Thursday, September 4, 2014

Bass EQ for Movies - How to improve sound quality on bass filtered movies

Would it not be great if you could bring back the lost bass in you favorite movies?
Well, perhaps you can.

By applying equalization customized for each movie during playback, it is possible to dig out some of the low bass lost due to filtering and processing in the studio.  

Why Bass EQ

When movies are mixed in the studio, the sound will be adjusted according to what they hear in that studio.
Sometimes limitations in the playback equipment, such as speaker system, will lead to adjustments that will compromise sound quality.

Typical examples of such undesired adjustments are high-pass filtering that removes the lowest frequency content.
On a limited system this may sound better, because the removal of content that can not be reproduced anyway will increase headroom for the mid and upper bass frequencies.
When played back on a full frequency range system the filtered version looses weight and impact, and also tend to sound less natural.

If this filtering is done in one of the very final stages of production, then it is a good possibility that at least some of the filtered content can be retrieved.
This is what Bass EQ tries to do.

The better your playback system is, and if you also like it loud, like 0dB/reference, then the difference will be very significant, and on some movies the whole experience is lifted to another level.
But also if you play at lower volumes, say -20dB, perhaps you have some smaller but still nice and good quality subwoofers, then the difference will most certainly be very noticeable.
This is not only about more shake and physical impact at house-wrecking volumes, the overall sound quality is improved when the natural wide frequency range of is restored.

Example frequency spectrum plots playing this scene from the movie Battleship:

Battleship, original and Battleship with Bass EQ playback:

There is a huge difference in output at low frequencies, and listening easily reveals that the perceived increase in sound quality is significant and very far from subtle.

How to Bass EQ

You must be able to implement equalization according to the Bass EQ graph for each individual movie.
This can be done in a DSP, if you have something like that in the playback chain.

In a bass-managed system the Bass EQ can be implemented on the subwoofer channel.

Computer playback is increasing in popularity, and it will eventually be the preferred playback device for all media content.
Then it is likely that equalization can be done very flexible and accurate using a plug-in or built-in processing in the player software.
JRiver media center is an example of player software that can do Bass EQ with individual settings for each move.

A simple graphical equalizer or bass tone control will not be able to provide Bass EQ.

To verify your equalizer setting you can play a pink noise file and compare the frequency responses - the unfiltered pink noise should be flat, and pink noise with Bass EQ should look similar to the Bass EQ curve.

Some movies require a very large boost at low frequencies, perhaps in the order +20dB gain below 20Hz.
This requires careful attention to what you are doing.
If such a filter is left in unintentionally, and you play a movie with flat full frequency content, something will overload.

Some movies are quite heavy in the mid bass region, equalizing this down will gain some headroom for the low bass as well as improving the overall spectral balance.
If there is noise at frequencies below usable output, say around 10Hz and below, then this can be removed using a high pass filter, and some more headroom is gained.
If the sound track is mixed very loud and dynamically compressed, there may not be enough headroom for the low bass we bring back, and the only solution is to reduce the level before applying the Bass EQ.
The lost gain is restored later in the chain, perhaps as simple as adjusting the master volume.
Exactly how this is done depends on what it used for equalization; different dsp and software may require different approaches.

How to recognize good candidates for Bass EQ and what to fix

Any movie where sound effects and bass is lacking in weight are potential candidates.
Looking at the Peak-Average graph from the The Low Frequency Content Thread (films, games, music, etc) thread can tell a lot about how a movie sounds.

Kon-Tiki is a film with a good sound track utilizing the whole frequency spectrum, observe that the curve is a slightly tilted line extending all the way down to the very lowest frequencies:

The storm scene has content all the way down:

This film does not need any Bass EQ.

Battleship has met with an accident somewhere in the sound-making process:

There is an obvious drop right below 35Hz, looks like a steep high-pass filter has been applied.
This is something to work on for Bass EQ.

A good target response is likely an approximately tilted straight line, that extends as low in frequency as possible.
Start with applying equalization that bring the Peak-Average curve closer to this straight tilted response.
Evaluation by listening is necessary to determine appropriate equalization, and care must be taken to ensure not to clip the signal anywhere in the chain.

How low in frequency should you try to equalize to flat. 
Depends on the original sound design, and whether there is any content to dig out, it may be buried in noise at the very lowest frequencies.
Fixing something destroyed with a 30Hz filter and mangaging to retrieve flat down to 20Hz can make a huge difference.
If you can extend it down to around 15Hz, even better.
Below around 15Hz is questionable, certainly depends on your playback system, as tactile feedback from floor or moving house structure may be required to notice it at all.
The lower you go the greater the risc of amplifying noise instead of usable content, and if you can bring a sound track with virtually no low bass back to life with significant content down to 15Hz, I would say that is a very good achievement.

Gravity, opening scenes (RTA from playback):

This film has a droning, constant tone around 20Hz, as can be seen in the curve.
This is part of the sound design.
The level below 20Hz drops off very quickly, but it is not likely that equalization can bring improvements, because likely there is no content that has been removed.
The relationship between frequency and time dictates that continuous tones, which have a long time span, are narrow in frequency distribution.
Impulse like transients, like cannons and gunshots, have short time span and a wide frequency distribution.
If there are no impulses, there may not be low frequency content to retrieve.

When the Explorer is hit by the debris, there are sound effects added that adds to the sensation of the incident, these sounds are more dynamic and impulse-like:

The spectrum reveals that there is content below the 20Hz drone, and that this content may have been filtered using a steep high pass around 20Hz.
Gravity is another candidate for Bass EQ.

Avatar, flight scene (RTA from playback):

This scene sounds good, the feeling of realism and athmosphere is good.
Right at the end of this scene, where the plane drops down the cliff, there is a sense of weightlessness, making it feel like you are on the plane.
The spectrum reveals why this effect is so good - there is significant content at the very lowest frequencies, peaking around 13Hz.

Avatar, monster stomp-stomp (RTA from playback):

Here the stomps sounds rather boomy and does not have the appropriate feeling of weight and impact.
The spectrum reveals why - the low frequency content below 25Hz is removed.
Considering the previous flight scene, the conclusion is that finding the best Bass EQ for Avatar will be a compromise.
Some scenes could benefit from a huge low-frequency boost, but then other scenes would sound horrible with too much in the low end.

Movies improving with Bass EQ

There is now a thread at data-bass listing Movies with Bass EQ:

The Bass EQ for Movies thread

Data-bass also hosts lots of other content about movies, subwoofers and sound quality related topics.
The Low Frequency Content thread is a highly regarded source for information about movie sound tracks.

Friday, August 8, 2014

My Bandcamp Music

On I have found lots of interesting music of very high quality, music that would never have reached me through old media distribution channels.  




A better way for music distribution

Bandcamp is a web-site where you can listen to and buy music.
You can buy for download directly to your computer, no need to hassle with ripping CDs any more, and lossless formats are available so you do not have to worry about encoding quality.

Today, when physical media such as CD is disappearing, many find that streaming services like Spotify is a good source for music.
However, there are very good reasons to prefer services where you buy and acquire the music and download it for local storage, on your own hard drive.
At least for the enthusiast, who cares about quality, this is the only way to ensure you have the right version of your favourite albums, and it will not suddenly go away if the streaming service goes down or you simply loose your internet connection.

I present for you some examples of music I have found, and describes what makes those special with respect to how they sound.
As I say on my Bandcamp page; "My review comments focus on sound - not many do so, and others are far better on the music part." 



The Flashbulb - Reunion:
A masterpiece of dynamics and excellent sound production.
Note the impact of the drums of tracks like Oak Lawn UFO and Walking Irrevocable.
But be warned, this is electronic, and everything is allowed, sometimes effects like distortion and changes in tonal balance are used in ways that can seriously disturb the typicial audiophile ears.
The dynamics and general composition makes it possible to play very loud and it will still sound quite pleasant, there is no Loudness-war disease here.

Emancipator - Safe In The Steep Cliffs:
What makes this special is the lively and exciting sound.
Listen to, or rather, feel, the drums on Rattlesnakes, note the big difference in both sound and tactile feel between the sharper smaller drums and the larger bass drum.

Panda Dub - Antilogy:
A dub production with unusual good overall sound quality, dynamic and detailed, pleasant to play loud.
If you like this one you should check out Panda Dub's other releases, particularly the older ones.




Emily Davidsson - BASS SOUNDS: Music for Unaccompanied Cello from the Early Baroque: 
This is a musical and technical masterpiece.
If you think this should be easy to do right - only one instrument, then check out some other releases in the same genre of classical music with few instruments, nowadays quite many of those are destroyed by bad production.

Seems Like Old Times:
A Jazz band in my room, simply.
No attempts to polish or amplify or make things sound bigger than they are.
And it is this simple and plain approach that actually achieves what others with large budgets and names try to do using boosts in the bass, compression, limiters, more compression, and eventually ending up with a flat and unnatural sound.
Turn it up and this sounds huge, dynamic and natural, it achieves to transfer some of the energy and liveliness of live music.

Join and find hidden treasures yourself

I have no affiliation to, I only encourage you to join and support the music and distribution platform, contribute by posting about music you find there, and enjoy the diversity of popular and established artists as well as the new or specialized ones.
Look at my personal collection at to see what I have found, and then you can use the to search for music.

Sunday, July 6, 2014

Pink Noise Calibration

Measuring more than one speaker and getting predictable and usable results can be challenging.

Using pink noise and a real-time analyzer makes it easy to check level and frequency response, and you can move the mic around to measure at different locations and still get meaningful observations.


When setting up a sound system you need measurements to verify what is going on with the sound, and the frequency response is the most important characteristic.
Location of listening positions and speakers, eq settings, room correction and room acoustics all affect the response.
To be able to make adjustments in the right direction it is necessary to measure.

Problems with sine wave sweeps and multiple sound sources

Sound from more than one speaker will sum up in strange patterns depending on type of sound, room acoustics and microphone position.
It is possible to measure two speakers with sine sweep, but that requires some understanding of what is going on, and the mic must be located within few mm exactly between the two speakers.

The uncorrelated pink noise solution

By using uncorrelated pink noise sent to all speakers the individual sound sources will sum more correctly like music or movie sound.
The frequency response can be observed using a real-time analyzer, which means you can see the frequency response changing when moving the mic.

By having multichannel pink noise files with different channel configurations it is quick and easy to measure different speakers in a surround system.


Pink noise and real-time analyzer method can only verify level and frequency response.
For other measurements, such as distortion and impulse response, it is necessary to measure with sine sweep, each speaker individually.
Also, there is no possibility to isolate the speakers direct sound from room reflections using gating, the pink noise will always measure all sound including all room contribution. 


You need REW measurement software and a calibrated microphone.
The software is free, and a good mic is cheap compared to what many are willing to pay for potential upgrades to their sound system.

Pink noise files can be downloaded from my web site:

pn full_fr -20dBFS 15s 7_1.flac
pn full_fr -20dBFS 20s L+R.flac
pn full_fr -20dBFS 20s LCR.flac
pn full_fr -20dBFS 20s C.flac

How to measure

- Play the pink noise file that corresponds to the speakers you want to measure.
- Open the RTA in REW
- Select Mode: RTA 1/48 octave
- Select FFT Length: 32768
- Select Averages: Exponential 0.88

A scaling where the 5dB/div lines are visible is fine.

Now you will see the frequency response being continuously updated, and you can move the mic around to check various positions.

A "good" response is one that most closely follows a tilted line, where the amount of tilt depends on room acoustics and preference.
Typical tilt is from 0dB (flat) up to around 10dB from 20Hz-20KHz, and generally a more live room has more tilt.
If you can get within +-5dB that is generally considered good. 

For single speaker measurements you can use the PN Pink Noise generator in REW, for more speakers this will not work because the noise signals will be correlated and will not sum up correctly. 

REW measurement software RTA window

Example measurements

7.1 System at multiple seats

I wanted to verify the response in The Moderate Cinema from all speakers, and see how it changes at different seats.
Response is nice and even across the mid range, the roll-off above 10KHz is due to the surround speakers falling off because they are not on-axis.
At low frequencies the better seats are good, but the two on the far left have some large dips.  

Pink noise all 7.1 channels, seat 1

Seats 1 to 5

Seats 1 to 5, 1/6 oct smoothing

L+R at multiple seats

The front L and R speakers are the most important, and especially for music it is important to have good linearity in the response for these.
For music listening we choose fewer seats, and see that seats 1, 2 and 4 has reasonably good response. 

L and R, seat 1

L and R, seat 1, 2, 4, 1/6 oct smoothing

Tuesday, May 6, 2014

How to make Audyssey room correction work

How to fix a too-bright Audyssey calibration

Audyssey room correction is included in many of the most popular AV-receivers.
By making adjustments to reduce the effects from bad room acoustics or bad speakers, Audyssey improves sound quality. 
And even for good systems in good rooms there may be a significant gain in clarity and definition of the sound.

However, limitations to the Audyssey implementations causes failure when used with some speaker and room combinations.

I will show what goes wrong, and how to make it work.


Initial calibration

This system consist of controlled directivity main front speakers and 4 compact Horn subwoofers located in the corners.
Distance, level and crossover settings are carefully calibrated, to give a reasonable flat tilted frequency response and volume level calibration according to 85dB SPL for -20dB master volume.

After running Audyssey the tonal balance is too bright, with excessive highs.
Selecting the 'Audyssey' curve only makes it worse, it ends up with a notch in the upper midrange, too bright, and the highest frequencies attenuated.

Also, the automatic settings for subwoofer crossover and distance is far off, causing the bass to be very strange.

All this can be confirmed by measuring the systems frequency response - which shows the loudness as a function of sound frequency.

Because Audyssey internally uses a different method to find the response it uses to calculate the correction, the result will vary depending on the speaker and room interaction. 
For some speakers and rooms it may work, for others, not so.

Frequency response, No Audyssey and Audyssey Flat with automatic settings

The red curve is the calibrated system without Audyssey, a fairly even response with a slight downwards tilt as the frequency rises.

The grey curve is with Audyssey Flat correction enabled, and all settings left like the automatic calibration suggested. There are severe dips in the bass range, and level above 2-3KHz is too high, causing a too bright sound balance.

These curves are not smooth, they show peaks and dips caused by room reflections. They are presented like this, with 1/24 octave smoothing only, so that we can see what is going on.

Restore settings

By restoring settings for subwoofer crossover and distance and level, the bass response is restored.
Crossover is set to 120Hz, distance is 5.40m.

Frequency response, Audyssey Flat, restored settings

The green curve is Audyssey Flat with tone control adjusted and crossover and distance settings restored. With no tone adjust the Audyssey Flat is equal to the grey curve above 1KHz. 

Adjust tilt

By using the tone controls it is possible to fix the tilt of the frequency response to match the around 3dB/decade fall, which will also give a flat on-axis response in this room with these speakers.

The tone control in this AVR is implemented in the master volume control circuit, and this same chip is used in many, if not most, newer AVRs.
This means the tone control works independent of the Audyssey processing, and it also happens to follow a nice tilting curve when adjusted.

Adjusting bass to +1dB and treble to -5dB causes the curves to match, adjusted by observing the frequency response measurements.
It is possible to adjust this by ear, using pink noise, and adjust until the tonal balance of the noise seems the same for no Audyssey and Audyssey with tone adjustment. 

Frequency response, No Audyssey and Audyssey Flat with tone control adjusted tilt

Now we can see that the tilt of the frequency response matches for both without and with Audyssey Flat enabled. The 1/1 smoothed curves show the averaged tilt of the reponses.

Further improvements

This set-up should be re-calibrated to get the best possible response in the 80-200Hz range, by selection of crossover, distance adjustment and Audyssey recalibration.
Here is how I would proceed:

1. Equalize the subwoofer system to flat using the subwoofer DSP.
2. Run Audyssey to calibrate.
3. Re-enable the house-curve on the subwoofer DSP.
3. Adjust crossover and distance for subwoofer to get the best possible response with Audyssey enabled.

Saturday, March 29, 2014

Audibility of peak limiting

Peak limiting and clipping is used to make music seem louder, but does it really work that way?
No - removing the peaks actually reduces impact and brutality and makes it sound flat and boring.


Typical sources of peak limiting in audio reproduction are loudspeakers and power amplifiers.
This can obviously easily be avoided by turning it down a bit, or get larger speakers with better sensitivity.

Music can also be destroyed in the production process, where removal of peaks using brickwall limiters is more common than not today.
Dynamic compression, brickwall limiting and peak clipping in music is well known today as the Loudness War.
The kind of signal processing used causes loss of transient peak amplitude and adds distortion.
It is this type of signal destruction that is investigated here.

Upon visual inspection one can see that the limited waveforms are clearly changed, and it may be difficult to understand why this is not also very easy to hear.
But the loss of signal amplitude happens in a very short period of time, it is not necessarily easy to detect unless you know what to listen for.
There is no apparent change in overall sound level, and the tonal balance is not changed at all.


Reduced transient peak amplitude will cause loss of tactile impact and punch when played reasonably loud through loudspeakers.


A music signal with very dynamic and transient content - mostly drums - is processed with a limiter to create peak limited test signals.
Three different test signals were made - original, -3dB limited and -6dB limited.

The original and the distorted signals are ABX-compared listening on headphones and on the big system.

Test signals



The less -3dB limited signal was difficult to distinguish from the original, and the difference was perceived as more noticeable when playing reasonably loud on loudspeakers.
The difference was noticeable also on headphones, the limited signal seems slightly flatter sounding on the loudest drum hits.
On loudspeakers there was a barely noticeable loss of physical transient impact.

For the heavily -6dB limited signal differences could be verified as audible even when not playing very loud, there was distortion causing a reduction of clarity and perceived sound quality.
On loudspeakers there was a clearly noticeable loss of physical impact.

ABX results, headphones:
Limited -3dB: Total: 8/10 (5.5%)
Limited -6dB: Total: 10/10 (0.1%)

ABX results, big system:
Limited -3dB: ABX: 16/14/0.21%
Limited -6dB: ABX: 10/10/0.1%


The results does not dismiss the hypothesis that peak transient amplitude is important for tactile impact and punch.

The less -3dB limited signal was difficult to distinguish from the original.
When looking at the waveforms the signals are clearly different, but when listening the differences are not so easy to detect reliably.
Even the -6dB limited signal could pass unnoticed if there was no original reference to directly compare it against.
Also, the reproduction equipment - mainly speakers - must be able to reproduce the transients without additional distortion.

The combined results from this limiting test and the phase distortion test indicates that it is possible for such errors to be introduced unnoticed in the music production process - they simply can not hear it.

The important part is that the severity of the transient distortion depends on how you listen.
When sitting down to really enjoy your favourite music, you turn it up, and that is when the lack of life and dynamics is most apparent.

Loud music production style utilizing heavy compression and limiting has several other negative effects on sound quality.
The negative consequences of lost transient impact investigated here is only one part of the destruction.

Tuesday, March 25, 2014

Audibility of phase distortion

Phase distortion at low frequencies causes audible degradation of music.
When is it audible, what causes it and how does it affect sound quality.


Phase distortion means that different tones gets a different time delay.
It has been a general assumption that phase distortion in audio reproduction is not audible.

Typical sources of phase distortion in audio reproduction are loudspeakers and room acoustics.

Music can also be destroyed in the production process, where dynamic compression can cause effects similar to phase distortion.
Dynamic compression in music is well known today as the Loudness War.
The kind of signal processing used causes loss of transient peak amplitude, and smearing of the same transients over time, to compensate for the amplitude loss.
It is this type of signal destruction that is investigated here.

Upon visual inspection one can see that the phase distorted waveform is clearly changed, and it may be difficult to understand why this is not also very easy to hear.
But phase distortion means that the only change to the signal is related to timing, the spectral frequency distribution is the same, and there is no nonlinear distortion added.
The energy of the signal is preserved, though very large phase shifts will cause the energy to be smeared out across a longer time interval.

One thing that may be important is that the transient peak amplitude is reduced in level, and this is what is presented as a hypothesis for audible difference here.
This reduction in peak level will potentially reduce the maximum peak sound pressure that is experienced.


Reduced transient peak amplitude will cause loss of tactile impact and punch when played reasonably loud through loudspeakers.


A music signal with very dynamic and transient content - mostly drums - is processed with an allpass-filter to create a phase shift that is large enough to change the signal so that the peak level is significantly reduced and the waveform is visually changed.
Three different test signals were made - original, phase distorted, severely phase distorted by running all-pass twice.

The original and the phase-distorted signal is ABX-compared by listening on headphones and on the big system.

The big system is a full-range system with reasonably flat phase and group delay through most of the bass range.

Test signals: Original, 1x allpass, 2x allpass


Listening on headphones, the phase distorted music could not be detected as different.
Only when comparing to the severely phase distorted signal could a difference be verified, though now the differences were very clear as the distorted signal sounded more boomy and smeared in the bass.

The phase distorted music signal could be verified as different from the original in the ABX-test, on the big system.
The observed subjective differences are that the phase distorted signal lost some impact and punch.

ABX results, headphones, allpass 2x:
Total: 10/10 (0.1%)

ABX results, big system, allpass:
ABX: 16/14/0.21%


Phase distortion at low frequencies is audible and can cause a significant degradation of music, in certain specific situations, such as when listening on high quality loudspeaker systems at fairly loud levels.

The results does not dismiss the hypothesis that peak transient amplitude is important for tactile impact and punch.

In other situations, such as when listening on headphones, or at lower volumes or on lesser capable speakers, it was not possible to detect any audible difference between the phase distorted and original signal, as long as the added phase change and time delay is within reasonable limits.
This also explains how it is possible that such errors are introduced in the music production process - they simply can not hear it.

Next up

A similar test for peak limiting is coming up soon - is it audible, and how does it affect the sound.

Tuesday, March 4, 2014

2-channel with subwoofers set-up

I present the set-up of a 2-channel system, with simple subwoofer calibration.

With measurements shown, so that we can see what is actually going on.

And I will show how to try without measuring, only using a pink noise signal that can be played back from a file.

This is a standard 2-channel system with digital or analog source, controlled by an analog preamplifier.
No DSP, no room correction, no bass management.  
The subwoofers have no digital processing, the only adjustments are level, crossover frequency (low-pass filter) and phase.

The main speakers will play full range down to whatever frequencies they can output, there is no low bass cut-off. 

This configuration is what many enthusiasts actually will have for a 2-channel system.
Now I will show that it is possible to integrate subwoofers into such a system with great success, even though there are limitations and compromises will have to be made.

The addition of capable subwoofers transforms this system into full-frequency range with reference quality bass.

This is a nice, smaller system, with satellite main speakers driven by a class-A amplifier with low output power.
Max SPL is rather low, we hope for a nice and pleasant sound with a true three-dimensional presentation and great bass with precision, slam and capacity all the way down to far below hearing range.

Summary of calibration adjustments:
  1. Placement not too far from the main speakers, but try to get positions with good gain and smooth response.
  2. Adjust phase individually on subwoofers to get the best response of subs only.
  3. Low crossover, 60Hz, max 80Hz.
  4. Use RTA (Real-Time Analyzer) to see effects of adjustments in real-time. 
  5. Adjust crossover and level on subwoofers to get as close to your target response as possible.
  6. While having the measurement gear out this is a good time to try alternative positions for the main speakers.


The important parts for this exercise are the main speakers, subwoofers and the room.
Source and amplifier is not that important for set-up and calibration, as the process and measurements will be the same for any amplifiers without processing for crossover and delay.

3.6m width x 4.5m length.
Door opening on right wall, large opening into other room through rear wall, window on left wall.
Other room length 4.1m together with this room defines lowest length node at approximately 8.6m.
Wood panel on all walls and ceiling, wood floor.
Some chairs and a round table, media console for audio equipment.
No additional acoustic treatment of significance.

Low frequency response of this room is dominated by the total length of both rooms and the door opening acting as the port in a resonator where the room is the cabinet. 
This causes resonances from around 15Hz up to around 25Hz, where room response is strong. 

Main speakers:
Small satellite system with 8" bass driver sealed, 2x 14cm mid, 1" dome HF.

2x small Compact Horn subwoofers with 10" driver (105dB/20Hz/2pi/1m, equals approx 12" ported or 15" sealed of high quality).

Measurement instrumentation:
REW measurement software, calibrated microphone, computer, USB I/O.

Initial placement

We start out with the system set up like this:

Room with L+R speakers and subwoofers initial placement

We want 2 subwoofers to be able to get a reasonably smooth response.
That also gives more output (+6dB), so that we can use smaller subwoofers, it is easier to place 2 smaller boxes compared to one giant monster.

The subwoofer locations can be determined by measurement, either by measuring at the listening position (LP) while moving subwoofers, or by placing one subwoofer at the LP and then move around with the mic.
Use the RTA in REW for this, run Pink PN Noise, then you can see the response in real-time while moving the mic around.

The fact that we have no way to adjust for time differences between mains and subwoofers will limit placement options.
Ideally the subs should be a little closer to the listening position (LP).
Here we start out with a practical location that also works; in front of the main speakers, towards the corner.
Bass is strong, and because the sound radiation is from the front of the subwoofer, it is radiating at some distance away from the corner, which usually gives a smoother response.
In a set-up where the best sound quality is the goal, we do not want the main speakers in the corners, so this location is free to use.

Placement of one subwoofer towards the rear of the room, behind the listening position, can also be an option.
What will work in your room will depend on the acoustic properties of the room, as well as obvious practical considerations.

Initial measurements

We measure the main L and R speakers from the listening position (LP):

Frequency response L+R no subwoofers initial position

And the 2 subwoofers:

Frequency response subwoofers before any adjustments

Sub phase adjustment

First the phase is adjusted on one of the subs to fill the response dip around 50Hz.
For this particular room and sub locations this adjustment makes a large difference, but that may not be the case in a different room.
Obviously, the room is not acoustically symmetric for both sub locations. 
Use RTA, adjust while monitoring the response in real-time.

RTA running for subwoofer phase adjustment

Frequency response subwoofers phase adjusted

Then the phase on both subs are adjusted so that they fill in with the main speakers.
Use RTA, watch how the response changes around the crossover frequency, adjust to max level.

Frequency response L+R+subwoofers initial position

Sub level and crossover

Adjust to achieve a reasonable frequency response that extends the natural downwards tilt, and you may prefer some extra level at the lowest frequencies below 40-30Hz. 
Consider choosing a crossover rather low, below 80Hz or lower, to minimise effects from time alignment issues.
Note that it may be necessary to adjust phase after changing the crossover.  

All this is best to do with the RTA, so that you can see the changes in real-time.

Adjustment without measuring

Using a pink noise signal and your ears to adjust phase, level and crossover for subs may at least give some improvement compared to no adjustment at all.

Play a 200Hz bandwidth-limited pink noise signal from file.
Adjust phase on one sub for loudest possible signal.
Then adjust phase on both subs to get loudest level around the crossover frequency.
This is the more difficult part, because is is not easy to know how the noise should sound when the setting is correct.
Level and crossover is not easy to adjust using pink noise, because you would have a problem knowing how it should sound when everything is right, unless having a reference readily available to compare with.
Headphones may be a solution - listen on headphones, then compare to how it sound on the system and adjust to same sound.
It may be better to use some known music with bass, as actual music is more likely to reveal when something is way off, compared to a noise signal that still sound like what it is - noise.
Obviously this is something that is not very easy to get right without measurement.
The result depends heavily on the chosen program material and the listeners ability.

Pink noise signal files can be downloaded from Kvålsvoll Design here:

Pink Noise 100Hz limited
Pink Noise full bandwidth

L+R position

Seems like the tilt is a bit too much down at higher frequencies, and it also sounds rather dark with recessed highs.
In the midrange the response could be more flat, this is likely caused by boundary reflections from walls and floor around the speaker.
So, we try to relocate the speakers a bit closer to the listening position, making the distance to the front wall larger.
The larger distance between the speakers and the front wall also usually improves imaging and perceived clarity in the midrange.
The speakers are also raised around 10cm to bring the tweeter on-axis.
Angling is adjusted so that on-axis points exactly towards the listening position.

L+R speakers moved to new position closer to listening postion and raised

The response now looks much better in the midrange, and the tilt is reduced.

Frequency response L+R+subwoofers position adjusted

Frequency response L+R+subwoofers before and after position adjusted

The impulse response is surprisingly good, especially considering the type of speaker and no acoustic treatment in the room.

Impulse response

The step-response can be used to see if the subs are properly time aligned with the mains.
Well, they are not, but that is not possible to correct when we have no delay adjustment on the mains.

Step response 

The group delay also provides useful information about timing issues.
If subs and mains are properly aligned they will end up in-line with the same average group delay in the area around the crossover.
This can be difficult to see because this frequency range is usually affected by room and boundary reflections causing large group delay deviations.

Group delay

Checking subwoofer capacity

We check the output and distortion of the subwoofers to see if it is likely that they can match the main speakers.

Distortion measurement sweep show 110dB at 20Hz with 1.7% THD

Indeed, the small Compact Horn subwoofers easily outperform the mains with 110dB at 20Hz with 1.7% distortion.
They can obviously do a lot more, I did not bother to check, as that requires recalibration of the mic amplifier for more headroom.

How does it sound

The subwoofers seem well integrated, providing full-size bass with a heavy bottom, both impact and weight, dry and powerful.
It does not get boomy or muddy in the bass even when the bass is running a little hot.

The relocation of the mains further away from the front wall improved perception of depth and clarity in the lower midrange. 

The biggest problem is limited output capacity, it simply can not play loud.
The bass range is not as smooth as one can experience from the best systems, and we know from the measurements that the response is not entirely flat.

Further improvements

The bass is quite heavy at the lowest frequencies, level is low around 50-70Hz, and there is a peak at 100Hz.
This can possibly be improved by moving one or both subwoofers, and adjust subwoofer level and crossover.

Since this set-up was done primarily for this article, I am satisified for now.
If anyone in the neighbourhood wants to hear and experience this system please feel free to contact me.

If you are interested in reading more on audio systems and set-up, check out my article How to  Set-up a Home Theater System.