Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#1

Postby Soundman2020 » Tue, 2020-Aug-18, 14:47

So what on earth is this thing called the "Schroeder frequency"? Or sometimes also called the "Transition Frequency"?

Before getting into the details, 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!


---

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... :shock:

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.... 8) :roll:

:shot:

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! :shock:

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.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, 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.

----


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:
CRFKUS-REW-FR-20..20k-1..24-BASELINE.png
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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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#2

Postby SoWhat » Tue, 2020-Aug-18, 15:48

Greetings Stuart,

Thanks for this!!!

So a question: Symphony Hall in Boston (home of the BSO) is well-known for not having ANY bad seats (sound-wise speaking; its true, I've been to many concerts there). Does this mean that there isn't a Schroeder Frequency happening (Best. Diffusion. Ever.)?

All the best,

Paul



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#3

Postby lostandfound » Tue, 2020-Aug-18, 15:56

Congratulations Stuart, :yahoo:
a very thorough explanation that is always good to read again :thu:

Lucio



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#4

Postby Soundman2020 » Tue, 2020-Aug-18, 16:40

SoWhat wrote:Source of the post So a question: Symphony Hall in Boston (home of the BSO) is well-known for not having ANY bad seats (sound-wise speaking; its true, I've been to many concerts there). Does this mean that there isn't a Schroeder Frequency happening (Best. Diffusion. Ever.)?

Well, that's a large room acoustically speaking. There's differences between acoustics in small rooms, and acoustics in large rooms. There's also differences in the goals, and the way they are achieved.

OK, for a large room, there really can be proper, statistical diffuse field (reverberant field), which is impossible in a small room. What that means in simple terms is this...

Imagine that you are standing at one end of a sewer pipe, with the speaker at the other end (let's assume it is a brand new, clean sewer pipe!). So the sound can only hit you from basically one direction: straight down the pipe. The chances of you hearing something from the speaker that came from BEHIND you, is zero. The chance that everything you here from the speaker came from directly in front of you, is 100%. Thus, there is no diffuse field: no reverberant field. Because the very definition of a diffuse field says that it is equally likely that the sound reaches you from any direction, as any other direction. So the sound seems to come at you from all directions at once, completely equally, with no single direction being prominent. In a sewer pipe, that is impossible. In a large hall, it is very possible!

Next case: same sewer pipe, same speaker, but you only start listening exactly at the instant the speaker is turned off. All of the sound STILL comes from in front of you! None from the sides, none from behind. There might be some resonance inside the pipe, and some reflections, but basically everything hits you from the front. But in a large hall, that is different: As the speaker turns off, the sound can bounce around all over the hall, from the walls, floor, ceiling, furniture, other people, chairs, stage, lights, etc. and then get to your ears: The chances in this case are equal in all directions: after the speaker turns off, and within a short time, everything you hear seems to come from everywhere, and you can't tell that it originally came from the speaker. It is just as likely that a sound wave hit you from behind, or above, or below, or anywhere, as it is that it came from in front. That's a true reverberant field. And that cannot happen in a sewer pipe, or even in a small room. There aren't enough "bounces" possible to produce a true diffuse, reverberant field. Some directions will always dominate, because the room just isn't big enough for all of those bounces to happen.

Small-room acoustics is different from large-room acoustics, for this reason. In a large room, there is still a Schroeder frequency, but the frequency is so low that the entire audible spectrum is above it! Or at least, the most important part is above it. And in a large room, there really is a valid statistical reverberant field, which you cannot get in a small room.

In other words, getting true diffusion in a small room is impossible.

OK, so that's part of it, but by no means the entire reason why places like Boston Symphony Hall have such great sound: If that were the only reason, then gyms would have great sound too! So would aircraft hangers, large warehouses, train stations, airport terminal buildings, and any other "big" space.... Clearly, that ain't so. You can't compare the average indoor basketball court or gymnasium to the Boston Symphony Hall ! :shock:

So what's the difference?

It's all about "psycho-acoustics". Acoustics deals with the way sound really is: psycho-acoustics deals with the way we humans perceive sound. Our ears and brains are very, very different from a microphone and spectrum analyzer! Our ears are very specifically shaped to change the sound wave that reaches them, in very precise ways, and our inner ears / brains are tuned to recognize those changes, and interpret them to create the sensation that we call "hearing". A well-designed room can "fool" the ear into hearing sounds better, more pleasantly, with better envelopment, warmth, etc. enhancing certain aspects of the sound, while suppressing other aspects.

One of the things the acoustic designer can do is to use the walls, floor, ceiling etc, to modify the diffuse field in pleasant-sounding ways. For example, by allowing diffuse reflections from the side walls to arrive at your ears in certain ways, and with certain time delays, it can make the sounds coming from the stage seem "wider", more "enveloping" as though the orchestra is "around" you, rather than "in front of" you. The designer can also control the decay of the reverberant field, so that it does not overpower the direct sound from the stage, or the subtle reflections from the walls. And he can even do "stuff" to make the hall sound the same with nobody in it, as it sounds when packed with a full house. For example, some symphony halls and high-end theaters these days have treatment built into the bottom of the seats, so that when you stand up and leave the room, the seat bottom flips up to expose that surface to the room, but when you are sitting down it is only exposed to the floor. The treatment in the seat bottom is designed to have a similar acosutic signature to your body when seated, so each seat sounds the same, regardless of whether there is someone siting in it, or not.

With a well designed space, such as the Boston Symphony Hall, the room sounds great everywhere, because the acoustics produces an even reverberant field that decays in the same way for all locations, and produces a similar set of diffuse field, reflections, and direct sound for all locations.

On the other hand, if he doesn't want to have "a single bad seat in the house", a smart acoustician simply won't put any seats in the bad spots! :ahh: He'll only have seats in locations where the sound IS good... :)

There's a lot more to it than that, of course: Try to get hold of the book "Acoustics and Psychoacoustics" by Howard and Angus, and also "Acoustics of Small Rooms" by Kleiner and Tichy. They both give good explanations of this whole "Psychoacoustics" thing.

One issue here is that when people are thinking about building their own control room at home, they think it would be cool to use some of the design features of large halls to make their small rooms sound larger, more spacious, and make the sound more "surrounding", "wider", "warmer" "airy"... Big Mistake! Yeah, it is possible to do that, to a certain extent, and yeah, it would sound cool and impress the hell out of friends and family... but it would be a really lousy control room! Great for a home theater, or audiophile listening room, but terrible for a control room. The entire purpose of a control room is to tell you the truth: the entire goal is that you can hear the speakers, only the speakers, and nothing but the speakers. The room CANNOT add anything to the sound coming from the speakers, and it CANNOT take anything away! That is often referred to as "coloring" the sound, but you do NOT want a control room that colors the sound! The only real reason why you have a control room at all, is so you can hear the tracks, and mix them. If the sound you are hearing is not the same as the sound coming out the speakers, then you are NOT mixing the tracks! You are "mixing the room". This is the number one, biggest, reason why mixes do not translate in many studios: because the engineer is mixing something different that is not actually on the tracks! He is mixing the tracks plus the room sound, all together... and he can probably make it sound great in that room... but then when you take the mix out to your car, or club, or shop, or play it on the radio, TV, movie house, etc.... it sounds ugly! Because it was mixed for a DIFFERENT room. It will just sound "off" in any other place... except the original room where it was mixed. On the other hand, if the mix is done to sound good in a neutral room that does not color it at all, then it will also sound good in ANY other room, since there will be no underlying "room signature" in the mix itself.

For example (a silly example, but it helps to illustrate): If your right speaker sounds 5 dB louder than your left speaker, then as you are balancing the mix, you'll subconsciously turn down things in the right speaker, to make them both sound the same. The mix will sound great in the room! Wonderful! Best mix ever! But when you take that to another place (eg, your car, or cell phone ear buds, or church, club, Boston Symphony Hall, etc.), you will immediately notice that everything is "skewed" to the left! The mix did not "translate", because it was "colored" by the incorrect balance between the channels. The same applies to all acoustic aspects of the room, not just the volume of each channel. There are many, many ways that a room can "color" the sound, and all of them will mess with your ability do produce a mix that translates well.

Simple analogy: get a great artist to paint a picture while wearing glass that are colored bright green. He can paint a picture that looks wonderful to him, when seen through his green glasses, but looks really bad to everyone else: all the colors are wrong! It only looks good if you wear the same glasses he was wearing, to distort your color perception in the same way. But when viewed in any other room, under any other lighting conditions, it looks ghastly. The exact same thing happens with a room that "colors the sound": any "sound picture" painted in there will be "off color", and sound lousy when heard in other places.

So, it's a big mistake to try to make a control room "sound good", like a symphony hall. Rather, it should sound totally neutral, natural, and "invisible". It should sound like there is no room, ideally.

Yet another thing to take into account when designing a control room! :)

- Stuart -



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#5

Postby SoWhat » Tue, 2020-Aug-18, 17:40

Greetings Stuart,

Thanks for the detailed response. Fortunately, I don't have to worry about a control room for my build (I wish I had the space to do so. It's not a bad problem to have...).

You can't compare the average indoor basketball court or gymnasium to the Boston Symphony Hall !


THE reason there were never concerts at the Boston Garden (especially the old one; most Boston rock concerts were held at the Worcester Centrum back then), but that design (steeply slanted bleachers) gives the Oregon Ducks a huge crowd-noise advantage at Autzen stadium.

All the best,

Paul



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#6

Postby shybird » Tue, 2020-Aug-18, 17:43

Such a fantastic explanation! It’s crazy how many misconceptions get thrown around about how modes work and their role in room acoustics. This puts it in a very easy to understand language. Thank you Stuart!

Cheers
Trevor



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#7

Postby Avare » Tue, 2020-Aug-18, 22:17

SoWhat wrote:Source of the post Greetings Stuart,

Thanks for this!!!

So a question: Symphony Hall in Boston (home of the BSO) is well-known for not having ANY bad seats (sound-wise speaking; its true, I've been to many concerts there). Does this mean that there isn't a Schroeder Frequency happening (Best. Diffusion. Ever.)?

All the best,

Paul

A coda to the great post by Stuart. Boston Symphony Hall has Schroeder frequency of 2.04 Hz going for 6 modes per Hz. BERANEK Concert Halls and Opera Houses gives detailed analysis of 100 venues.


Good studio building is 90% design and 10% construction.

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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#8

Postby SoWhat » Wed, 2020-Aug-19, 11:02

Greetings Andre,

Thanks for that.

BERANEK Concert Halls and Opera Houses gives detailed analysis of 100 venues.


How did I know that there had to be a publication which dealt with such things??? I guess my years in academia should taught me that EVERY subject, no matter how specialized, has been written about.

All the best,

Paul



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#9

Postby Soundman2020 » Wed, 2020-Aug-19, 12:28

Avare wrote:Source of the post Boston Symphony Hall has Schroeder frequency of 2.04 Hz going for 6 modes per Hz.
Thanks, Andre! I knew it was low, but didn't realize it was that low. I should get a copy of that book, to add to my library.

- Stuart -



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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#10

Postby Avare » Wed, 2020-Aug-19, 23:07

Avare wrote:Source of the post
SoWhat wrote:Source of the post Greetings Stuart,

Thanks for this!!!

So a question: Symphony Hall in Boston (home of the BSO) is well-known for not having ANY bad seats (sound-wise speaking; its true, I've been to many concerts there). Does this mean that there isn't a Schroeder Frequency happening (Best. Diffusion. Ever.)?

All the best,

Paul

A coda to the great post by Stuart. Boston Symphony Hall has Schroeder frequency of 2.04 Hz going for 6 modes per Hz. BERANEK Concert Halls and Opera Houses gives detailed analysis of 100 venues.
I just noticed my typing error. The Schroeder Frequency is 20 Hz.

My apologies.


Good studio building is 90% design and 10% construction.

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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#11

Postby Avare » Wed, 2020-Aug-19, 23:51

The Schroeder frequency has nothing to do with diffusion. It is the frequency where modes are so close that they overlap such that one half bandwidth of modes is less than the spacing between the modes See the appendix in RD 1992-8.
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Good studio building is 90% design and 10% construction.

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Modes, room ratios, and the "Schroeder Frequency" or "Transition Frequency"

#12

Postby terminator1987 » Fri, 2021-Feb-26, 15:34

Soundman2020 wrote:Source of the post 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.

Soundman2020 wrote:Source of the post 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

Soundman2020 wrote:Source of the post 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.


:idea:

It got me thinking and I came up with an idea, that is actually widely practised, but it occured to me that it might just be connected to this very topic. I am talking about oblique panels usually put on the front wall of a control room in studio designs. It occured to me, that having those panels angled adequately, effectively creates a faux fourth pair of parallel walls in the room, which would create yet another set of standing waves, and thus, increase the modal variety in the low end. I have made a very basic visual representation of what I mean in MS Paint, attached. And so, sound waves reflected perpendicularly from those panels and then reflected by the wall on the other side of the room would again fall perpendicularly on the other panel and so back and forth, creating a standing wave. Simultaneously, the real wall is still "active", since 1) there is a large chunk of it left uncovered, 2) we are considering mainly low-end frequencies, for which a barrier of a single sheet of drywall or MDF isn't really an impermeable obstacle. In my example rooom of 600 x 500 x 400 cm it would add another dimension to the room, which would be ca. 1190 cm, so almost double the length of the room!

I even came up with another idea, based on the same principle, which is to make a "double ceiling" (double for low-end frequencies) that would consist of concrete upper ceiling, at the height in my example 400 cm, and a drywall "hung ceiling" (I don't know or forgot the professional term for that), a the height of 320 cm in my example. This also should increase the modal variety of the room in the low-end, due to the partial permeability of a drywall sheet to low frequencies. Of course, higher frequencies would not go through, but very low ones will and should resonate in additional modal nodes. Also, imagine what kind of beast bass trap that could be if you would fill it with absorption (up to 80 cm thick!), and yet, the ceiling would look normal, unaffected. The obvious disadvantage is a reduction in the volume of the room, which would end up being in this particular example exactly 20% lower (reduction from 120 m3 to 96 m3). So that would effectively make me a "fifth pair" of parallel walls.

The ratios I used are also not coincidental - the main ratio of 1.00 : 1.25 : 1.50 is very close to Sepmeyer's 2nd ratio and both are within all three major recommendations (Bolt's, EBU/ITU, IEC) and both sit in the dark grey area on the Cox's plot (see attached screens).

And of course, I am aware that those waves and modes would not be as potent as the axial modes between the three main pairs of walls, probably these additional axials would be of the magnitude of regular obliques, but still, I reckon it should be far better to have those modes than a gap of nothing between the "baseline" modes in the room untreated in such way?

I've made a "simulation" with amroc for those three "virtual rooms working inside one room" and merged those calculated modes on same scales together in the attachement. Of course it would not be so simple to just add those modes, as some modes are generated by the other two walls (other than the one that has been modified in a particular calculation). But still one can see, and thus hope, that three or more modes start to accumulate from circa 53 Hz upward, and if that would be true, that would mean that the transition (Shroeder) frequency of the room has effectively halved with these two simple treatments from 100 Hz to ca. 53 hz. Of course it is only a presumption, and I noted some issues I already see in my chain of thought above.

So, what do you, acoustic experts, think of this theory? If it is rubbish, please explain me why :horse: , because I have quite convinced myself already to build it that way :D :mrgreen: :geek: :ugeek:
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