Kpgushue wrote:Looks like its going to be a fun little room. My question is, is it possible to plot out a predictive frequency response curve for the full audio spectrum?
That's a good question! The answer is yes, it is possible... but actually it isn't really necessary. The mid and high frequencies won't be nearly as bad as the lows, in terms of frequency response. It's only the low end, with all the modal stuff, SBIR, and things like that, where the major issues are.
This is all related to something called the "Schroeder frequency". I'll go into that a little, but before I do, I should point out that the "Schroeder frequency" isn't really a valid concept in a small room, because in order to have a true Schroeder frequency you would also need a true diffuse sound field in the room, which cannot happen in a small room for complex reasons: so, in the strictest technical sense, "Schroeder frequency" isn't the right term here... but people still use it anyway! It would be more correct to call it the "transition zone".
OK, so now that you know it isn't valid, but it's there anyway, what exactly is it?
In simple terms, the "Schroeder frequency" marks the spot on the audio spectrum where the dominant type of acoustic response changes from modal, to diffuse. Once again, there isn't really a diffuse field in a small room, in the strict technical sense: that can only happen in a large room. But here too people use the term wrongly all the time... In simple terms, a diffuse sound field is one where the ambient sound of the room is equally likely to come at you from an direction, regardless of where you stand in the room. Or in other words, the ambient sound is all around you, equal in all directions and at all locations, with no variation. By "ambient sound", I mean the sound that does not come directly from the speakers: it's the sound that did originally come from the speakers, but then it hit the walls, floor, ceiling, furniture, people, etc., bounced around all over the place, bounce after bounce, getting scattered with each additional bounce, and it did that many times over, so that it is now moving pretty much at random... and therefore it seems to come from all around you, not from any specific direction. It's more complex than that, though, in the strict technical sense, but that's the basic idea.
So the Schroeder frequency tells you what the lowest frequency is where the sound field is "diffuse". Above Schroeder, its smooth and gentle (sort of...), below Schroeder, it's a mess! Above Schroeder, the frequency response is a wiggly line that doesn't stray too far up or down from the median. Below Schroeder, it looks like the mountains of the moon, blended with the Grand Canyon!
But WHY?
That's actually not too hard to understand either! It's all about modes... This is a little long, but important if you want to understand what Schroeder is really about, and why it isn't necessary to worry about the overall frequency response above the Schroeder frequency for a room. So here goes! I wrote this a while back, somewhere else, so I'm just doing a "cut and paste" job here, with some editing, but it saves me typing the same thing all over again!
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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 within 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 room boundaries (walls, floor, ceiling). 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.
However, 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 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 given 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 in bandwidth? 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 after that one, 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. In simple terms: "Many modes close together on the spectrum" = good. "Just a few modes, far apart" = bad.
But now let's use a bit of music theory and 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), let's 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.
Sure, there are harmonic modes of all those notes higher up the scale. 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. And this is where Mr. Schroeder comes into the picture: he figured out that if you have three modes for any given note on the scale, you are fine (sort of... he phrased it a bit different, but that's the idea). So, as you go up the scale, the modes get closer and closer, more and more dense, until eventually there are at least 3 for each note. That point, where you first get three modes per note, is the Schroeder Frequency.
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: Schroeder was the guy who 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...)
In fact, there's a very simple equation for calculating what the Schroeder frequency is for any give room:
f(sch) >= 2000*sqrt(T60/V)
Where:
T60 is the 60 dB decay time for the room,
V is the cubic volume of the room.
It's that simple.
This next part is more for people who are able to design their room from scratch, where they can change their dimensions a bit for the walls and ceiling height. It's not relevant to your question here, nor to Abraham's room since his walls are fixed and he can't move them, bit it does help to understand modes better.
So if modes are a big problem, what can we do about that?
In reality, not much! If you can vary the dimensions of your room, then you have the luxury of having SOME control... but not much. In fact, 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, if you can avoid it.
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. It turns out that as long as they are different by 5%, you are fine. So that room with the 10 x 10 x 10 dimensions would be much better if the width was 5% narrower, at about 9'6", and the ceiling were 5% higher, at about 10'6". That's a better ratio.
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 three modes for every note on the musical scale, (ie, the Schroeder frequency would have to be lower than 20 Hz...) 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 that "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! A simple analogy: 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 worst 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. Take a look at the design for Abraham's room, and you'll see some enormously massive bass trapping in the front corners. There will be more trapping in the rear corners too (not designed yet), but those guys in the front will have a useful effect on some of the modal issues.
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. Yes, it is true that tangential modes are lower in intensity than axials, and that oblique modes are lower still, but they can still cause you trouble. If you look at the very top graph that Abraham posed, you can see some faint vertical lines: those mark the predicted frequencies and intensities for the modes in his room. The faint red lines are axial modes, the faint green lines are tangential mods, and the faint blue lines are obliques. Those red lines are longer because the axials are more powerful: the blues lines are shorter, because they are the least powerful obliques. If you compare the predicted modes to the actual modes, you'll see that, indeed, the axials are very strong.. but there still some sign of tangentials, and even obliques in there. So you can't ignore those. If you find a calculator on the internet that only calculates axial modes, forget it: its no use.
Use one of these Room Ratio calculators to figure out the best dimensions for your room:
http://www.bobgolds.com/Mode/RoomModes.htmhttp://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, after having said all of that, modes aren't that important, despite all the hype they get: Modes are just 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.
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Whew! End of long waffling rant about modes!
But now I can answer your actual question better! The Schroeder Frequency marks the spot on the spectrum where the modal issues stop dominating, because there are enough modes per note to smooth things out. So, above the Schroeder frequency, there won't be any wild swings in frequency response (no huge peaks or enormous valleys): just somewhat milder variations, that aren't so important usually. So you don't need to predict that. It is possible to predict it, but it isn't really needed. And there's one other issue: the higher you go up the scale, the more modes there are, so the slower your prediction process goes... at the top end, there are thousands of modes for each note, so calculating all of those then summing them, is mathematically intensive. And thus, not often done.
To show you more graphically WHY it isn't needed, here's a frequency response diagram for a typical room:
You can see what I'm talking about, visually there. At about 350 Hz, the peaks and valleys stop. Below that, it's all "mountains of the moon", but above 350 Hz, the line gets a hell of a lot flatter, with only minor variations. Thus, you could assume that the Schroeder frequency for this room is somewhere around 305 Hz. ... and you can see why it isn't really necessary to predict the modal response above that, because it's mostly flat. The remaining variations are not even modal in nature, but rather from things like reflections, comb filtering, and suchlike, so even trying to predict them is non-trivial. It's easier to measure the actual response of the room after it is built, then just treat the issues that are really there.
If you are still awake after reading through all of that, then hopefully you found something useful in there! And if you are asleep, then I'll shut up and let you carry on sleeping, peacefully ....
- Stuart -
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