOM.tink.tink.tink.tink.BOOOOOM.tink.tink.tink.BOOOOOM.tink.tink...."
Not a happy picture.
There are harmonic modes of all those notes higher up the scale, sure. But in the low end, your modes are very few, and very far between.
So, what some people say is "If modes are bad, then we have to get rid of them". Wrong! What you need is MORE modes, not less. Ideally, you need a couple of modes at every single possible note on the scale, such that all notes sound the same in your room. In other words, the reverberant field would be smooth and even. Modes would be very close together, and evenly spread.
So trying to "get rid of modes" is a
bad idea. And even if it were a good idea, it would still be impossible! Because modes are related to walls, the only way to get rid of modes is with a bulldozer! Knock down the walls...
That's a drastic solution, but obviously the only way to get a control room that has no modes at all, is to have no walls! Go mix in the middle of a big empty field, sitting on top of a 56 foot (17 M) ladder, and you'll have no modes to worry about....
Since that isn't feasible, we have to learn to live with modes.
Or rather, we have to learn to live with the LACK of modes in the low end. As I said, the problem is not that we have too many modes, but rather that we don't have enough of them in the low frequencies.
Obviously, for any give room there is a point on the spectrum where there are "enough" modes. Above that point, there are several modes per note, but below it there are not.
There's a mathematical method for determining where that point is: a scientist called Schroeder figured it out, years ago, so it is now known as the Schroeder frequency for the room. Above the Schroeder frequency for a room, modes are not a problem, because there are are lots of them spaced very close together. Below the Schroeder frequency, there's a problem: the modes are spaced far apart, and unevenly. (The Schroeder frequency is a bit more complex than just that, since it also considers treatment, but this gives you an idea...)
So what can we do about that?
All we can do is to choose a "room ratio" that has the modes spaced out sort of evenly, and NOT choose a ratio where the modes are bunched up together. For example, if your room is 10 feet long and 10 feet wide and 10 feet high (3m x 3m x 3m), then
all of the modes will occur at the exact same frequency: 56.5 Hz. So the resonance when you play an A1 on the bass, or cello, or hit an A1 on the keyboard, will by tripled! It will be three times louder. The nulls will be three times deeper. That's a bad situation, so don't ever choose room dimensions that are the same as each other.
You get the same problem for dimensions that are multiples of each other: a room 10 feet high (3m) by 20 feet wide (6m) by 30 feet long (9m) is also terrible. All of the second harmonics of 10 feet will line up with the 20 foot modes, and all of the third harmonics will line up with the 30 foot modes, so you get the same "multiplied" effect. Bad.
In other words, you want a room where the dimensions are mathematically different from each other, with no simple relationship to each other.
That brings up the obvious question: What ratio is best?
Answer: there isn't one!
Over the years, many scientists have tested many ratios, both mathematically and also in the real world, and come up with some that are really good. The ratios they found are named after them: Sepmeyer, Louden, Boner, Volkmann, etc. Then along came a guy called Bolt, who drew a graph showing all possible ratios, and he highlighted the good ones found by all the other guys, and predicted by mathematical equations, plus a few of his own: If you plot your own room ratio on that graph, and it falls inside the "Bolt area", then likely it is a good one, and if it falls outside the "Bolt area", then likely it is a bad one. Sort of.
So, there are no perfect ratios, only good ratios and bad ratios.
It is impossible to have a "perfect" ratio in a small room, simply because that would require enough modes to have one mode for every note on the musical scale, but that's the entire problem with small rooms! There just are not enough modes in the low end. So you can choose a ratio that spreads them a bit more this way or a bit more that way, but all you are doing is re-arranging deck chairs on the Titanic, in pleasant-looking patterns. The problem is not the location of the deck chairs; the problem is that your boat is sunk!: Likewise for your studio: the problem is not the locations of the modes: the problem is that your room is sunk. No matter what you do with the dimensions, you
cannot put a mode at every note, unless you make the room bigger. It is physically impossible.
But that does not mean that your room will be bad. That's the common perception, and it is dead wrong.
All of this leads to the question you didn't ask yet, but are probably heading for: What can I do about it?
Here's the thing: Modes are only a problem if they "ring". The wave is only a problem if the energy builds up and up and up, with each passing cycle, until it is screaming, and then the "built up" energy carries on singing away, even after the original note stops. That's the problem. If you stop playing the A1 on your guitar, and the room keeps on playing an A1 for a couple of seconds, because it "stored" the resonant energy and is now releasing it, then that's a BIG problem! The room is playing tunes that never were in the original music!
If a mode doesn't ring like that, then it is no longer a major issue. (It is still an issue for other reasons, just not a major one....)
So how do you stop a mode? You can't stop it from
being there. But you
CAN stop it from "ringing". You can "damp" the resonance sufficiently that the mode dies away fast, and does not ring. You remove the resonant energy and convert it into heat: no more problem! In other words, it's not good if you own a large angry dog that barks all the time and bights your visitors, but it's fine to own a large angry dog with a muzzle on his mouth, so he cannot bark and cannot bight!
You do that with "bass trapping". A bass trap is like the dog muzzle. It doesn't get rid of the problem, but it does keep it under control. You use strategically placed acoustic treatment devices inside the room that absorb the ringing of the mode, then it cannot ring. There are several ways to do that, with different strategies, but the good news is that in most rooms it is possible to get significant damping on the modes, so that they don't ring badly, and don't cause problems. Note that bass trapping does not absorb the
mode: it just absorbs the
ringing. Some people don't understand this, and think that the bass trapping makes the modes go away: it doesn't. All it does is to damp them. The modes are still there, and still affect the room acoustics in other ways, but with good damping, at least they don't "ring" any more.
And that is the secret to making a control room good in the low end! Choose a good ratio to keep the modes spread around evenly, then damp the hell out of the low end, so modes cannot ring. It's that simple.
The smaller the room, the more treatment you need. And since those waves are huge (many feet long), you need huge bass trapping (many feet long/wide/high/deep). It takes up lots of space, and the best place for it is in the corners of the room, because that's where all modes terminate. If you want to find a mode in your room, go look for it in the corner: it will be there. All modes have a pressure node in two or more corners, so by treating the corners, you are guaranteed of hitting all the modes.
As I said, there is no single "best" ratio, but there are good ones. You can use a "Room Mode Calculator" to help you figure out which "good ones" are within reach of the possible area you have available, then choose the closest good one, and go with that. And stay away from the bad ones.
Arguably, Sepmeyer's first ratio is the "best", since it can have the smoothest distribution of modes... but only if the room is already within a certain size range. Other ratios might be more suitable if your room has a different set of possible dimensions. So there is no "best".
But that's not the entire story: So far, all the modes I have mentioned are only related to two walls across the room, opposite from each other. I mentioned modes that form along the length axis of the room (between the front and back wall), others that form along the width axis (between left and right walls), and others that form on the height axis (between floor and ceiling): Those are the easiest ones to understand, because they "make sense" in your head when you think about them. Those are called "axial modes", because they form along the major axes of the room: length axis, width axis, height axis.
However, there are also other modes that can form between
four surfaces, instead of just two. For example, there are modes that can bounce around between all four walls, or between the front and back walls as well as the ceiling and floor: those are called "tangential modes". And there are other modes that can form between all
six surfaces at once: they involve all four walls plus the ceiling and the floor. Those are called "oblique modes".
The complete set of modes in your room consists of the axial modes, plus the tangential modes, plus the oblique modes.
That's what a good room mode calculator (a.k.a. "room ratio calculator") will show you. There are bad calculators that only show you the axial modes, which is pretty pointless, and the good ones show you all three types.
Use one of these Room Ratio calculators to figure out the best dimensions for your room:
http://www.bobgolds.com/Mode/RoomModes.htm
http://amroc.andymel.eu/
Both of those are very good, and will help you to decide how best to build your room. They give you tons of information that is really useful to help figure out the best dimensions.
However, modes aren't that important, despite all the hype they get: Modes are one aspect of room design, but there are many more. It's wise to choose a ratio that is close to one of the good ones, or inside the Bolt area, but you do NOT need to go nuts about it! There's no need to nudge things around by millimeters or smalls fractions of an inch, hoping to get a "better" ratio. Just stay away from the bad ones, get close to a good one, and you are done. End of story.
Sorry about the long rant, but it's VERY important to understand this, to see why it is terribly wrong to want to "get rid of modes".
- What will be the best size/place to build the vocal booth wall? Compromise between room nodes etc for both spaces?
I think you mean "modes" not "nodes", but for a vocal booth there's no need to worry about modes anyway: it is just too small to have any useful modes low down, so your only real option with a small booth is to treat the hell out of it, until it is very dead. When choosing the dimensions for a vocal booth, a much more important aspect than modes, is comfort! The booth has to be large enough that the talent does not feel "hemmed in", or claustrophobic, and has enough space to set up the mic, music stand, stool, and whatever else he/she might need, in a comfortable arrangement, and still be able to open the door without moving any of it. So the biggest factor in determining booth size, is ergonomics, not modal response. On the other hand, if making the booth bigger also makes the CR smaller, then you have a major paradox to resolve! Do you want the best possible CR dimensions, for the best possible acoustics in there? Or do you want a great space for the talent to perform, so they can give it there best in an inviting booth with good vibe? You can make the vocal room small and cramped, so the won't perform so well, in order to get a great control room. Or you can shrink the control room so the talent is happy, but mangling the CR acoustics, without any hope of being able to fix it...
- Which orientation would be better for my actual desk and setup? Facing the booth or facing the side wall?
Haas time. That's the key factor. You want the mix position far enough from the rear wall that all of your reflections from that rear wall fall outside the Haas time. For a large room, that's not a problem, and you can probably set up facing either way. But for a small room it IS a problem, and your only hope is to set up the room length-wise, with the speakers pointing down the longest axis. You want that rear wall as far behind you as you can get it, but you CANNOT push the desk forward to do that, since that would put your head in a bad spot, acoustically, and require a toe-in angle on the speakers that squishes up the sweet spot, and stretches your sound-stage too wide, and messes up your frequency response and time-domain response...
I'm hoping you are starting to see some of the hundreds of aspects that you have to take into account, if you really do want to get: " a control room that is relatively flat for mixing. The task of designing a studio means that you have to juggle all of these things as you go, optimizing and compromising, until you get the best possible balance between them. Not an easy task.
- What should I do with the floor in the booth? I've read around this site that concrete is fine generally - but should I be isolating the booth floor from the main floor?
Probably not necessary if you have a good slab-on-grade floor. You would only need to worry about that if you are getting major vibration in that slab, such as perhaps impact noise from a drum kit in the rehearsal space, or some type of machinery in the building (pump, HVAC motor, elevator, etc.)
One other major error you are showing in your rough sketch: Symmetry: Your control room MUST be symmetrical at the front. If not, then you won't get a lean, balanced stereo image. The left half of the room must be a mirror image of the right half, such that your left ear hears the exact same thing as your right ear.
Overall you have a decent sized space if all you want is a control room. Borderline if you want to add a vocal booth. And probably not much use if you also want an iso booth.
The other big issue is budget: as Greg mentioned, your budget isn't realistic. You have 25 m2 (rounded) and 5k. You are saying that you can spend $200 per square meter: that isn't realistic. Quote the cost per square meter of of 50m2 drywall, joists to hold it up while spanning 3.5m, 25m2 laminate flooring, 25m2 underlay, nails, and 25m2 insulation 15cm thick, and you'll see that you'd be eating up a large chunk of that just from having a ceiling and floor covering that size, without any walls, doors, windows, electrical, treatment, sealing or HVAC. HVAC alone will eat up a third to a half of your entire budget. I'd suggest that you need to re-think your budget. What you want to do is not going to happen on that budget. Sorry.
- Stuart -