Golden ratio rooms for bass

Do golden ratios work for bass? I must admit I'm more than a little skeptical. Talk of golden ratios has always sounded like nonsense to me, the kind of thing that often turns out to be silly when you actually start measuring. I'll investigate this here with some simulations with the FRDC room simulator.

Here is a golden ratio room - 4.8 wide x 7.8m deep x 3m ceiling.


Image courtesy of Cardas Audio
This is just one implementation of Golden Ratios, but could be applied to rooms of different sizes.

Listening is in an equilateral triangle spaced 2.1m from the front wall and 1.3m from side walls. Speakers are 2.1m apart and listening position is the same distance direct from each speaker.




The result is suprisingly good. The bold line shows the bass transfer function of the mains. It is very good! If you actually got that out of a normal room, it would be something to dance around the room about like a nutter. It is flat +/- 5db! 15 - 20 db is more typical.

The purple line is a corner sub combined with the mains. On it's own, the sub is flatter, except for a nasty dip at 60 Hz. Using this setup as a starting point, an excellent result could be achieved easily with a little tuning.

Is it a fluke?

Let's find out what happens when we start breaking the golden rules ...

If we move the listening position back further away, the reponse gets progressively worse, until we see a broad dip centred at 50 Hz at 2m further away.



If we move sideways half a metre, the midbass imrpoves slightly but we see a nasty dip around 120 Hz.

If we move the speakers back but keep the same listening position, so that the speakers are 1m clear of the front wall, we get a narrow dip at 60 Hz.

If we make the room much wider, as if it were now a living room adjacent to a meals and kitchen area (10m), it's not so bad. Finally a change that we don't get punished for!

If you can't beat 'em, join 'em!

I'm surprised to admit that there appears to be something in these golden ratios!

Actual results will vary. The room simulated has a lot of damping and reflects either a lossy room, or one that is well treated for bass absorption.

So if you are building a room you plan to use for audio, and you were going to build a typical 5 x 7m room with 2.7m ceiling, consider this option. Change the dimensions a little, and set up the room a little differently than you might have. Try to stick to it as close as you can. It seems you can get away with changing some things and not others. The beauty of this option is that you can get to a good result very simply. In fact, most will be happy with a simple plug and play setup. A pair of stereo speakers placed as per the ratios with no EQ or special room treatment. All this assumes a lightly constructed room with no concrete or bricks in the enclosing space.

If this doesn't work for you then you will need to work a lot harder for good bass.

More reading

Cardas Audio - Golden Cuboid Listening Room Diagram
Cardas audio - Setting Up Speakers In A Rectangular Room>

Audio myth series

In the audio community, there are a lot of myths that are very persistent. In this series, I'm going to explore many of them. Not everything covered in this series will necessarily turn out to be a myth.

Why are there so many audio myths?

People believe what they want to believe. Once they have formed a belief, many reject any new information that contradicts their established opinion. This is human nature.

To overcome this, an open mind and some education is needed as well as a more scientific approach. Science changes it's opinion based on new information. It sounds simple enough, but this approach while very sensible and based on common sense, isn't so common.

The audio myth series

Myth 1 - small speakers are faster
Myth 2 - fast bass
Myth 3 - cube rooms have bad bass

Cube rooms have bad bass

Do cube shaped rooms have bad bass? The idea is that a room having all the same dimensions will have very bad room modes as they will be the same between opposing wall pairs, thus reinforcing each other. Let's see if it's true, using the FRDC room simulator. This won't prove anything for every single room, but it will show one example.

Here are the results of all the rooms:



The red line is a 3m cube room - you might think it's the worst, but actually it gives the best result! Even better than a typical room of 5 x 7 x 2.7m, shown in black.

The rooms simulated are:

1. 3 x 3 x 3m with speakers 0.6m clear of walls and the listening position centred on the back wall.
2. 4 x 4 x 4m with the speakers 1m clear, listening in the same spot
3. 5 x 5 x 5m as above
4. As above but with the listening chair 1m into the room
5. 6 x 6 x 6 with the listening chair 1m in from the rear wall and speakers 1m clear of walls.



All of these results are good except the standard room! It has a large wide dip that is not easily fixed. It is far too big to EQ and acoustic room treatement will most likely do little to solve it. This room will make a beastly sub sound wimpy compared to it's potential. It will be lacking punch.



The 5m cube looks good until we start moving away from the rear wall. We start to see a dip in the upper bass range. Generally it is better to sit away from walls for imaging, so this arrangement suggests multi subs.

Conclusion

Cube rooms are not necessarily bad for bass. Bass in a room is more complicated than that. This is just a snapshot. Things will look different in a real.

There are a few different factors here:

• size of the room (very small and very large rooms are very different to most)
• where you sit makes a big difference
• where you place bass sources changes everything
• room construction varies

The main point is this: cube rooms aren't necessarily bad for bass. They may in fact be better than a room you expect to be good. Don't assume anything.

Basic measurement setup

Why measure?

Every system can potentially benefit from using measurements. If you are designing or modifying your own speakers, or setting up a subwoofer, measurements are essential. Even if you have a simple 2 channel system there is still some benefit. Measurements won't replace critical listening skills, but they will help you make better choices, including many that simply can't be made by ear. It is a learning process, where you take measurements as well as listen carefully. In this process, you learn what to look for in the measurements since better looking measurements don't always sound better. Expectations often need to change.

Isn't it better to everything by ear, since it is the ear that is the final judge?

Find the answer here:
Measurements vs doing it by ear >

The best $150 you've ever spent on audio?

It's affordable and not exceptionally difficult. In the past, the cost was much greater where a measurement setup would most likely cost more than $1k. Now low cost tools will do the job.




Essential:
Behringer ECM8000 measurement mic >
Behringer XENYX 502 mixer >
Sound card which supports full duplex operation
Mic tripod (you can use a camera tripod but it's inconvenient)

Highly Recommended:

Cross spectrum calibrated mics >
(slightly more expensive than a stock ECM mic, but far more reliable results)
Boom mic stand

You'll find it much easier with a proper stand and if you plan to measure on a fairly regular basis, the extra expense is certainly worth it.

Why can't I just plug the mic into the PC?

The signal will be too low and you will not get a measurement at all.




Software

Fortunately, this part is free.

For bass measurements, download the free program REW from the HT shack here >

 

For full range measurements, Holm Impulse is both free and very easy to use:
Download Holm Impulse here >


Do you need a calibrated mic?

This depends on what you will measure. For fullrange measurements - definitely. For bass optimisation, you be the judge. Here is a chart that shows a number of the Behringer Mic unit to unit variation:


Image courtesy of Cross Spectrum Labs who offer a calibration service, and supply calibrated mics (including the Behringer mic shown here) at a very attractive price.
View Cross Spectrum Labs website >

As you can see, you get about +/- 2db at 40 Hz, worse at 20 Hz but not as bad higher up. The most you are likely to see is 2db out above this point, but if you are lucky you may get 1db or less. In truth that is probably enough, but then when you consider that it doesn't cost much more to be sure I think most would simply pay the extra.

If you already have a mic, you are probably best to sell it and simply buy a new one direct from the lab that has already been calibrated:

Cross spectrum calibrated mics >

The cost shipped to Australia is little more than the stock ECM mic.

There is a thread on the HT shack about this service, with some very useful info:

More info on the service >

Cables and connections

You will need balanced mic cable to connect the mic to the mixer and it's a good idea to pick up a good length like 10m, with XLR connectors on each end. Connect to a PC with jacks on "main out." The simple way is to connect jack > RCA adaptors then just run an RCA cable to PC. You can get a cable with RCA on one end and mini jack on the other, or again use an adaptor.

What kind of results will I see?

The most common use will be to get the bass right in your room. The best bass can't be bought - it must be tuned to your room.

Here is an example of in-room bass measurements >

In that example you will see examples of the mains and subs, how they are combined and a final result with EQ applied.

In the most basic system, it will show you which sub and speaker placements work best. In a more sophisticated system, it will help with placing multiple subwoofers and with using EQ without killing headroom.

How do I measure?

There are various methods to measure covered here:


Measurement techniques - an introduction

Tutorial: Hornresp - getting a small horn to go deeper

Previously we looked at the impact of the rear chamber >

Now we'll take that one step further and see how that impacts extension. Here is our 40 Hz horn with Peerless XLS.



This trick relies on some room gain. Here is a measurement of the in-room bass in my room:



Green: left sub
Red: right sub
Black: both combined
Horizontal divisions are 8db

You can see there is a lot of gain here. So if we use this gain, we can make a small horn get down a bit lower. Many would design a horn flat down to 40 or 50 Hz. That gives better results in the simulation, but in the room you get a big peak in the midbass that requires EQ to remove.

So instead of a horn that will go flat down to 40 Hz, we might instead try extending it lower with low tuning. We'll need a fairly small rear chamber with a sharp knee and we will see a less appealing response with midbass dip, but this will be deliberate. The room will fill in this dip. The ideal response would be close to the inverse of the room transfer function, but we won't get that. We are now making a design that will work best for one room.

Now let's combine the two:



The grey line shows combined room response of corner subs that are flat from 20 - 80 Hz. The red line is simulated response of a 30 Hz undersized horn. It isn't really big enough to get down that low (more like 40 Hz) but it's intended to work with room gain. You can see the midbass response dips down where room gain will bring it back up and there is a knee in the bottom end. In-room response should get down to about 28 Hz. Unfortunately the 70 Hz dip will be present and so we need another bass source there to fill it in.

Don't make the box too big. It will smooth the knee and it won't get down quite as low, and excursion won't be as well controlled.



They grey version is what you would do if you didn't know room response. The black version has a smaller chamber and lower tuning.

No guess work

You need to measure your room to benefit from this. Otherwise it's a game of pin the tail on the donkey - you have no idea what you are dealing with.

Tutorial: Hornresp tweaking

Want to know how to get better results with Hornresp? Read on.

Here is our front loaded horn with the Peerless XLS driver. It's designed to extend to 40 Hz and has some compromise to make it smaller.



Changing the compression chamber



Press F4 and you will see in light grey the previous plot for all charts. In grey you can see a rear chamber of 10L, but in black 15L. You can see how it smoothes out the knee, and also shows up in the excursion plot:



You can see greater volume means higher excursion. In this case, the bigger volume means xmax is exceeded with 500w. You might think this would not be an issue as the output would not be needed, but in reality these levels would not be reached as they are based on a perfectly solid room with corner loading.

The 15L version has the maximum volume that should be used. If the chamber were made larger, the excursion would increase further. As it stands, this design is fairly robust and the 10L version is even more robust.

Let's see what happens if we make the volume bigger or smaller. Too big: 100L and too small: 5L.



The undersized chamber causes a sharp knee and loss of midbass as well as early roll-off. The oversized chamber isn't too bad, although it doesn't help if we are trying to extend the response a bit lower.



The excursion chart tells us more. 5L leads to very low excursion and this is why we see the midbass dip, but the 100L version loses it's grip on excursion to the point that we need a rumble filter to protect it! The obvious solution is to use a sensible rear chamber volume so that a rumble filter is not needed. In this horn, 10 - 15L should be used. The smaller volume will suit high power use.

Next: How to get a small horn to play deeper >

Tutorial: Hornresp bass horn - basic version

Here's a crash course in knocking up a quick simulation of a bass horn in hornresp.


First, download it here:

Hornresp download >

We'll design a front loaded horn.

1. Choose your driver and enter in it's parameters:



I've entered TS parameters for the Peerless XLS driver. Use mms for mmd. If you don't have either Rms or Cms, they can be calculated. Select Tools/Calculate parameter.

2. Enter Ang and Eg



Ang: double click until it cycles through to 2pi. This means it will correspond to simulations you would get in programs like WinISD. Otherwise you get an exaggerated output figure.

Eg: double click then enter the nominal impedance of the driver. You will now see the efficiency with 1w of input with simulations.

3. Auto generate horn

Select Tools/System design/with driver

In this case, let's choose 40 - 150 Hz. Now you weill notice that fields are filled in:



Press calculate and view the results:



This is a very good result with very high efficiency of around 106 db 1w1m. Normally this driver would have an efficiency around 87 db so we have gained around 19 db. Make sure you use the correct values of Ang and Eg or the efficiency will not be correct.

The schematic shows that the horn is over 2000L in volume! This is too big to be practical and the compression ratio is too high. Compression ratio is SD : S1 and should be 2 for a conventional driver. Now we need to modify the horn to get it down to a practical and workable solution.

4. First attempt at changing some numbers

Remove the throat chamber - enter zero for both Vtc and Atc.

Increase the size of the rear chamber to 15L

Set S1 to half the value of SD

Double click on hyp and a box will open up:

Choose a value for S2 that isn't crazy. This is the mouth area. Use a calculator and work it out in cm. I'll choose 50 cm wide x 120 cm high which gives 6000 cm2.

Now click on L12 - this is the length. We'll let hornresp calculate this based on F12 which is the number we'll input for our cut off - 40 Hz. We hope to get the horn to extend to this point. Select calculate and it works out the length. Now click save and the new numbers are entered:



Now click calculate to see the new results.



Not quite as impressive as before but we have maintained the extension and efficiency except for a midbass dip and the volume is now around 500L.

Let's simulate for corner loading. Change Ang to 0.5 and for Eg double click again and input 0.0625w. This compensates for 12 db of acoustic gain that inflates the efficiency.



Now we have decent performance and it's smooth enough. There isn't much need to try to get it flatter as room response will do much worse. Efficiency has dropped off a little but it's still very high.

Further tweaking

You might like to experiment with different sizes for the rear compression chamber. You will see a change in the excursion chart - a smaller size will cause a sharper peak and lower excursion. A larger size will see a plateau rather than a sharp peak. You will also see a change in the response where a smaller chamber gives a small peak in the bottom end and a larger chamber sees a rounded knee and often slightly less efficiency.

If you've measured the transfer function of your room, then you have some useful info. Suppose you had a 10 db peak at 30 Hz. You could lower the cut off and it would probably work with the gain better, extending the in-room result down to 30 Hz. If you are designing for a particular room, it's very helpful to have this information and incorporate it into the design.

Next: see how you can get better results >