[SanjiWatsuki]

Hello, Head-Fi Sound Science! I'm looking for critique on my current view on distortion.
 
Introduction
I've been looking recently into the audibility of nonlinearities. As established by studies by both ALMA International [0] and Geddes [1], we know that traditional forms of measuring nonlinearity (THD and IMD) fail to accurately depict the audibility of the nonlinearities. Large amounts (30%+) of 2nd and 3rd order distortion, for example, can go unnoticed to a listener thanks to psychoacoustics.
 
We will focus on headphones in particular for this analysis, rather than source equipment. Headphones are known to generally be heavy in 2nd and 3rd order distortion when they distort, unlike electronic components. This suggests that the distortion effects should be relatively benign.
 
Flaws in the Traditional Methods (THD/IMD)
It appears that the typical forms of measuring distortion have several flaws as established by [1]:
 
1. Distortion higher in frequency is harder to distinguish from lower frequency distortion. This is backed up by the studies cited in [3]. For example, we should expect distortion at 300hz to be more noticeable than higher frequency distortion.
 
2. Distortion farther from the original excitation is easier to perceive. To tie back to THD/IMD, this means higher order distortion is worse than lower level distortion. The masking effect of the ear can sometimes mask massive amounts of low order distortion, but it will fail to mask massive amounts of high order distortion. Recognize that THD is normally DOMINATED by lower order distortion and this makes THD very difficult to use.
 
3. Distortion byproducts at low signal levels are easier to perceive than at high signal levels. Basically, this means amplifier and DAC distortion is worse than headphone distortion. Headphones and loudspeakers distort a lot more as they get louder, but source equipment can sometimes distort even at low signal levels. To quote Geddes, "Haven't you ever wondered how it is that you could hear .1% of electronic distortion through a loudspeaker that is typically 1-5%?" Since the masking effect is stronger with louder signal, we can expect a lot of the distortion from headphones to be masked by the louder volume.
 
Consider this a perfect example of how we aren't just listening to sine waves. Sine wave testing fails to capture the psychoacoustic effects that can make distortion difficult to perceive. It seems like sine waves are likely the "worst case scenario" for distortion.
 
What Does That Mean for Us?
We don't have access to measurements like PTHD or Gm for most headphones which adjust for those problems. What we do have access to are regular distortion measurements, sometimes with the different orders of distortion shown on the graph. 
 
Although our methods can't be perfect, I believe that we can improve our interpretation of the information available to us in the following ways:
 
1. Weigh distortion measurements in lower frequencies more than higher frequencies. 
2. Avoid making many judgments about 2nd and 3rd order distortion measurements -- focus on 4th and higher level distortion.
3. If information about the order of the distortion is not available like from sites like InnerFidelity, recognize that the distortion data may not be as useful as we originally expected. If the THD in the measurements are caused almost entirely by 2nd order distortion, for example, it may not be audible at all.
4. Weigh power handling less -- the louder the signal, the greater the masking effect, so an increasing amount of distortion can be acceptable.
5. Don't compare raw distortion numbers directly. 5% THD on one headphone may have a relatively benign effect whereas 1% THD in another may be nasty.
 
Furthermore, we should weigh typical distortion measurements less in general. They're just not descriptive enough to be useful in many contexts.
 
Addressing Ethan Winer's Critique of Geddes Work
After noticing the video posted about the AES Damn Lies workshop, I feel the need to address this argument. Winer presents two arguments in the video:
 
1. The Geddens study uses contrived distortions from complex mathematical formulas, and it doesn't accurately depict actual distortion characteristics.
 
This is completely true, but kind of misses the point of the paper. The point of the paper isn't to prove the complete inaudibility of nonlinearities, but to show a failing in the THD measurement. The examples are totally contrived to make a point -- the point being that there are types of distortion that THD fails to accurately depict in terms of audibility and that THD overly punishes certain types of distortion that are not very audible.
 
2. Distortion is more about the audibility of artifacts, regardless of their type or cause. If the sum of all artifacts is 80dB or lower below the music, it won't be heard regardless of its make-up.
 
In general, I feel this argument is correct, but I don't think it applies much to headphones. Headphones rarely have distortion that low. It doesn't actually seem like a critique of Geddes' work, though -- current psychoacoustic research suggests that we hear different types of distortion differently, so a straight sum of the distortion products (or their square) is an inaccurate measure of the audibility of the distortion. I don't believe this dismisses the arguments shown in this post.
 
[0] http://www.almainternational.org/assets/PapersLibrary/2013WinterSymposium/measurement%20of%20harmonic%20distortion%20audibility-listen%20inc-alma%20ws%202013.pdf
[1] http://www.gedlee.com/downloads/Distortion_AES_I.pdf http://www.gedlee.com/downloads/Distortion_AES_II.pdf
[2] http://www.audioholics.com/room-acoustics/human-hearing-distortion-audibility-part-3
[3] http://www.diyaudio.com/forums/multi-way/121253-geddes-distortion-perception-2.html#post1482908

 

[xnor]

  1. Distortion higher in frequency is harder to distinguish from lower frequency distortion. This is backed up by the studies cited in [3]. For example, we should expect distortion at 300hz to be more noticeable than higher frequency distortion.

This needs further qualification. What happens at lower bass / sub bass? What about high frequencies where the upper harmonics fall outside the human hearing range?
 
 

2. Distortion farther from the original excitation is easier to perceive. To tie back to THD/IMD, this means higher order distortion is worse than lower level distortion. The masking effect of the ear can sometimes mask massive amounts of low order distortion, but it will fail to mask massive amounts of high order distortion. Recognize that THD is normally DOMINATED by lower order distortion and this makes THD very difficult to use.

I don't understand. Since THD is usually low-order dominated and low-order harmonics are masked easier isn't THD everything but difficult to use?
(Maybe you mean a single THD number vs. a distortion/frequency plot?)
 
Anyway, since harmonic and intermodulation distortion go hand in hand it should be minimized anyway.
 
 

3. Distortion byproducts at low signal levels are easier to perceive than at high signal levels. Basically, this means amplifier and DAC distortion is worse than headphone distortion. Headphones and loudspeakers distort a lot more as they get louder, but source equipment can sometimes distort even at low signal levels. To quote Geddes, "Haven't you ever wondered how it is that you could hear .1% of electronic distortion through a loudspeaker that is typically 1-5%?" Since the masking effect is stronger with louder signal, we can expect a lot of the distortion from headphones to be masked by the louder volume.

What? The harder you drive an amp or even DAC, the higher the distortion will be. As you turn the volume down, the distortion products will usually fall overproportionally and finally be drowned by the noise floor.
 
I don't know which volume levels you're talking about, but as you turn down the volume the distortion products will be masked additionally by environmental noise.
 
Also, do you have something to back up the "masking effect is stronger with louder signal"?
 
 

Consider this a perfect example of how we aren't just listening to sine waves. Sine wave testing fails to capture the psychoacoustic effects that can make distortion difficult to perceive. It seems like sine waves are likely the "worst case scenario" for distortion.

I don't understand. Music basically is just sine waves (and noise). Sine waves are not used for listening tests because they're annoying.
 
 
 

1. Weigh distortion measurements in lower frequencies more than higher frequencies.

Do you have a psychoacoustic weighting curve for distortion handy?

 
 

2. Avoid making many judgments about 2nd and 3rd order distortion measurements -- focus on 4th and higher level distortion.

I disagree because high low-order distortion will also increase offensive IMD.
 
Also, didn't you say before that usually distortion products get weaker and weaker with higher order? So if the 4th and higher harmonics have a high level then 2nd and 3rd will be even stronger and in turn raise THD accordingly.
 
 

3. If information about the order of the distortion is not available like from sites like InnerFidelity, recognize that the distortion data may not be as useful as we originally expected. If the THD in the measurements are caused almost entirely by 2nd order distortion, for example, it may not be audible at all.

Only if the headphone doesn't produce IMD, which is physically impossible with high THD (no matter how low order the distortion products are).
 
 

4. Weigh power handling less -- the louder the signal, the greater the masking effect, so an increasing amount of distortion can be acceptable.

The problem here is the measurements. At lower SPL the distortion will be much lower and environmental noise will dominate THD+N.
Power handling is important because you want loud peaks to be reproduced as cleanly as the rest of the music.
 
 

5. Don't compare raw distortion numbers directly. 5% THD on one headphone may have a relatively benign effect whereas 1% THD in another may be nasty.

I doubt that, but maybe you can find two headphones where that is the case.

 

[SanjiWatsuki]

  This needs further qualification. What happens at lower bass / sub bass? What about high frequencies where the upper harmonics fall outside the human hearing range?
 
Good point. The explanation, as far as I know, is that in sub-bass frequencies, you can get audible tones from sounds that you otherwise would only feel. Sound from nothing, so to speak. High frequencies where it falls out of the human hearing range backs up higher frequency harmonic distortion being harder to hear, since you can't hear the supersonic frequencies.
 
I don't understand. Since THD is usually low-order dominated and low-order harmonics are masked easier isn't THD everything but difficult to use?
(Maybe you mean a single THD number vs. a distortion/frequency plot?)
 
Anyway, since harmonic and intermodulation distortion go hand in hand it should be minimized anyway.
 
THD is dominated by low-order distortion, but low-order distortion is the hardest distortion to hear, arguably inaudible with complex tones. Thus, the metric mostly measures junk. Both the THD number and distortion/frequency plot have this issue -- unless the plot breaks it down by the harmonics.
 
What? The harder you drive an amp or even DAC, the higher the distortion will be. As you turn the volume down, the distortion products will usually fall overproportionally and finally be drowned by the noise floor.
 
I don't know which volume levels you're talking about, but as you turn down the volume the distortion products will be masked additionally by environmental noise.
 
Also, do you have something to back up the "masking effect is stronger with louder signal"?
 
You can expect the distortion to rise by pushing the amp or DAC harder, but the effects are very small. The O2, for example, rises from like 0.001% to 0.002% before clipping. I'd link to the graph, but I can't link to the site in question.
 
The effect in question here is the masking effect. The masking effect decreases with lower volume, meaning you hear more of the distortion products. That effect overwhelms the increase in distortion as a result of higher volume (without clipping).
 
Here is backing up the masking effect stronger with louder signal. http://www.gedlee.com/downloads/Distortion_AES_I.pdf Figure 4 is a great example. It's also backed up by Psychoacoustics - Facts and Models Third Edition
 
 
I don't understand. Music basically is just sine waves (and noise). Sine waves are not used for listening tests because they're annoying.
 
Masking effect differs with complex tones versus test tones. Chapter 4 in Psychoacoustics - Facts and Models discusses this a bit, if you're interested.
 
Do you have a psychoacoustic weighting curve for distortion handy?

 
There is some curves against FR related to masking in the book I'm reading, but the book is kind of over my head in technicals, so I'm not even entirely sure if I can use it like a contour curve.
 
I disagree because high low-order distortion will also increase offensive IMD.
 
IMD encounters similar issues to THD. It has a NEGATIVE r-value for the samples given as being predictive of audible distortion in the Geddes-Lee study. A lot of the nastiest nonlinearities are missed by both THD and IMD, even if IMD is better than THD. Admittedly, it was with contrived examples, but they are examples of really bad distortion that are missed by both IMD and THD.
 
Also, didn't you say before that usually distortion products get weaker and weaker with higher order? So if the 4th and higher harmonics have a high level then 2nd and 3rd will be even stronger and in turn raise THD accordingly.
 
Usually, but not always. I don't think I said that here, but that is the typical pattern. Even then, though, Geddes suggests that even 10% 2nd order would sound a lot better than 1% 6th order, for example. The SRH1840, I believe, is actually dominated by 5th order distortion in the bass frequencies, if I recall correctly.
 
The problem here is the measurements. At lower SPL the distortion will be much lower and environmental noise will dominate THD+N.
Power handling is important because you want loud peaks to be reproduced as cleanly as the rest of the music.
 
I'm talking about 90dB vs. 100dB distortion measurements at InnerFidelity. Since the masking effect grows with volume, higher distortion may not necessarily sound worse. 
 
I doubt that, but maybe you can find two headphones where that is the case.
 
I can't think of any good examples off the top of my head. Sadly, the better distortion benchmarks aren't calculated publicly.

.

 

[bigshot]

Speakers had MUCH higher distortion than headphones, yet they sound better. Something else must be the primary determiner of sound quality (frequency response, room acoustics)

 

[wnmnkh]

 

5. Don't compare raw distortion numbers directly. 5% THD on one headphone may have a relatively benign effect whereas 1% THD in another may be nasty.

I doubt that, but maybe you can find two headphones where that is the case.

 
Best example would be Shure's SRH1840 vs Grado headphones in general.
 
If you actually go listen Shure SRH1840, which is probably the worst THD case ever measured by Tyll, you will find that those distortions are very warm and smooth, making the headphones very smooth sounding like HD650 despite clear treble spikes shown on the measurements.
Grados, in contrast... well, for instance, I can clearly hear some serious bass distortion on any Grado headphones (except Joseph ones), including the most expensive PS1000.... you can hear very disturbing bass distortion in very low volume... rather, the bass is the distortion itself basically. 

 
 
Sure, as Purrin once said SRH1840 sounds like AM radio sometimes, but it is still much better and pleasing than Grado headphones.

 

[xnor]

   
Best example would be Shure's SRH1840 vs Grado headphones in general.
 
If you actually go listen Shure SRH1840, which is probably the worst THD case ever measured by Tyll, you will find that those distortions are very warm and smooth, making the headphones very smooth sounding like HD650 despite clear treble spikes shown on the measurements.
Grados, in contrast... well, for instance, I can clearly hear some serious bass distortion on any Grado headphones (except Joseph ones), including the most expensive PS1000.... you can hear very disturbing bass distortion in very low volume... rather, the bass is the distortion itself basically. 

 
 
Sure, as Purrin once said SRH1840 sounds like AM radio sometimes, but it is still much better and pleasing than Grado headphones.

 
But Purrin's measurements show the opposite.
 
SRH1840 has dominant 3rd and 5th order harmonic distortion. The Grados have dominant 2nd order harmonic distortion. 3rd/5th are more offensive to begin with, but the Shure additionally has higher overall distortion.
 
 
I think this is once again a simple matter of frequency response. Uncontrolled treble spikes in the Grados make them unlistenable for me too, regardless of distortion. The Shure has a much smoother and flatter response.
If I had to pick one of those two I'd probably also choose the Shure, despite its abysmal distortion (characteristics).

 

[xnor]

 
Good point. The explanation, as far as I know, is that in sub-bass frequencies, you can get audible tones from sounds that you otherwise would only feel. Sound from nothing, so to speak. High frequencies where it falls out of the human hearing range backs up higher frequency harmonic distortion being harder to hear, since you can't hear the supersonic frequencies.

http://en.wikipedia.org/wiki/Auditory_masking#Similar_frequencies figure B seems to suggest the opposite. Low frequencies seem to mask higher order distortion products better than high frequencies, when those products are still in the audible range of course.
 
But I guess the loudness contours play a big role here. Starting with 20 Hz, as the frequency rises you need much lower SPL to hear the tone equally loud.
 

THD is dominated by low-order distortion, but low-order distortion is the hardest distortion to hear, arguably inaudible with complex tones. Thus, the metric mostly measures junk. Both the THD number and distortion/frequency plot have this issue -- unless the plot breaks it down by the harmonics.

"Complex tones" consist of many different frequencies, so even low-order distortion will cause more offensive IMD.
 
Don't you agree with: "Anyway, since harmonic and intermodulation distortion go hand in hand it [THD] should be minimized anyway."?
Of course it would be nice to both reduce THD and to make sure the distortion spectrum is falling off with higher order.
 
 

You can expect the distortion to rise by pushing the amp or DAC harder, but the effects are very small. The O2, for example, rises from like 0.001% to 0.002% before clipping. I'd link to the graph, but I can't link to the site in question.  
The effect in question here is the masking effect. The masking effect decreases with lower volume, meaning you hear more of the distortion products. That effect overwhelms the increase in distortion as a result of higher volume (without clipping).
 
Here is backing up the masking effect stronger with louder signal. http://www.gedlee.com/downloads/Distortion_AES_I.pdf Figure 4 is a great example. It's also backed up by Psychoacoustics - Facts and Models Third Edition

I took a quick look at the paper and there doesn't seem to be a mention of the dB SPL used for "high/low signal level".
 
"Low" could still have been well above hearing limits so that the distortion products will not be masked by environmental noise and "high" may have been high enough to trigger the stapedius reflex which may change perception of distortion products substantially.
 
Obviously the O2 has very low distortion, but other products do not. Some tube amps have strongly rising distortion when you push them. Some DACs clip when the signal is getting close to 0 dBFS (uDAC

).
Granted, those are kinda "broken" components that shouldn't be considered hi-fi..
 
 
Since I am a low volume listener I actually like the idea of a weaker masking effect, but this only works if there's no background noise. So this only works with no children around.

 
 
 

There is some curves against FR related to masking in the book I'm reading, but the book is kind of over my head in technicals, so I'm not even entirely sure if I can use it like a contour curve.

That sounds very nice.
 
 

IMD encounters similar issues to THD. It has a NEGATIVE r-value for the samples given as being predictive of audible distortion in the Geddes-Lee study. A lot of the nastiest nonlinearities are missed by both THD and IMD, even if IMD is better than THD. Admittedly, it was with contrived examples, but they are examples of really bad distortion that are missed by both IMD and THD.

I understand what you're saying but if those examples don't or extremely rarely happen in reality then they're kinda useless. It's like measuring the vibrations in a car at 800 km/h when in reality we hardly drive over 160 km/h.
 
 

I'm talking about 90dB vs. 100dB distortion measurements at InnerFidelity. Since the masking effect grows with volume, higher distortion may not necessarily sound worse. 

It would be interesting to find out if there's a difference between very short loud peaks and listening to music at a high average SPL regarding perception of distortion. Because I doubt that many people are listening at ~100 dB *average* SPL.

 

[SanjiWatsuki]

  http://en.wikipedia.org/wiki/Auditory_masking#Similar_frequencies figure B seems to suggest the opposite. Low frequencies seem to mask higher order distortion products better than high frequencies, when those products are still in the audible range of course.
 
But I guess the loudness contours play a big role here. Starting with 20 Hz, as the frequency rises you need much lower SPL to hear the tone equally loud.
 
I think you're right on that. Alright -- the masking effect seems to have a broader effect in lower frequencies, but the loudness contour curve results in the frequency dependence of the effect.
 
"Complex tones" consist of many different frequencies, so even low-order distortion will cause more offensive IMD.
 

 
You're right, but the paper discusses the audibility of IMD as well.
 
Here's a graph of 10 test tones and the masking effect that their create. Notice how such a broad part of the frequency range is now masked pretty heavily as a result of the complex tones. Essentially, when we combine tones, you can mask distortion in a huge range that wouldn't be masked for a single tone. This can really wreck the audibility of IMD in some cases, because you may be able to cause that distortion, but it might get masked entirely by the complex tone's masking effect.
 
Taking advantage of this is actually how the MP3 codec was first invented.
 
Don't you agree with: "Anyway, since harmonic and intermodulation distortion go hand in hand it [THD] should be minimized anyway."?
Of course it would be nice to both reduce THD and to make sure the distortion spectrum is falling off with higher order.
 
Generally speaking, yes. I mean, I drive the HD800s with the ODAC and the O2 against advice from pretty much everyone that owns the HD800s.
 
That said, I believe that there is work to determine if such a thing as "euphonic" distortion with the masking effect exists. I've looked around, but I haven't been able to find the study if it is published, but Geddes claims that his work has found that lower order distortion is preferred by listeners relative to lower distortion: http://www.diyaudio.com/forums/multi-way/121253-geddes-distortion-perception.html#post1482578
 
Therefore, the chance that this hypothesis is correct seems to me like it theoretically could be worth it to get something with an acceptable amount of lower order distortion and that distortion may not be bad, if it has good measurements otherwise and excellent sighted reviews (flawed as they might be).
 
Like I said, though, I haven't found an AES peer-reviewed study yet, so consider this portion very controversial. I don't accept it yet myself, but I will admit that I find the possibility of it existing plausible, but unconfirmed.
 
I still think it's a smarter choice to get a amp that measures well, rather than getting one that measures worse in specific ways, but it's something to keep an eye on!
 
I took a quick look at the paper and there doesn't seem to be a mention of the dB SPL used for "high/low signal level".
 
"Low" could still have been well above hearing limits so that the distortion products will not be masked by environmental noise and "high" may have been high enough to trigger the stapedius reflex which may change perception of distortion products substantially.
 
Page 6,  Distortion Perception Principle #3. I think figure 4 shows off the effect graphically.
 

Here's one of the graphs out of the Psychoacoustics book. This one shows off how the masking effect grows both in size and width with louder volume. 
 
Obviously the O2 has very low distortion, but other products do not. Some tube amps have strongly rising distortion when you push them. Some DACs clip when the signal is getting close to 0 dBFS (uDAC

).
Granted, those are kinda "broken" components that shouldn't be considered hi-fi..
 
You're right that poorly designed components can get nuts on the distortion, like the uDAC in particular. I generally agree on tubes, but I'm watching the research to see what comes of it, as stated above.
 
 
Since I am a low volume listener I actually like the idea of a weaker masking effect, but this only works if there's no background noise. So this only works with no children around.

 
Heh. Good point.
 
That sounds very nice.
 
 
I understand what you're saying but if those examples don't or extremely rarely happen in reality then they're kinda useless. It's like measuring the vibrations in a car at 800 km/h when in reality we hardly drive over 160 km/h.
 
The study may have used examples intended to get a p value of 0.0001 or whatever, but think of the implications -- if 2nd and 3rd order distortion under complex tones, like music, are basically inaudible then a THD measurement is mostly dominated by noise in real world applications. Loudspeaker and headphone distortion are really almost the perfect case for applying that knowledge since they mostly create 2nd and 3rd order distortion.
 
And also, there are more important things to focus on. The types of distortion that get past the masking effect seem to be much more harmful than distortion that gets masked, so we need difference measurements. Hence the development of the Gm and PTHD (different study came up with that benchmark, but it is very similar).
 
Compare the total THD curve against the 2nd order distortion curve in HD measurements that break down via the order of distortion. i'd say in most of the curve, it is virtually identical to the 2nd order distortion curve -- pretty much 100% junk data as far as we're concerned. Because of how heavily weighted the 2nd harmonic is in THD, we really can't tell the audible effects of the distortion from just a THD curve.
 
It would be interesting to find out if there's a difference between very short loud peaks and listening to music at a high average SPL regarding perception of distortion. Because I doubt that many people are listening at ~100 dB *average* SPL.
 
That'd be interesting as well. I haven't found many other authors doing awesome distortion work besides Geddes, and he has said that he's done with non-linear distortion. He thinks that he's done enough and that his studies have survived the peer review for a decade now, since they were quite controversial when they first came out.

 
Alright, responded to your points and I got some graphs out of the psychoacoustics book.

 

[xnor]

On IMD:
The thing is you can construct really trivial examples where the negative effects of IMD are very simple to hear, even with just 2nd order harmonic distortion. For example a 200 + 250 Hz tone (running through a system that produces only a 2nd harmonic for a single tone) will result in a IM product at 450 Hz that will be about 6 dB louder than the 2nd harmonics of each tone.
 
With some high amount of distortion for testing you can hear how disharmonic the processed file sounds. Adding the 2nd order distortion for each tone separately, so that there won't be an IM product at 450 Hz, sounds much more pleasant, but this result is impossible to achieve in practice.
 
The MP3 encoder can make use of this because it can analyze the spectrum beforehand and guesstimate what will very likely be masked and what will not be masked.
 
 
Euphonic distortion is supposed to be a nice sounding nonlinearity. I don't think such a thing exists during reproduction. Sure, there might be distortion profiles which are less audible, less annoying, less destructive ... but any kind of (audible) distortion is bad by definition.
 
 

And also, there are more important things to focus on. The types of distortion that get past the masking effect seem to be much more harmful than distortion that gets masked, so we need difference measurements. Hence the development of the Gm and PTHD (different study came up with that benchmark, but it is very similar).

I just find it unlikely to see low levels of high-order harmonics not being masked by real music. Maybe in some artifical test, yes. (like with special test signals that cause maximum audibility of jitter, but switching to real music increases the threshold of its audibility by magnitudes)
 
Maybe we can do a little ABX test with some differently processed files (high amount of mainly low-order vs. lower amount of higher-order distortion)?
 
 

Compare the total THD curve against the 2nd order distortion curve in HD measurements that break down via the order of distortion. i'd say in most of the curve, it is virtually identical to the 2nd order distortion curve -- pretty much 100% junk data as far as we're concerned. Because of how heavily weighted the 2nd harmonic is in THD, we really can't tell the audible effects of the distortion from just a THD curve.

Yeah, if the 2nd order distortion product dominates then it will dominate the THD. If THD is low enough I'm really doubting that plotting each order separately will help. If it isn't, then plotting each order separately would only help those that have to have that particular headphone (for whatever reason) despite its high distortion.
 
The SRH1840 seems to be such an exception. But its distortion is so high that even if the THD were dominated by mostly 2nd order, I wouldn't want it.