THD vs. Hearing – Please Help.

[b_panther_g]

Hello everyone,

I thought I understood THD. Then I read this article:
http://www.ampzilla2000.com/thequest1.html

Mr. Bongiorno, the author, states…

“…Before we go on, let’s talk about some numbers so that we have a basis to work with concerning distortion. Virtually everyone relates to distortion numbers incorrectly. For example, if an amplifier had say 1% THD as read on a distortion meter, is it really one percent? Actually, it isn’t. The distortion amounts that are read on a distortion analyzer are in Volts and the ear doesn’t hear Volts, it hears power. So, if we convert the 1% to power we get a totally different perspective. Let’s say a nominal 200 watt per channel amp is producing 1% THD. As read on the analyzer this would be –40dB’s. But –40dB’s in power is 1/10,000th or 20 milliwatts. On the other hand, since the ear’s hearing curve is logarithmic, 40dB’s represents a RATIO of only 16 to 1. In other words, for every doubling (or halving) of the loudness it takes 10 TIMES (or 1/10th) the power. 20dB’s equals 4 times (or 1/4th) and 30dB’s equals 8 times (or 1/8th) and 40dB’s equals 16 times (or 1/16th). Therefore, if you divide 100 by 16 you get, you guessed it, 6.67%. Now that’s a long ways from 1%. You can scale this up or down in either direction and the RATIO of the results will be the same. So when you apply these true numbers to the human hearing curve it is easy to see why anomalies and distortion artifacts that are buried in the noise can be detected by the ear. There is no black magic here. The so-called golden eared types actually can hear this stuff. The descriptions and verbiage associated with this situation may be a whole different can of worms. I have prepared a chart that shows the true relativity of all these factors.


<table width="80%" border="1" bordercolor="#000000">
<tr>
<td width="16%"><div align="center"><strong>THD Reading</strong></div></td>
<td width="7%"><div align="center"><strong>Db’s</strong></div></td>
<td width="18%"><div align="center"><strong>Distortion Power</strong></div></td>
<td width="20%"><div align="center"><strong>Distortion Watts</strong></div></td>
<td width="18%"><div align="center"><strong>Hearing Ratio</strong></div></td>

<td width="21%"><div align="center"><strong>True Distortion</strong></div></td>
</tr>
<tr>
<td><strong>10%</strong></td>
<td><strong>-20</strong></td>
<td><div align="center"><strong>1%</strong></div></td>
<td><strong> 2</strong></td>

<td><strong> 4:1</strong></td>
<td><strong> 25%</strong></td>
</tr>
<tr>
<td><strong>1%</strong></td>
<td><strong>-40</strong></td>

<td><div align="center"><strong>.01%</strong></div></td>
<td><strong>20mW</strong></td>
<td><strong>16:1</strong></td>
<td><strong>6.67%</strong></td>
</tr>
<tr>
<td><strong>.1%</strong></td>

<td><strong>-40</strong></td>
<td><div align="center"><strong>.0001%</strong></div></td>
<td><strong>200uW</strong></td>
<td><strong>64:1</strong></td>
<td><strong>1.56%</strong></td>
</tr>

<tr>
<td><strong>.01%</strong></td>
<td><strong>-80</strong></td>
<td><div align="center"><strong>.000001%</strong></div></td>
<td><strong>2uW</strong></td>
<td><strong> 256:1</strong></td>

<td><strong> .39%</strong></td>
</tr>
<tr>
<td><strong>.001%</strong></td>
<td><strong>-100</strong></td>
<td><div align="center"><strong>.00000001%</strong></div></td>
<td><strong>20nW</strong></td>

<td><strong> 1024:1</strong></td>
<td><strong> .098%</strong></td>
</tr>
<tr>
<td><strong>.0001%</strong></td>
<td><strong>-120</strong></td>

<td><div align="center"><strong>10(-12)</strong></div></td>
<td><strong>200pW</strong></td>
<td><strong> 4096:1</strong></td>
<td> <div align="left"><strong>.024%</strong></div></td>
</tr>
</table>

You will immediately notice the staggering difference between what the distortion meter is reading verses the true distortion numbers. The first line shows that the true distortion is actually 2½ times greater. The second line shows that the distortion is actually 6.67 times greater. The third line shows that the true distortion is really 15.6 times greater. The fourth line shows that the true distortion is actually 390 times greater. And the fifth line shows that the true distortion is actually almost 1000 TIMES greater, etc. It should be quite obvious to everyone now as to the fact that humans CAN hear artifacts down in the mud. Quite simply put, it is the RATIO of loudness factors that determine what we perceive acoustically and not the THD numbers off of the distortion analyzer…”​

​

If I understand correctly, Mr. Bongiorno states that published THD numbers are misleading. The % THD, as read from a measuring device, represents volts. Since we do not hear in volts, we need to convert those number into what we actually hear. He then has a conversion table (see above).

Is this article true? If so, what of speakers? Do the % THD numbers show what I'm actually hearing or are they the % read off the measureing device.


Thanks for your help.

Later,
B

P.S. Sorry for the weird looking post.

 

[Rip Van Woofer]

James Bongiorno is a serious, respected amp designer with several well-regarded designs to his credit including the Ampzilla back in the day. (I think he's with Amplifier Technologies these days - and they make very good amps at non-ripoff prices). He's also outspoken and sometimes controversial. Peter Aczel of The Audio Critic once (fondly) called him a "graying badass boy wonder". So anything he has to say is potentially interesting!

I haven't read the whole article (I'm off to work) but there is a large body of scientific work out there on human hearing and distortion that has established thresholds of what's audible. For a brief summary see the relevant section of Doug Self's article "Science and Subjectivism in Audio" -- see my Webpage for the link.

While interesting as an excercise in statistics, I'm not sure that this means that anyone can hear lower distortion than the accepted threshold.

 

[b_panther_g]

Hello Rip,

Thanks for the additional info. I’ll check it out.

You wrote…
” While interesting as an excercise in statistics, I'm not sure that this means that anyone can hear lower distortion than the accepted threshold.”

For the most part I agree. I’d really just like to know more about what I’m hearing.

When I read that subwoofer XXX plays at +100 Db with 10% THD, does that mean that 25% of what I’ll be hearing is garbage? I’d really like to know.

Later,
B

 

[Dan Banquer]

Distortion

Here's some stuff on distortion from my web site. As usual it's not as simple as some folks make it out to be.

"Dave: Your power amp specs give your Total Harmonic Distortion (THD) at 0.1% which is pretty high for a solid state amp. Yet I don't hear that usual aggravating solid state distortion.

Dan: Your're right, it is high compared to most solid state amps but there is a reason you can't hear the distortion. The harmonic distortion in the LNPA 150 is all second order distortion!

Years ago a number of papers were written on human hearing and harmonic distortion. What they found was that the human ear is very insensitive to harmonic distortion that is close to the main signal, and increases in sensitivity to harmonic distortion further away from the main signal. The second harmonic, which is an octave away from the main signal, is the hardest to hear, especially when you are driving a loudspeaker.

The best estimates that I can give you is that we can detect somewhere between 1% and 3% of second order harmonic distortion. Which is why you can't hear it. If the sum total distortions were farther away from the main signal you would be able to hear it. Some solid state designs can have pretty low distortion but they can get to be aggravating after awhile. That's because the distortion generated by the amp is further away from the main signal where the ear is more sensitive.

Dave: I never knew that. You read all these magazines that tell you that solid state has these aggravating odd order distortions, and tubes have these muddy sounding even order distortions. Your amps don't really follow the norm do they?

Dan: It's a shame that most magazines out there don't explain what is already known about the human ear and distortion. I remember years ago when The Audio Critic reviewed the LNPA 150 and found about the same harmonic distortion that I did and proceeded to howl about how bad it was. It really shows how unaware they are about science and the human ear.

If objectivist reviewers would only "characterize" where the harmonic distortion is in a particular unit instead of doing the usual THD + N measurement, which just lumps everything together, then the public would have greater respect for objectivist reviews than it does today.
Dave: Didn't The Audio Critic also say you had slewing induced distortion too?

Dan: Yes they did Dave. But this is simply not the case. If they had done a full power frequency response they would have found that this wasn't true. They could have also done a slew rate measurement with an oscilloscope and found that this was not the case. They based their decision on the THD + N measurement. The Audio Precision One is an incredible test measurement system. If people would only take the time to really learn how to use it, they wouldn't make incorrect assumptions, and mislead people, including themselves."

I'm really not trying to market my own stuff here, but there's more to distortion than is what is usually presented in consumer audio.
d.b.

 

[WmAx]

While I have no itention of reading the article at the moment, distortion %(THD = squareroot(HD2^2 + HD3^2 + HD4^2 + etc. )) is guaged by amplitude difference, not by power ratio in BOTH perceptual tests and by standard measurement protocols. However, it should be noted that the ear varies in sensitivey to harmonic distortion dependant on frequency and order. 1%(in reality most people appear to have actual theshold in 2-3% range) amplitude is generally accepted as a [1]threshold of audibility for the most sensitive listeners of musical playback in the sensitive bands of hearing with distortion threshold rising as you leave the sensitive hearing range. For example, 15% THD is the approximate threshold under 100 Hz. Distotion can be identified at much lower levels in pure tones(assuming sufficient duration to pick up the pattern), but pure tones are not represenative of real-world application(s) for reproduction systems. While the current standard of electronic specs given by publications in their product measurements is not weighted to hearing as accurate as it could be, their is not much incentive to refine it for the purpose of electronics specifications IMO. Current technologies in recording and playback electronics allow levels far below known audible levels for musical playback. However, I would warn to watch out for some popular DIY(or ANY limited condition) measurements given today, such as the Right Mark Audio Analyzer results usually given on forums for different soundcards, etc.. While RMAA is an accurate product given a linear soundcard, the measurements published are usually of a single frequency and terminated into unknown loads and at unknown power. All of these things are dynamic and a single perspective measurement reveals insufficient data to estimate real-world performance(s). Ironically, Stereophile has the best and most useful measurement sets I've found in any publication of consumer reviews. They are good for this.....

I will add that in the past I have not personally been able to identify 1% THD either odd or even order with statisically significant results in ABX tests(music) performed on reference quality headphones.

-Chris

Footnotes
[1] Just Detectable Distortion Levels
James Moire, F.I.E.E.
Wireless World, Feb. 1981, Pages 32-34 and 38

Hello everyone,

I thought I understood THD. Then I read this article:
http://www.ampzilla2000.com/thequest1.html

Mr. Bongiorno, the author, states…

“…Before we go on, let’s talk about some numbers so that we have a basis to work with concerning distortion. Virtually everyone relates to distortion numbers incorrectly. For example, if an amplifier had say 1% THD as read on a distortion meter, is it really one percent? Actually, it isn’t. The distortion amounts that are read on a distortion analyzer are in Volts and the ear doesn’t hear Volts, it hears power. So, if we convert the 1% to power we get a totally different perspective. Let’s say a nominal 200 watt per channel amp is producing 1% THD. As read on the analyzer this would be –40dB’s. But –40dB’s in power is 1/10,000th or 20 milliwatts. On the other hand, since the ear’s hearing curve is logarithmic, 40dB’s represents a RATIO of only 16 to 1. In other words, for every doubling (or halving) of the loudness it takes 10 TIMES (or 1/10th) the power. 20dB’s equals 4 times (or 1/4th) and 30dB’s equals 8 times (or 1/8th) and 40dB’s equals 16 times (or 1/16th). Therefore, if you divide 100 by 16 you get, you guessed it, 6.67%. Now that’s a long ways from 1%. You can scale this up or down in either direction and the RATIO of the results will be the same. So when you apply these true numbers to the human hearing curve it is easy to see why anomalies and distortion artifacts that are buried in the noise can be detected by the ear. There is no black magic here. The so-called golden eared types actually can hear this stuff. The descriptions and verbiage associated with this situation may be a whole different can of worms. I have prepared a chart that shows the true relativity of all these factors.

​

​

 

[Dan Banquer]

Distortion

"For example, 15% THD is the approximate threshold under 100 Hz. Distotion can be identified at much lower levels in pure tones(assuming sufficient duration to pick up the pattern), but pure tones are not represenative of real-world application(s) for reproduction systems."

Hi Chris:
I have always wondered that if we had real low distortion transducers at low frequencies would the 15% figure drop? Having recently finished a prototype headphone amp, I am still really sceptical of not only headphone distortion figures but frequency response also.
d.b.

 

[WmAx]

Hi Chris:
I have always wondered that if we had real low distortion transducers at low frequencies would the 15% figure drop? Having recently finished a prototype headphone amp, I am still really sceptical of not only headphone distortion figures but frequency response also.
d.b.

While I have measured headphones for certain criteria in the past, I have not tried to measure full band distortion simply because I did not want to construct an air tight head size jig containg mics to get accurate LF measurements. I do not know the distortion numbers to expect at low frequencies from typical headphones. Do you have such data? I may construct such a jig in the future. How do you mean to be skeptical of frequency response for headphones? Please clarify.

Thanks.

-Chris

 

[b_panther_g]

The rabbit hole gets deeper!

Soooooooo. According to WmAx, the people with the best (most accurate) hearing, can detect 1% THD, as read on a measuring device, when listening to music.

Hmmmmm. This is getting more and more complicated. If I understand Dan correctly, it’s not just about THD. It also depends on the type of distortion. That seems logical; I don’t think people are equally sensitive to all types of distortion. But what are the thresholds? Where can I find info about this?

Later,
B

 

[Dan Banquer]

Distortion

From what I understand there has been much contoversy on how to measure headphone distortion. Some have claimed to you must model the inner ear and others claim you don't. Some headphone "experts" have stated that if the headphone is not placed perfectly over the ear then none of the distortion as frequency response numbers they give will be meaningful. Quite frankly I don't know what to believe here.
As far as frequency response is concerned most of the recording engineers who use headphones on a daily basis that I have talked to and my own experience with a few different brands of headphones leads me to conclude at the moment that both frequency response and distortion specs appear to be dubious.
If the headphone needs to be placed perfectly over the ear for the their specs to be real then realistically how often does that happen?
BTW: If you have any papers or articles on this subject of headphones please e mail me or send me the links. I have the distorion paper by Jamie Moir. I have read it at least ten times
d.b.
P.S. Thanks for the articles you sent me earlier, if I didn't thank you already.

 

[Dan Banquer]

Distortion

There is no shortage of papers written on distortion. The Jamie Moir article was written in Electronics and Wireless world (An English Magazine), and numerous other related articles from the folks like Doug Self, and the late J.L. Linsley Hood to name a few. There is also no shortage of papers at www.aes.org
It's a fun subject.
d.b.

 

[WmAx]

Soooooooo. According to WmAx, the people with the best (most accurate) hearing, can detect 1% THD, as read on a measuring device, when listening to music.

Hmmmmm. This is getting more and more complicated. If I understand Dan correctly, it’s not just about THD. It also depends on the type of distortion. That seems logical; I don’t think people are equally sensitive to all types of distortion. But what are the thresholds? Where can I find info about this?

Later,
B

I was specifically referring to an article that took under consideration several controlled perceptual research tests on the issue. 1% is an estimated 'safe range', per say. I know that I have failed to detect that amount on my own blind test attemps. I tried to make it clear that senstivity is dependant on the signal, duration of that signal, the band and the order of the distortion.

-Chris

 

[Dan Banquer]

Distortion

To B panther: What I believe Chris and myself are trying to tell you is that from the studies that have been done, at low frequencies it is typically harder to hear distortion, and much easier to hear distortion at midrange to some frequency in the treble region. The other thing that needs to be taken into account is the order of the distortion and how many ears weight(percieve) that distortion.
I am going to assume for a minute that you know nothing about this so let me give a quick explnation. If I have a pure undistorted sine wave at 1kHz and I introduce this pure sine wave into the object we are testing I can then observe with some test equipment about what this unit is doing or not doing to this sine wave. One thing we can look at is distortion.
When we look at distortion we look at the harmonic content of what the unit does to our pure sine wave which has next to no harmonics. So what's a harmonic? If we go back to out 1kHz sine wave then the second harmonic is at 2 kHz (double the frequency) and the third harmonic is at 3 kHz (triple the frequency) etc.etc.
Hope this helps.

 

[b_panther_g]

Chris wrote
“…1% is an estimated 'safe range', per say…”

I understand. That’s fine. If the BEST people can start to hear THD at 1% on the music signals where hearing is most sensitive, then that’s some of the info that I’m after.

Thanks,
B

 

[WmAx]

From what I understand there has been much contoversy on how to measure headphone distortion. Some have claimed to you must model the inner ear and others claim you don't. Some headphone "experts" have stated that if the headphone is not placed perfectly over the ear then none of the distortion as frequency response numbers they give will be meaningful.

Looking at the issue as logically as I can, it is not disputable that frequency response varies considerably with a headpnone mesured in open space vs. a headphone coupled to an ear/canal structure. The various cavity structurs cause peaks/nulls in the uppermidrange and treble bands that cause signficant frequency response deviation(s). Logically, when the amplitude efficiency of a specific frequency is raised and coincides with the harmonic of a lowr fundamental(e.g.; 5khz peak and it's relation to 2.5khz fundamental), the amplitude of the measured harmonic product will be higher resulting in a different THD value upon analysis. So in this respect a THD measurement, if to be accurate represenation of what the ear detects, must weight the frequency response effects of these cavities*. But then one can debate this -- as is the point to measure the characterisic of the headphone or of the cavity effects upon the headphone? But this effect is not the same in low midrange and bass frequencies. At lower frequencies, the response is different for an open air vs. coupled headphone onto a stucture as well, but this is due to the proximity, air cavity and it's relative air volume compliance effect not the specific cancellations/peaks in respnose due to the specific dimensions of the canal, pinnae and contained space(s). Obviously, once the wavelenghts reach a certain length in air, the cavities can not cause cancellation/nulling and peaks due to the small dimensions. A simulation device with approx. correct proximity mic placement and volume of space should not require a precisely simulated ear/canal structure.

*(Ref. from above) Ironically, considering the effect of path lengths and effect on FR/resonance(s), one must also think about the accuracy of referring to low frequency distortion in speakers, if one does not account for the room effects that must differ from the open-space characteristics considerably.

As far as frequency response is concerned most of the recording engineers who use headphones on a daily basis that I have talked to and my own experience with a few different brands of headphones leads me to conclude at the moment that both frequency response and distortion specs appear to be dubious.

INdeed, I believe them to be correct, if by this you mean correlation of FR vs. the same data from a speaker measurement. With the headphone being coupled directly to the ear and with no HRTF(head related transfer function) or crossfeed effect as naturally occurs with speakers, the FR measurements of both can not be weighted identically, at least not into the midrange and treble bands. However, I suspect if one was to measure speakers using a binarual head and then match this response with headphone on the head, that the resulting sound would be comparable. I'll get around to trying this one day...

If the headphone needs to be placed perfectly over the ear for the their specs to be real then realistically how often does that happen?

Good question. The ear structures of differing people, while averagable, are unique between individuals. This does prevent an absolute accurate method of measurement. However, I believe that average useful measurements that are 'mostly' accurate and useful are entirely feasible.

BTW: If you have any papers or articles on this subject of headphones please e mail me or send me the links. I have the distorion paper by Jamie Moir. I have read it at least ten times

Unforunately, I am not aware of any specific articles on THD and relation to headphones specifically.

P.S. Thanks for the articles you sent me earlier, if I didn't thank you already.

My memory is not so good about this, I'm afraid. I can not remember sending you any articles. LOL. EDIT-I now remember the papers I sent. Your welcome.

-Chris

 

[mtrycrafts]

"For example, 15% THD is the approximate threshold under 100 Hz. Distotion can be identified at much lower levels in pure tones(assuming sufficient duration to pick up the pattern), but pure tones are not represenative of real-world application(s) for reproduction systems."

Hi Chris:
I have always wondered that if we had real low distortion transducers at low frequencies would the 15% figure drop? Having recently finished a prototype headphone amp, I am still really sceptical of not only headphone distortion figures but frequency response also.
d.b.

I am sure thresholds are tested on very good equipment Certainly in other papers they were.
Furthermore, these may have been done with headphones? I need to recheck the paper

 

[Dan Banquer]

Distortion

If you ever had a close look at the distortion figures of most woofers, even the one's that are considered "good" I still think you would be asking the same question. Personally, one of the things I find offensive about practically all loudspeakers is the amount of distortion coming out of the lower registers.
Maybe it's my musicl education here; I minored in tympani when I was In music school.
d.b.

 

[b_panther_g]

According to Dan
“…Personally, one of the things I find offensive about practically all loudspeakers is the amount of distortion coming out of the lower registers…”

All this talk about the distortion characteristics of loudspeakers makes we wonder 2 things...

1) How can anyone seriously claim to hear the differences in certain types of amps? I mean even if humans can hear the difference between .01% THD vs. .0001% THD, how would anyone know? It seems like even very good speakers still produce thousands of times more distortion. Even if we were on Fantasy Island and the speakers are set up perfectly in the perfect acoustical space, they would still produce all that distortion right? Please let me know if I'm missing something.

2) Wouldn't it be more useful for speaker reviews to include a chart that has THD vs. Db vs. Freq. I think this would go a long way to help understand the sound. Even if the reviewer gives a description of their room and takes the measurements from the listening spot. This would help the reader visualize what the speaker might sound like in their space. Or if it’s even worth auditioning the speaker.

Would anyone else be interested in such measurements?

Later,
B

 

[Dan Banquer]

Distortion

Yes and no. Loudspeakers typically put out 2nd, 3rd, and 4th order harmonics. Note some of the waterfall plots taken on loudseakers. Then note audibilty of upper order distortions like 5th order distortion on up as opposed to the audibilty of lower order distortion. Once again, it's just not that simple, but yes I would like to see some of the measurements you have described. Who knows, it might embarass the loudspeaker industry enough to do something about it. ( O.K., I'm dreaming here)
In addition, I stongly suspect that many people are simply used to hearing certain kinds of distortion and "learned" to accept this as normal.

d.b.
P.S. Bongiorno did note that the musical scale does deviate from the "perfect" electronic scale, and he is correct. In the treble region the musical scale is "bent" so to speak, and I think this is one of the reasons that upper order distortion is considered harsh and aggravating. It's almost (?) a form of dissonance.

 

[b_panther_g]

OK. But regardless of the type of distortion, reducing it would still be an improvement, right?

It’s becoming common to see THD vs. Db vs. Freq. measurements in subwoofer reviews. Why not do it for all speakers? I think it’ll be useful.

I think those measurements have had an affect on sub manufactures. There’s competition to produce the sub with the deepest and cleanest bass. Don’t you think that will carry over to the rest of the speaker market, if similar measurements are performed? I do.

Later,
B

 

[Dan Banquer]

Distortion

If a cetain type of distortion is known to be inaudible at a pre determined level, is it bad? The way I'm looking at it is if it's inaudible I'm not worried about it and I can direct my attention to more worthy matters.

"Don’t you think that will carry over to the rest of the speaker market, if similar measurements are performed? I do."
You are far more optimistic than I am. I hope you're right however.
d.b.