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Study of the effects of Nonlinear Distortion on the Perceived Sound Quality

Pinox67

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Introduction
As a hi-fi enthusiast for many years I have always tried to deepen the themes underlying sound reproduction and psychoacoustics. For the latter topic, some time ago I came across the interesting book (on line here) "Premium Home Theater - Design & Construction" by Earl Geddes & Lidia Lee (or GedLee). Here are some considerations that have changed a lot the way I conceive of audio playback. At page 58, it is reported verbatim, about the relationship between classic distortion measurements and listening sensation:
  • There is virtually no correlation between Total Harmonic Distortion (THD) or Intermodulation Distortion (IMD) measurements of a system and the subjective impression of the sound quality of that system. The correlations were weak, but most shockingly they were negative—according to these tests people liked THD distortion. This is actually somewhat true in general that people prefer some forms of distortion to no distortion.
  • Signal based distortion measurements (THD, IMD, MTD), which are based on a purely mathematical formula which does not take into account the characteristics of human hearing, do not hold out much hope for ever being an accurate measure of subjective impression.
  • Measures need to be based on the actual nonlinear characteristic of the system and scaled to account for the human hearing system.
I would like to remind you briefly that nonlinear distortions are due to the different gain value that an amplifier applies for different input signal levels, generally independent of its frequency. These create new harmonic components that are added to the original signal, the shape of which then determines effects in listening. I omit from the following considerations the effects of linear distortions, on which it is relatively easier to act.

The preference of the presence of distortion (even if of a specific type, as we will see shortly) over its absence may at first appear contrary to common sense. In fact, it is to be expected that, to obtain the same sensations desired by the artist, it is necessary to reproduce the original music track with a system that playbacks any music track with the highest level of fidelity. Therefore, among the various parameters that characterize the components of a system, the nonlinear distortion should be as low as possible.

By integrating personal experience with an in-depth reading of the works of GedLee and others, such as that of Bob Katz (here) or Nelson Pass (here) to name a few, it emerges that we need to consider the entire chain of sound, from production to reproduction. From the moment the signal is captured from the source to its recording on disk (to be nostalgic), the audio signal passes through a series of inherently non-linear electronic systems. Then it moves on to the reproduction chain, again consisting of non-linear components. Each component in the chain adds nonlinear distortions to the signal output from the previous component. All these distortions, despite being singularly very small to the elementary test signals, are much less small with the real signals and multiply in the signal chain, resulting in high order harmonic distortions on our loudspeakers. These can be potentially audible and they have nothing to do with the sound as it was generated by the original source. Unfortunately it is practically impossible to identify and eliminate these distortions that create effects such as listening fatigue and lack of naturalness, even assuming that the sound engineer has not made any mistakes.

How to get out? A help is offered to us by nature, which has endowed us with a highly complex and nonlinear hearing system. Specifically, we can leverage the effect of masking, which manifests itself by raising the threshold of hearing of signals close to others of a higher level. Lossy compressors such as MP3 are also based on this principle. Many details are always in GedLee's book, Chap. 2: below a graph from the book showing the threshold raising depending on the dB level of a masking tone.

Screenshot 2021-07-01 at 09.49.44.png

Hence the justified practice of building amplifiers that add low-order nonlinear distortions in the playback, that is, low-order distortions; audiophiles with a preference for "tube sound" are familiar with them by the name of "euphonic" distortions. These generally have the dual effect of:
  1. add a sort of loudness to the original music content;
  2. hide unwanted higher order distortions (already contained in the music track or created by the playback chain).
However, the excess of these components has the effect of obscuring the sonic details or making it too artificial. In fact, the quantity of the different harmonics added is one of the aspects that most determines the "character" of an amplifier and affects the "winning" combinations with other audio components.

My study described below, which has just begun using personal and friends' resources, therefore aims to investigate in detail how specific amounts of low order distortions affect perceived sound quality, using real music. For the above, I expect that preferences can be different depending on:
  • audio playback chains;
  • type of music;
  • mastering of audio track;
  • listening levels.

Test Preparation
As first step, I wrote a program that adds a configurable amount of second and third harmonic distortion (asymmetric and symmetric distortions, respectively) to a digital audio track of any sample rate or bit depth. In this way it is simulated the addition of "good" nonlinear distortions in the "original" signal. The output track is (automatically) compensated to avoid clipping and to eliminate any DC introduced. Moreover, in order to avoid further distortions, it is subject to dithering and noise shaping in the recoding downstream of the high-precision internal processing. The idea is that if we use a downstream amplification chain that is as "transparent" as possible, we can thus get a fairly precise idea of the effect on the perception of these harmonics.

To test the program I worked first with test signals. For example, a pure tone input at 1KHz 0dBFs (96KHz / 24bit) has this spectrum:

Screenshot 2021-06-30 at 16.16.18.png

The program outputs tones of this shape by setting -40dB and -60dB of second and third harmonic distortion respectively:

Screenshot 2021-06-30 at 16.17.34.png

For a bi-tonal signal at 5KHz and 6KHz, 44.1KHz / 16bit:

Screenshot 2021-06-30 at 16.24.18.png

We have in the output for distortion at -40dB of third harmonic:

Screenshot 2021-06-30 at 16.25.01.png

While for distortion at -40dB of second harmonic only we have:

Screenshot 2021-06-30 at 16.25.33.png

Below is what happen when a distortion of -70dB in both the second and third harmonics is applied two times to a pure tone at 1KHz, 96KHz / 24bit (it simulates a chain of two devices with same nonlinear distortion):

Screenshot 2021-06-30 at 18.16.28.png

The level of second and third harmonics are increased of 6-7dB and appear higher order harmonics (fourth and fifth), albeit at low levels.

With real musical tracks, I tried to subtract the original signal from the distorted one, obtaining a distorted copy at very low level of the original track, quite similar at listening.

After the program testing, to start with real listening sessions, I selected 4 well known Jazz / Pop music tracks with a good recording quality. For each I have created 2 further versions: one with main distortion of the second harmonic (-50dB) and the other of the third (-70dB). I chose high values in order to make the perceptual effect of each type of distortion evident. The value of Gm(f), the metric of GeeLee that tries to correlate distortion to subjective rating taking into account the masking effect, i.e.:

Screenshot 2021-06-30 at 17.30.23.png

is always less than 1 with these values (T(x,f) is the nonlinear transfer characteristic). From each music track it has been therefore selected significant parts of 15-20 seconds, each predominantly for female voice, or for percussion, wind or string instruments.


Test Execution
The 3x4 music tracks above were played at controlled levels (about 82dB) several times at a very close distance on a couple of high quality solid-state audio systems, inserted in dedicated medium-small rooms treated acoustically. In each session the listeners naturally did not know which of the three songs they were listening to, randomly labeled with a number. For each session I asked to answer the questions:
  • which song is the most pleasant to listen to;
  • perceived differences between songs, if any.
At the moment I have only run test sessions with 3 people with experience in both audio production and reproduction.


Test Results
The small sample is quite concordant in the results:
  • Tracks with second harmonic distortion were preferred in about 75% of cases; 25% those of the third; surprisingly never the original tracks.
  • Tracks with second harmonic distortion was considered the warmer and with more "body"; other times too soft and a little confused.
  • Tracks with third harmonic distortion was considered the brightest and most defined; other times excessively defined and tiring.

Preliminary Conclusions
At the date the test results appear to be in line with those of GeeLee and other works. Of course, more extensive tests are needed with more people, also not trained and on medium quality audio systems, combining different distortion levels with listening levels and then with more audio playback systems, music types and recordings. Yes, it is not a fast task!
However, comments and suggestions are welcome to refine the study, as well as comparisons with similar experiences.
 
Last edited:

FeddyLost

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It would be great to know parameters of reproduction chain "end-to-end" and noise floor to be sure that additional distortion is not masked by anything.
82 Db is not much, but -60 and -70 Db is really low and barely achievable in real speakers.
Also in would be great to see measurement of exact spectrum at the listening place. Maybe your -50 Db in file became -35 in midbass at LP and induced a lot of IMD.

And you should in principle add somethind more "dense" like big orchestra with choir. "Warmth" and "body" will change labels with high distortion levels.
Something heavy might be exemplary also, but will require familiar listeners...
 
Last edited:

mt42

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The distortions in real audio are somewhat different (and a bit more complicated) from what you test for.
1) The main distortions in class-AB amplifiers are crossover distortions. These max at the output ~ 2V. They can not be modelled by a polynomial.
2) The main distortions in loudspeakers are bass / mid-range intermodular 2nd and 3rd order. While the 2nd order can be modelled by a polynomial, the 3rd can not.
3) The worst distortions are the distortions inserted during recording by incompetent sound engineers/producers trying to "improve" sound. There is nothing you can do about it.
 

Blumlein 88

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You might find software written by Pkane to be useful to you.

https://distortaudio.org/

https://distortaudio.org/pkharmonic.html

You've already written software yourself, but Paul's has some other features you might find useful and convenient.

Just as a thought, you could let test takers access the PKharmonic plug in and dial in 2nd and 3rd harmonics until they like it the best, and see if a common range is preferred by most people.
 

amirm

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Test Execution
The 3x4 music tracks above were played at controlled levels (about 82dB) several times at a very close distance on a couple of high quality solid-state audio systems, inserted in dedicated medium-small rooms treated acoustically. In each session the listeners naturally did not know which of the three songs they were listening to, randomly labeled with a number. For each session I asked to answer the questions:
I suggest first running a control test to make sure any audible effect is detected. Only then enter phase 2 of quantifying the differences if they exist.

You also need to perform a statistical analysis to make sure distortion was a significant factor and chances of guessing was less than 5%.
 
OP
Pinox67

Pinox67

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You might find software written by Pkane to be useful to you.

https://distortaudio.org/

https://distortaudio.org/pkharmonic.html

You've already written software yourself, but Paul's has some other features you might find useful and convenient.

Just as a thought, you could let test takers access the PKharmonic plug in and dial in 2nd and 3rd harmonics until they like it the best, and see if a common range is preferred by most people.

Yes, I had already seen this SW, very interesting. The problem is that my work environment is on MacOS, not Windows.
 
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Pinox67

Pinox67

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The distortions in real audio are somewhat different (and a bit more complicated) from what you test for.
1) The main distortions in class-AB amplifiers are crossover distortions. These max at the output ~ 2V. They can not be modelled by a polynomial.
2) The main distortions in loudspeakers are bass / mid-range intermodular 2nd and 3rd order. While the 2nd order can be modelled by a polynomial, the 3rd can not.
3) The worst distortions are the distortions inserted during recording by incompetent sound engineers/producers trying to "improve" sound. There is nothing you can do about it.

The goal of my study is not to identify every form of "bad" distortion (i.e., high-order) created in production that creates unpleasant effects to listen to. It is practically impossible to measure and eliminate it once inserted. If you know of any studies on the subject, I would be happy if you would point it out to me.

The goal of the study is to understand how the distortions you have indicated can be masked with other "good" distortions (i.e. low-order), specifically injected at some point in the reproduction chain, which make the sound more pleasant, without hiding the details of the original sound texture.
 
Last edited:

Gorgonzola

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...
Test Results
The small sample is quite concordant in the results:
  • Tracks with second harmonic distortion were preferred in about 75% of cases; 25% those of the third; surprisingly never the original tracks.
  • Tracks with second harmonic distortion was considered the warmer and with more "body"; other times too soft and a little confused.
  • Tracks with third harmonic distortion was considered the brightest and most defined; other times excessively defined and tiring.

Preliminary Conclusions
At the date the test results appear to be in line with those of GeeLee and other works. Of course, more extensive tests are needed with more people, also not trained and on medium quality audio systems, combining different distortion levels with listening levels and then with more audio playback systems, music types and recordings. Yes, it is not a fast task!
However, comments and suggestions are welcome to refine the study, as well as comparisons with similar experiences.
FWIW, and maybe no surprise to you, (though apparently to some), your results are also consistent with the subjective listening preferences professed by many, many, (dare I say hundreds of thousands :cool: ), of long-term audiophiles.

Congratulations, and keep up the good work. :)
 

MrPeabody

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Introduction
...
Hence the justified practice of building amplifiers that add low-order nonlinear distortions in the playback, that is, low-order distortions; ...

This inarguably implies that it is appropriate for the designer of an amplifier to design the amplifier to modify the sound in any way that the designer believes the owner of the amplifier will like, and to do this in a way where the owner has no control over it, i.e., the owner has no ability to switch it off, and no ability to adjust the level to suit their personal preference. This is inarguably a strong and manifest implication of what you wrote, and it just does not seem a particularly good idea to me.

If I went down to the corner audio store and the salesperson tried to impress me with an amplifier that obviously exaggerated treble and there were no provision for me to switch off this effect, I would be flabbergasted. Why is it deemed more tenable for non-linear distortion to be added in a manner not controllable by the user, vs. treble emphasis to be added in a manner not controllable by the user? This makes no sense to me, before I even think about the fact that whereas non-linear distortion cannot be reversed once it has been added, a treble emphasis is not difficult to reverse. Why would it be desirable for an amplifier to change the sound in a way that isn't controllable by the user and that once done cannot be removed?

I'll also mention that what you have advocated in effect, in the statement that I excerpted above, is that reality ought to be as lots of people imagine, where each different amplifier has its own distinct, characteristic sound signature. This idea does not appeal to me in the least. I shudder at the thought that the sound produced by my system would be affected by the amplifier in like manner as it is affected by the speakers. Isn't speaker coloration enough to have to contend with? In my notion of what is ideal, speakers should be like good amplifiers, i.e., not color the sound in an obvious way. Your statement that I excerpted above advocates the opposite, that amplifiers should be more like speakers. The very idea makes me cringe and makes me want to write stuff like I'm writing now. Except more strongly stated than I'm stating it now.

If anyone is predisposed to advocate the desirability of adjunct processors that add distortion of various types and at levels controllable by the user, this is a perfectly reasonable concept. I'm not certain that it would sell very well, but at least the idea isn't an affront to the fundamental principle of amplifier accuracy.
 

FeddyLost

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The very idea makes me cringe and makes me want to write stuff like I'm writing now. Except more strongly stated than I'm stating it now.
Being positive about presumed intent of researchers, I'd like to show you another side of this idea: distortion profiling.
Before hardware prototyping currently engineer usually simulate schematics and see how it will work with different loads, signal levels, etc. I think it might be useful when one designs amplifier that might sound good even in worst case scenario (first watt trouble or just klipping).
Good example of such profiling (intentional or not, i don't know) is here
https://www.stereophile.com/content/gryphon-essence-mono-power-amplifier-measurements
Class A biasing have short harmonics trail, Class AB have long harmonics trail with dominating 2nd.
And if we will measure different cases (i.e. up to 500 mW into low impedance = medium volume for medium floorstander with pair of woofers), a lot of "good sounding" and "bad sounding" amps with equal THD will differ at distortion spectrum.
For sure, if engineer is put into tight economy restrictions, he can deliberately increase distortion up to acceptable border to prevent something "not pleasant for ear" otherwise. Like adding +10 db 2nd harmonics to mask long trail of higher orders that can't be removed within fixed BOM.
PS And some amps are made for powering guitars and bass combos, for example.
 

pkane

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Introduction
As a hi-fi enthusiast for many years I have always tried to deepen the themes underlying sound reproduction and psychoacoustics. For the latter topic, some time ago I came across the interesting book (on line here) "Premium Home Theater - Design & Construction" by Earl Geddes & Lidia Lee (or GedLee). Here are some considerations that have changed a lot the way I conceive of audio playback. At page 58, it is reported verbatim, about the relationship between classic distortion measurements and listening sensation:
  • There is virtually no correlation between Total Harmonic Distortion (THD) or Intermodulation Distortion (IMD) measurements of a system and the subjective impression of the sound quality of that system. The correlations were weak, but most shockingly they were negative—according to these tests people liked THD distortion. This is actually somewhat true in general that people prefer some forms of distortion to no distortion.
  • Signal based distortion measurements (THD, IMD, MTD), which are based on a purely mathematical formula which does not take into account the characteristics of human hearing, do not hold out much hope for ever being an accurate measure of subjective impression.
  • Measures need to be based on the actual nonlinear characteristic of the system and scaled to account for the human hearing system.
I would like to remind you briefly that nonlinear distortions are due to the different gain value that an amplifier applies for different input signal levels, generally independent of its frequency. These create new harmonic components that are added to the original signal, the shape of which then determines effects in listening. I omit from the following considerations the effects of linear distortions, on which it is relatively easier to act.

The preference of the presence of distortion (even if of a specific type, as we will see shortly) over its absence may at first appear contrary to common sense. In fact, it is to be expected that, to obtain the same sensations desired by the artist, it is necessary to reproduce the original music track with a system that playbacks any music track with the highest level of fidelity. Therefore, among the various parameters that characterize the components of a system, the nonlinear distortion should be as low as possible.

By integrating personal experience with an in-depth reading of the works of GedLee and others, such as that of Bob Katz (here) or Nelson Pass (here) to name a few, it emerges that we need to consider the entire chain of sound, from production to reproduction. From the moment the signal is captured from the source to its recording on disk (to be nostalgic), the audio signal passes through a series of inherently non-linear electronic systems. Then it moves on to the reproduction chain, again consisting of non-linear components. Each component in the chain adds nonlinear distortions to the signal output from the previous component. All these distortions, despite being singularly very small to the elementary test signals, are much less small with the real signals and multiply in the signal chain, resulting in high order harmonic distortions on our loudspeakers. These can be potentially audible and they have nothing to do with the sound as it was generated by the original source. Unfortunately it is practically impossible to identify and eliminate these distortions that create effects such as listening fatigue and lack of naturalness, even assuming that the sound engineer has not made any mistakes.

How to get out? A help is offered to us by nature, which has endowed us with a highly complex and nonlinear hearing system. Specifically, we can leverage the effect of masking, which manifests itself by raising the threshold of hearing of signals close to others of a higher level. Lossy compressors such as MP3 are also based on this principle. Many details are always in GedLee's book, Chap. 2: below a graph from the book showing the threshold raising depending on the dB level of a masking tone.


Hence the justified practice of building amplifiers that add low-order nonlinear distortions in the playback, that is, low-order distortions; audiophiles with a preference for "tube sound" are familiar with them by the name of "euphonic" distortions. These generally have the dual effect of:
  1. add a sort of loudness to the original music content;
  2. hide unwanted higher order distortions (already contained in the music track or created by the playback chain).
However, the excess of these components has the effect of obscuring the sonic details or making it too artificial. In fact, the quantity of the different harmonics added is one of the aspects that most determines the "character" of an amplifier and affects the "winning" combinations with other audio components.

My study described below, which has just begun using personal and friends' resources, therefore aims to investigate in detail how specific amounts of low order distortions affect perceived sound quality, using real music. For the above, I expect that preferences can be different depending on:
  • audio playback chains;
  • type of music;
  • mastering of audio track;
  • listening levels.

Test Preparation
As first step, I wrote a program that adds a configurable amount of second and third harmonic distortion (asymmetric and symmetric distortions, respectively) to a digital audio track of any sample rate or bit depth. In this way it is simulated the addition of "good" nonlinear distortions in the "original" signal. The output track is (automatically) compensated to avoid clipping and to eliminate any DC introduced. Moreover, in order to avoid further distortions, it is subject to dithering and noise shaping in the recoding downstream of the high-precision internal processing. The idea is that if we use a downstream amplification chain that is as "transparent" as possible, we can thus get a fairly precise idea of the effect on the perception of these harmonics.

To test the program I worked first with test signals. For example, a pure tone input at 1KHz 0dBFs (96KHz / 24bit) has this spectrum:


The program outputs tones of this shape by setting -40dB and -60dB of second and third harmonic distortion respectively:


For a bi-tonal signal at 5KHz and 6KHz, 44.1KHz / 16bit:


We have in the output for distortion at -40dB of third harmonic:


While for distortion at -40dB of second harmonic only we have:


Below is what happen when a distortion of -70dB in both the second and third harmonics is applied two times to a pure tone at 1KHz, 96KHz / 24bit (it simulates a chain of two devices with same nonlinear distortion):


The level of second and third harmonics are increased of 6-7dB and appear higher order harmonics (fourth and fifth), albeit at low levels.

With real musical tracks, I tried to subtract the original signal from the distorted one, obtaining a distorted copy at very low level of the original track, quite similar at listening.

After the program testing, to start with real listening sessions, I selected 4 well known Jazz / Pop music tracks with a good recording quality. For each I have created 2 further versions: one with main distortion of the second harmonic (-50dB) and the other of the third (-70dB). I chose high values in order to make the perceptual effect of each type of distortion evident. The value of Gm(f), the metric of GeeLee that tries to correlate distortion to subjective rating taking into account the masking effect, i.e.:


is always less than 1 with these values (T(x,f) is the nonlinear transfer characteristic). From each music track it has been therefore selected significant parts of 15-20 seconds, each predominantly for female voice, or for percussion, wind or string instruments.


Test Execution
The 3x4 music tracks above were played at controlled levels (about 82dB) several times at a very close distance on a couple of high quality solid-state audio systems, inserted in dedicated medium-small rooms treated acoustically. In each session the listeners naturally did not know which of the three songs they were listening to, randomly labeled with a number. For each session I asked to answer the questions:
  • which song is the most pleasant to listen to;
  • perceived differences between songs, if any.
At the moment I have only run test sessions with 3 people with experience in both audio production and reproduction.


Test Results
The small sample is quite concordant in the results:
  • Tracks with second harmonic distortion were preferred in about 75% of cases; 25% those of the third; surprisingly never the original tracks.
  • Tracks with second harmonic distortion was considered the warmer and with more "body"; other times too soft and a little confused.
  • Tracks with third harmonic distortion was considered the brightest and most defined; other times excessively defined and tiring.

Preliminary Conclusions
At the date the test results appear to be in line with those of GeeLee and other works. Of course, more extensive tests are needed with more people, also not trained and on medium quality audio systems, combining different distortion levels with listening levels and then with more audio playback systems, music types and recordings. Yes, it is not a fast task!
However, comments and suggestions are welcome to refine the study, as well as comparisons with similar experiences.

You may want to take a look at this informal internet blind test and the results that followed:

http://archimago.blogspot.com/2020/01/internet-blind-test-is-high-harmonic.html
http://archimago.blogspot.com/2020/05/blind-test-results-part-i-is-high.html
https://archimago.blogspot.com/2020/06/blind-test-results-part-ii-is-high.html
 
OP
Pinox67

Pinox67

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This inarguably implies that it is appropriate for the designer of an amplifier to design the amplifier to modify the sound in any way that the designer believes the owner of the amplifier will like, and to do this in a way where the owner has no control over it, i.e., the owner has no ability to switch it off, and no ability to adjust the level to suit their personal preference. This is inarguably a strong and manifest implication of what you wrote, and it just does not seem a particularly good idea to me.

If I went down to the corner audio store and the salesperson tried to impress me with an amplifier that obviously exaggerated treble and there were no provision for me to switch off this effect, I would be flabbergasted. Why is it deemed more tenable for non-linear distortion to be added in a manner not controllable by the user, vs. treble emphasis to be added in a manner not controllable by the user? This makes no sense to me, before I even think about the fact that whereas non-linear distortion cannot be reversed once it has been added, a treble emphasis is not difficult to reverse. Why would it be desirable for an amplifier to change the sound in a way that isn't controllable by the user and that once done cannot be removed?
...

In your words you touch on interesting topics. To answer you, I will summarize how the study I presented was born.

In the last few years I have been lucky enough to be able to measure and listen in my acoustically treated room several dozen peramps and power amps from many price ranges and well-known brands: Audio Research, Krell, Mark Levinson, Nagra, Threshold, Kondo, Xindak, Luxman, to name the main ones.

I am also in contact with few small local designers who build custom handmade pre-amps and power amps for home use, both tube and solid state. One of these asked me a "one million dollar" question: which technical characteristics should a preamplifier have to be considered “well sounding” for an audiophile, considering the relationship between the perceived sound quality and the measurements of the amplifiers mentioned?

From their experience "in the field" it emerged that, once some requirements on the interface parameters were met and good measurements were reached on parameters such as Frequency / Phase Response, CrossTalk and Noise Floor, harmonic distortions (i.e. THD and IMD) should not be so small (or rather, of a certain type) to get satisfaction from their customers. They want to get what I think any audiophile is looking for from its system: an emotionally capable sound that gives the illusion of being in front of the live musical event (essentially, what Dave Wilson calls in his interviews "dynamic contrast" and "harmonic expression" for its loudspeakers). They are not very interested in the technicalities of how they come to this.

By correlating their experiences with personal ones on "branded" preamps, I had to agree with them, despite a bit of reluctance: my soul as an engineer was looking for a logical explanation for this. I have thus delved into the subject of psychoacoustics and in the studies I have already mentioned I have found confirmation of this experience, namely that people prefer sound containing a certain amount of (good) distortion injected into the reproduction chain rather than having none at all.

Hence the study that I started, to better investigate these aspects, with larger samples of people/systems and in a well-controlled way. From this study I expect as result that there is no optimal value of “good” harmonic distortion to be injected. This is variable and depends on the factors I have already illustrated:
  • musical content (type and number of instruments and voice components);
  • recording (distortion injected into recording by production chain);
  • reproduction system (distortion injected by reproduction chain);
  • listening level (it changes the masking effect).
There is probably nothing really new in this, the R&D departments of the big audio brands already know these aspects well and do not disclose them clearly, as these are the main aspects that distinguish their products. If all were confirmed, this result would open an interesting opportunity for my designer friends: that of building preamps that have a knob that allows the user to inject any amount of low order distortion at will, in order to adapt the resulting sound to all the factors mentioned. Very simple to say, much more complicated to do...

On the subject of the distortions introduced by amplifiers and speakers, I suggest you listen to this interview (at least the first 20 minutes) with Earl Geddes, very illuminating on the subject.
 
Last edited:

FeddyLost

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If all were confirmed, this result would open an interesting opportunity for my designer friends: that of building preamps that have a knob that allows the user to inject any amount of low order distortion at will, in order to adapt the resulting sound to all the factors mentioned. Very simple to say, much more complicated to do...
Single knob that must work like that?
https://spl.audio/en/spl-produkt/tube-vitalizer/
If we'd like to make one solution for all combinations of variables that you have mentioned, we'd need to make some decisions what do we inject in chain depending on these variables and that's really troublesome.
Maybe some plugin in digital domain for first iteration?
 

SIY

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I suggest first running a control test to make sure any audible effect is detected. Only then enter phase 2 of quantifying the differences if they exist.

You also need to perform a statistical analysis to make sure distortion was a significant factor and chances of guessing was less than 5%.

^This. Step 1 has to be determining if there actually is an audible difference. Then one can move on to preferences.

From a fast scan of this, it seems that there was no double blinding? If there was, great. If there wasn't, that needs to be incorporated in the protocol. Also, one needs to rigorously check that there are no level differences. This caused me some grief once in testing some SET amp until I realized that the distortion was high enough to raise the RMS level by 0.5 dB. Lesson learned.
 

pkane

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Single knob that must work like that?
https://spl.audio/en/spl-produkt/tube-vitalizer/
If we'd like to make one solution for all combinations of variables that you have mentioned, we'd need to make some decisions what do we inject in chain depending on these variables and that's really troublesome.
Maybe some plugin in digital domain for first iteration?

https://distortaudio.org/ has two sliders on the right that, in different combinations, control the amount and type of harmonics (shape of the nonlinearity). You can also control individual harmonic levels directly. And then, you can do the same with this plugin:

https://distortaudio.org/pkharmonic.html

both attempt to set equal levels after each adjustment by computing the new response level using pink noise.
 

Gorgonzola

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If I went down to the corner audio store and the salesperson tried to impress me with an amplifier that obviously exaggerated treble and there were no provision for me to switch off this effect, I would be flabbergasted. Why is it deemed more tenable for non-linear distortion to be added in a manner not controllable by the user, vs. treble emphasis to be added in a manner not controllable by the user? This makes no sense to me, before I even think about the fact that whereas non-linear distortion cannot be reversed once it has been added, a treble emphasis is not difficult to reverse. Why would it be desirable for an amplifier to change the sound in a way that isn't controllable by the user and that once done cannot be removed?
...
If anyone is predisposed to advocate the desirability of adjunct processors that add distortion of various types and at levels controllable by the user, this is a perfectly reasonable concept. I'm not certain that it would sell very well, but at least the idea isn't an affront to the fundamental principle of amplifier accuracy.

There is probably nothing really new in this, the R&D departments of the big audio brands already know these aspects well and do not disclose them clearly, as these are the main aspects that distinguish their products. If all were confirmed, this result would open an interesting opportunity for my designer friends: that of building preamps that have a knob that allows the user to inject any amount of low order distortion at will, in order to adapt the resulting sound to all the factors mentioned. Very simple to say, much more complicated to do...

On the subject of the distortions introduced by amplifiers and speakers, I suggest you listen to this interview (at least the first 20 minutes) with Earl Geddes, very illuminating on the subject.

In fact a few years ago I had an analog parametric equalizer from Behringer that actually had a knob that would permit you to change the sound by the injection of distortion created by a vacuum tube. By cranking the knob you could definitely change the sound for a mellower effect was, at the same time, less detailed and dynamic. I never really used the facility.
 

pkane

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In fact a few years ago I had an analog parametric equalizer from Behringer that actually had a knob that would permit you to change the sound by the injection of distortion created by a vacuum tube. By cranking the knob you could definitely change the sound for a mellower effect was, at the same time, less detailed and dynamic. I never really used the facility.

Here’s a similar device I tested before: https://www.audiosciencereview.com/...us-bluetube-v2-adjustable-hybrid-preamp.8795/
 
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Pinox67

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Single knob that must work like that?
https://spl.audio/en/spl-produkt/tube-vitalizer/
If we'd like to make one solution for all combinations of variables that you have mentioned, we'd need to make some decisions what do we inject in chain depending on these variables and that's really troublesome.
Maybe some plugin in digital domain for first iteration?

An interesting device, which acts on a lot of aspects. It is used in production by professional people.
In reproduction, for a "normal" person it takes something simpler. I agree, a single knob is probably too little. I think you need at least a couple of them, one for the second harmonic (or even harmonics) and one for the third (or odd harmonics), to do simple things.
The digital tests on the audio tracks are used to get an idea of the effects of each of the variables involved and therefore understand what "minimum" degrees of freedom must be inserted in playback.
 
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MrPeabody

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In your words you touch on interesting topics. To answer you, I will summarize how the study I presented was born.
...
They want to get what I think any audiophile is looking for from its system: an emotionally capable sound that gives the illusion of being in front of the live musical event ... They are not very interested in the technicalities of how they come to this.
...
namely that people prefer sound containing a certain amount of (good) distortion injected into the reproduction chain rather than having none at all.

I am going to watch that interview in a few moments.

A couple of thoughts. First, I admire you for the undertaking, which should be useful in a broad sense. The more we understand about what kinds of distortion matter, the better. My sense, though, is that this may be something that is already understood fairly well, thanks to prior work by a variety of other researchers. As such, before undertaking something as ambitious as what you are undertaking, I would first search the literature exhaustively. In fact, a paper that definitely summarizes the existing investigations and findings would be very useful all on its own, possibly deserving of publication, independently of the independent research you are planning to do.

Second, I cannot help but notice something that seems a bit curious, in what you wrote and that I excerpted above. You alluded to realism, i.e., "the illusion of being in front of the live musical event". Implicitly you are saying that in order to achieve this illusion, the sound must be altered so that it does not sound the same as what was recorded the live event, in order that the listener's emotional response will be more like what it is for a listener at the live event. This is what you are saying in essence, and since it is, it seems to me that you should state this in the plainest manner possible.

Third, I don't think that there can be any genuine reason for not giving the listener the ability to control the level of added distortion. I think it self-evident that it is highly desirable for the listener to be provided the ability to control the level of added distortion, and even the ability to vary the makeup of the distortion. It is self-evident to me that the listener should be given control over anything that alters sound in any way, including the ability to disable the effect via a by-pass switch. It follows (directly) that any distortion added to amplification should be thought of as adjunct processing. I do not know of any good, genuine way to avoid this observation, yet this observation is never made by people who advocate that it is desirable for amplifiers to add distortion along with the amplification. This strikes me as patently disingenuous, and this is the stronger of the two reasons why people who argue for distortion in amplifiers seem disingenuous to me. (The other reason has to do with the uncertainty as to whether the difference in distortion characteristics applies in the normal circumstance where neither amplifier is in overload condition. The uncertainty is with whether it is realistic to expect that the tube amplifier will routinely be marginally within overload condition such that distortion is audible but only barely so, such that it will be audible but not so overwhelming at the volume peaks that you'll dislike it. I'm not certain about this, because I think it is a complex question, however a possibility that occurs to me is that in order for the pleasing 2nd-order distortion to be truly pleasant, it needs to be well moderated at the loudest peaks, in which case you probably will not hear it at all during quieter passages. This is one reason why I'm inclined to agree with something many people have said: that the difference in the sound of the two kinds of amplifier, when it is real, is less likely due to any difference in non-linear distortion than to the effect that high output impedance has on the voltage split between the speaker and the amplifier's output impedance.)
 
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