whittling away at what wont work, Im looking towards what known ratios that work would be. I keep thinking 6 to 5? Is there a resoure you might point me towards?
Room ratios is whole major subject in studio design. Overblown, in my opinion, but important nevertheless. The problem is that some people tend to think that if only they can get their ratios and dimensions "perfect", the studio acoustics will also be perfect, and they'll have the best studio on the planet. That simply isn't true. Ratios are important, to a certain extent, but they are not the single most aspect of studio design that some people make them out to be. You can have a fantastic studio that is based on a not-so-good ratio, and conversely you can have a terrible studio that is based on Sepmeyer's first ratio (arguably the best there is).
Bluntly speaking, there is no such thing as a "perfect" ratio for a control room. There are merely good ones and bad ones, and that's it.
It works like this: The walls of your studio create natural resonances in the air space between them. 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 the 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 mode.
Conversely, if you have a mode (standing wave) that forms at a specific frequency, then changing to 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 nuls 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 lost. 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 payed 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".
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.
So let's go back to thinking about those room modes (also called "eigenmodes" sometimes): remember I said that they occur are 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 a mode for D, a different mode for E 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. Rember 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!
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, E0 on the organ keyboard), the wavelength is over 56 feet! So your room would have to be 56 feet 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, 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. Obviously, most home studios do not have modes at 20 Hz, because there's no way you can fit a 30 foot control room into most houses!
So clearly, the longest available distance defines your lowest mode. If we take your own proposed dimensions as an example (since it is pretty typical of home studio sizes), your longest available dimension would be 13 feet, so the lowest mode you could possibly have in your room, would be at about 43 Hz. That's an "F1" on your bass guitar.
The next highest mode that your room could support is the one related to the next dimension of the room: In your case, that would be width, at 10 feet. 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 will likely end up at about 8 feet, 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 the keyboard), you get huge massive ringing at F, A# and C#, while all the other notes sound normal. 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 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. 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.
So what can we do about that?
All we can do is to choose a ratio that has the modes spaced 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, 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 by 20 feet wide by 30 feet long 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.
Back to your original 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: 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, but not actually that simple.)
So, there are no perfect ratios, only good ratios and bad ratios.
It is impossible to have a "perfect" ratio, simply because that would require enough modes to have one 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 by moving the walls. 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, but were 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, 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 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.
So how do you kill a mode? You can't. But you
CAN prevent 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!
You do that with "bass trapping". You use strategically placed acoustic treatment devices in the room to absorb the ringing of the mode, so that 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.
And that is the secret to making a control room good in the low end! Damp the hell out of the low end, so modes cannot appear. 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). 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 velocity node in two or more corners, so by treating the corners, you are guaranteed of hitting all the modes.
OK, I said I was going to get back to your question, but I didn't:
What is the best ratio?
As I said, there is no single "best", 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 only mentioned are 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 two walls plus 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.
Here's my two favorites:
http://www.bobgolds.com/Mode/RoomModes.htm
http://amroc.andymel.eu/
In both cases, just plug in your room dimensions and let it do all the hard work for you. Both of them show a lot of additional information, which is very useful.
A the start, I did say that modes aren't that important, despite all the hype they get: I'm serious about that too. 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 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.
I hope that helps!
- Stuart -
You missed a couple... see above link... 
Glad to help!