The ABC of speakers - Distortion - the human ear is seduced by low distortion

[siddharthdas]

Distortion is one of the ways our brain is trained to understand loudness. It might come as a surprise to some that you can play music to deafening loudness without realising it. It is only when you try to talk to someone next to you, that you realise how loud the sound really is. Even if that were not the case, you do not wish your speaker to add or subtract anything to the source - also known as distortion. One type of distortion that we pay attention to, is harmonic distortion - i.e. spurious signals generated by the audio chain, that are multiple of the fundamental frequency. Other signals that are not harmonic are called noise. So THD+Noise is often a measure of total distortion generated by a system.

It is clearly desirable that sounds produced by a system, that are not present in the input signal, be of such loudness that they are undetectable by and therefore inaudible to the human ear. Before we get to how low is really low, lets understand magnitude. -24db of THD+N is 2^8 times OR 256 times less loud than the primary signal. At -24 db distortion, it sounds incredibly good to me intuitively. So anything over -30db of THD is really goo/d.

The human ear is pretty good at ignoring uncorrelated noise. Hence in the THD+N we actually focus predominantly on THD. Measuring that is also rather straightforward. Play a "fundamental" tone really loud and measure all the harmonic frequencies generated spuriously by listening for them. As long as those are all below -48 db, we are in good shape. And if not, you know where you stand. So yes, great

Great speaker systems have very low distortion.

Speakers aside, tube amps are known for their even order distortion attributes. They might sound pleasant even, but they are not true to source. Which brings up that other question of "truth" (original signal) vs. "preference" (an even order harmonic is many a time pleasant to listen to), and no more is that more relevant than the unique sound of the tube amp. Cheers!

 

[siddharthdas]

Distortion is one of the ways our brain is trained to understand loudness. It might come as a surprise to some that you can play music to deafening loudness without realising it. It is only when you try to talk to someone next to you, that you realise how loud the sound really is. Even if that were not the case, you do not wish your speaker to add or subtract anything to the source - also known as distortion. One type of distortion that we pay attention to, is harmonic distortion - i.e. spurious signals generated by the audio chain, that are multiple of the fundamental frequency. Other signals that are not harmonic are called noise. So THD+Noise is often a measure of total distortion generated by a system.

It is clearly desirable that sounds produced by a system, that are not present in the input signal, be of such loudness that they are undetectable by and therefore inaudible to the human ear. Before we get to how low is really low, lets understand magnitude. -24db of THD+N is 2^8 times OR 256 times less loud than the primary signal. At -24 db distortion, it sounds incredibly good to me intuitively. So anything over -30db of THD is really goo/d.

The human ear is pretty good at ignoring uncorrelated noise. Hence in the THD+N we actually focus predominantly on THD. Measuring that is also rather straightforward. Play a "fundamental" tone really loud and measure all the harmonic frequencies generated spuriously by listening for them. As long as those are all below -48 db, we are in good shape. And if not, you know where you stand. So yes, great

Great speaker systems have very low distortion.

Speakers aside, tube amps are known for their even order distortion attributes. They might sound pleasant even, but they are not true to source. Which brings up that other question of "truth" (original signal) vs. "preference" (an even order harmonic is many a time pleasant to listen to), and no more is that more relevant than the unique sound of the tube amp. Cheers!

I wrote that while rather groggy with sleepiness. So missed the most essential part - which is for those of us who'd like to know how to measure distortion, and the difference between noise and harmonic distortion.

Since pretty much every natural sound has harmonics (pure tones sound horrible; natural sound has harmonics because every vibrating object vibrates multi-modally and thus generates multiples of any fundamental frequency naturally. Did that make sense?

Well, so natural sounds produced by natural sources consist of say, a 100hz fundamental and lot of harmonics which are EVEN multiples of 100 hz - 200 hz, 400hz etc. You can easily see that that membranes, strings and columns or air only vibrate with EVEN harmonics. So, in the hierarchy of distortion there's, even order harmonic distortion, odd order distortion and finally noise which consists of frequencies which are not multiples of the fundamental, and therefore uncorrelated to it.

Turns out since such sounds (uncorrelated i.e..not multiples of the fundamental i.e. noise) are not confused with part of the original by our brain, they are more easily ignored by the brain or at least noticed by our brain as alien, as not part of the intended reality.

ODD order harmonics are unnatural and therefore unpleasant. ODD order harmonic distortion is what probably makes sound irritating. EVEN order harmonics, since also naturally produced by natural sound sources, are likely to be confused by our brains as part of the original, and are not unpleasant and therefore deceptive - they add pleasantly to the illusion of reality, except they are unreal - like by tube amps.

The way to read distortion data then is to look separately for EVEN, ODD and noise while playing a fundamental and do that for the entire range for a particular driver. And pay particular attention to ODD order harmonics.

So there!

 

[Hari Iyer]

Noise can be used to mask distortion. If the Noise level is higher than distortion, you shall hear the Noise and not the distortion. Try this - in a distorted recording playing in a quite room , switch on your noisy ceiling fan. Suddenly the distorted music sounds better as the distortion is getting masked by the Noise. If you jack up the volume to exceed the Noise level of the fan again the same music sounds distorted.

 

[siddharthdas]

Noise can be used to mask distortion. If the Noise level is higher than distortion, you shall hear the Noise and not the distortion. Try this - in a distorted recording playing in a quite room , switch on your noisy ceiling fan. Suddenly the distorted music sounds better as the distortion is getting masked by the Noise. If you jack up the volume to exceed the Noise level of the fan again the same music sounds distorted.

Likewise, undistorted music sounds amazing at night when ambient noise i.e. noise floor falls by 20-30 db. As much as a city's ambient noise seems inaudible inside homes, it's quite amazing intuitively realise how sound just opens up at night. Which also means that as much as ultra-low levels of sound aren't consciously detectable as signal or noise, they are quite perceptible in the way they mask the faintest signals and thus decrease dynamic range.

Corollary - dithering

 

[Kannan]

In a phase coherent setup as ambiant noise drops, especially at night and even more so in relatively untreated rooms, the stage opens up to feature a darker background even at lower decibels. Subtle details become audible and instrument separation is that much more cleaner.
A well treated room already has the ambiant noices well under control.

 

[siddharthdas]

In a phase coherent setup as ambiant noise drops, especially at night and even more so in relatively untreated rooms, the stage opens up to feature a darker background even at lower decibels. Subtle details become audible and instrument separation is that much more cleaner.
A well treated room already has the ambiant noices well under control.

In a phase coherent setup as ambiant noise drops, especially at night and even more so in relatively untreated rooms, the stage opens up to feature a darker background even at lower decibels. Subtle details become audible and instrument separation is that much more cleaner.
A well treated room already has the ambiant noices well under control.

Interesting topic. Soundproofing controls ambient noise. Room treatment alone may not entirely accomplish that as in there are trade-offs. Highly absorbent rooms kill reverberant sound fields too and start to sound unnatural. If they don't they won't make any meaningful difference to ambient noise unless of course the room itself it soundproofed.

 

[Kannan]

Interesting topic. Soundproofing controls ambient noise. Room treatment alone may not entirely accomplish that as in there are trade-offs. Highly absorbent rooms kill reverberant sound fields too and start to sound unnatural. If they don't they won't make any meaningful difference to ambient noise unless of course the room itself it soundproofed.

Yes .. treatment for HT and 2-channel audio needs a different approach. I have seen many high end showrooms now having dedicated home theater auditions where they also demo stereo.

 

[Vineethkumar01]

To play the devil's advocate, here is a summary of research done by Earl Geddes, which says non-linear distortion in loudspeakers is imperceptible if it is reasonably low enough and that there is not much point in going for arbitrarily low distortion levels (in loudspeakers)

http://www.gedlee.com/Papers/The%20Perception%20of%20Distortion.pdf

He has done a lot more research in this area and has come up with a metric that correlates well with perceptible distortion, unlike THD, which has a very low correlation. All those papers can be obtained from his website.
He also says that linear distortion, especially when accompanied by early delay times, is highly audible and that audibility is level dependent.. i.e., such distortions are more easily perceived at higher playback levels than lower playback levels. The most commonly found linear distortion of this category is diffraction effects caused by improper design of loudspeakers.

On the other hand there are companies like Purifi which have identified some forms of audible distortion and as per them, have taken adequate steps to minimize it in their drivers. Relevant resources
1) https://purifi-audio.com/2019/05/02/distortion-the-sound-that-dare-not-speak-its-name/
2) https://purifi-audio.com/2019/12/12/imd/
3) https://purifi-audio.com/2019/12/07/amfm/
4) https://purifi-audio.com/2020/04/28/dist/

 

[siddharthdas]

To play the devil's advocate, here is a summary of research done by Earl Geddes, which says non-linear distortion in loudspeakers is imperceptible if it is reasonably low enough and that there is not much point in going for arbitrarily low distortion levels (in loudspeakers)

http://www.gedlee.com/Papers/The%20Perception%20of%20Distortion.pdf

He has done a lot more research in this area and has come up with a metric that correlates well with perceptible distortion, unlike THD, which has a very low correlation. All those papers can be obtained from his website.
He also says that linear distortion, especially when accompanied by early delay times, is highly audible and that audibility is level dependent.. i.e., such distortions are more easily perceived at higher playback levels than lower playback levels. The most commonly found linear distortion of this category is diffraction effects caused by improper design of loudspeakers.

On the other hand there are companies like Purifi which have identified some forms of audible distortion and as per them, have taken adequate steps to minimize it in their drivers. Relevant resources
1) https://purifi-audio.com/2019/05/02/distortion-the-sound-that-dare-not-speak-its-name/
2) https://purifi-audio.com/2019/12/12/imd/
3) https://purifi-audio.com/2019/12/07/amfm/
4) https://purifi-audio.com/2020/04/28/dist/

So Linkwitz has a detailed page on linear distortion. Very informative plus times of data - https://www.linkwitzlab.com/diffraction.htm
Appears to draw the exact opposite conclusion of earl geddes. The only thing we can do I guess is experiment and trust our own judgement.

Have been tracking purifi for a while now - their drivers can potentially solve a lot of design problems in the entire midrange to upper bass region. (Unrelated- does anyone have any experience with them?). Although have to confess i didn’t quite understand their write ups. Didn’t quite understand how they solve the problem of IM distortion from simultaneous reproduction of sound at two ends of the spectrum by the same driver. Also given their super large magnets, I wonder about their suitability for open baffle applications.

Meanwhile, I too did not mention linear distortion at all. But I guess it is worth mentioning that linear distortion is about changes to primary response from artifacts such as baffle and the room itself. If the measured response is ok plus dispersion. Is also ok then I guess the speaker passes muster on that count. Room
Room related issues are altogether another thing - enough has been said about that. I myself like dipoles or controlled directivity solutions that address that. I do not entirely ageee with Geddes that non linear distortion doesn’t matter. End result of an implementation design though is all that matters. I’d keep THD+N as low as possible especially if it bothers me, which alas it does

 

[Vineethkumar01]

So Linkwitz has a detailed page on linear distortion. Very informative plus times of data - https://www.linkwitzlab.com/diffraction.htm
Appears to draw the exact opposite conclusion of earl geddes. The only thing we can do I guess is experiment and trust our own judgement.

Linkwitz was a great engineer. However, I trust Earl Geddes on different aspects of waveguide design, part of which is the study of diffraction and its impact on the overall speaker design. The problem with Linwitz's article on diffraction is that it is a completely frequency domain-based study and analysis of diffraction. The crucial aspect of impact of diffraction in the time domain doesn't seem to be talked about at all. The main problem with diffraction is not only the frequency response anomalies it causes but also the very early reflections well within the 5ms window. The amplitude of these reflections becomes more significant at higher SPLs and causes fragmentation of the soundstage and other undesirable effects. This aspect has been proven in Dr Earl Geddes experiments too. Also, this view is shared by other world-renowned designers. In my builds too, I have experienced this to some extent. Hence I believe in this theory.
Of course, all of us can trust our judgements as with anything else..

Didn’t quite understand how they solve the problem of IM distortion from simultaneous reproduction of sound at two ends of the spectrum by the same driver.

Well, Purifi tries to solve the problem of force factor modulation due to the BL non-linearity, which causes the intermodulation distortion products. Here is how they do it and more from Lars Risbo himself:

(from around 27minutes onwards)
I can assure that the 2 hours spent watching this video is worth it and really helps one understand the issues and potential solutions involved in modern loudspeaker driver design.

Also given their super large magnets, I wonder about their suitability for open baffle applications.

Open baffle may not probably be the application Purifi drivers were designed for in the first place. They tried to address the problems involved in making a small speaker with big bass and clean midrange first. That said, their driver designs, sizes, and overall scope of applications are expanding fast. Maybe they will come up with one for dedicated open baffle applications in future. Even now people are reporting good results in open baffle midrange applications like in this interesting thread.

Purifi Drivers for Open Baffle

Hi All, since reading about Purifi drivers, I'm thinking about using them in an open baffle system. Those drivers show fantastic test results from @HiFiCompass , erinsaudiocorner.com etc. Most of the parameters should be very nice for using them in OB systems: high xmax, very low distortion...

www.diyaudio.com

 

[siddharthdas]

Linkwitz was a great engineer. However, I trust Earl Geddes on different aspects of waveguide design, part of which is the study of diffraction and its impact on the overall speaker design. The problem with Linwitz's article on diffraction is that it is a completely frequency domain-based study and analysis of diffraction. The crucial aspect of impact of diffraction in the time domain doesn't seem to be talked about at all. The main problem with diffraction is not only the frequency response anomalies it causes but also the very early reflections well within the 5ms window. The amplitude of these reflections becomes more significant at higher SPLs and causes fragmentation of the soundstage and other undesirable effects. This aspect has been proven in Dr Earl Geddes experiments too. Also, this view is shared by other world-renowned designers. In my builds too, I have experienced this to some extent. Hence I believe in this theory.
Of course, all of us can trust our judgements as with anything else..


Well, Purifi tries to solve the problem of force factor modulation due to the BL non-linearity, which causes the intermodulation distortion products. Here is how they do it and more from Lars Risbo himself:

(from around 27minutes onwards)
I can assure that the 2 hours spent watching this video is worth it and really helps one understand the issues and potential solutions involved in modern loudspeaker driver design.


Open baffle may not probably be the application Purifi drivers were designed for in the first place. They tried to address the problems involved in making a small speaker with big bass and clean midrange first. That said, their driver designs, sizes, and overall scope of applications are expanding fast. Maybe they will come up with one for dedicated open baffle applications in future. Even now people are reporting good results in open baffle midrange applications like in this interesting thread.

Purifi Drivers for Open Baffle

Hi All, since reading about Purifi drivers, I'm thinking about using them in an open baffle system. Those drivers show fantastic test results from @HiFiCompass , erinsaudiocorner.com etc. Most of the parameters should be very nice for using them in OB systems: high xmax, very low distortion...

www.diyaudio.com

Well so with narrow enough baffles @Vineethkumar01 only the super upper registers will be impacted, say above 4K where driver and baffle dimensions can no longer be managed for linear distortion. I imagine - that plus using stuff like felt around drivers for absorption probably is all we can do to manage these effects. Should be enough for most part, no?

 

[Vineethkumar01]

@siddharthdas: Diffraction mitigation can be done in multiple ways. The classic approach is to use significant rounding at baffle edges, chamfers, and rounded chamfers (probably the best approach in this category). Using rounded chamfers will also give benefits in the directivity transition from mid to tweeter.
Eg: One of the best approaches with all direct radiating drivers

Next approach is to use waveguides in an appropriately shaped baffle like in my build. Offcourse wavguide itself should be made properly for this to happen. Here the rounding needs to start at the edge of wavguide ideally. But due to manufacturing constraints I couldn't get it done.

The next approach is even better. The entire mid+tweeter cabinet itself is made to act like a waveguide along with the middriver that acts as the tweeter waveguide in this coaxial driver config.


The overall best approach is not create diffraction in the first place. Use infinite baffle or significantly large baffle mounting of the drivers. Eg: Properly designed in wall/on wall speakers with large enough rounded transition to walls. For this i don't have a pic yet