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Audibility thresholds of amp and DAC measurements

Blumlein 88

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How do you expect to hear THD of 0.05% or even 0.005% when loudspeakers are having THD of app 0.5% (above app 200Hz)?

Btw, right now I'm listening to my tube amp with THD of 0.2% and SNR of 70dB and cannot hear neither that THD nor noise when switching to my Rotel amp which has far better specs than that. How do you explain that?
Well, you could hear .5% vs .55% perhaps if you get to compare the two immediately one right after the other.
 

Blumlein 88

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Please don't "implement" that.
I was trying to call attention to the insignificance.



My personal experience was from listening to a single tone: 1 dB is difficult to discern.

A smaller change in dB over a broader range of frequencies (low-Q) may be more noticeable as the difference in available sound energy can significantly greater than over a narrow-Q, higher dB shift. One may notice tonal shifts like this (music becomes slightly more bass-heavy, or treble-oriented, etc). But, at what center frequency and over what range is this 0.5 dB shift reliably audible ?
This gets into why level matching by ear doesn't work. You will have trouble with knowing you are hearing a 1 db level shift or less. Yet if you were blind tested you'll reliably choose as better the 1 db louder file.

Also like was mentioned with the low Q FR differences being audible, broad multi-octave response differences can be reliably chosen as different when compared to a flat file directly. Yet if you listen in isolation your not likely to pick up on one version being slightly drooped in the top 3 octaves by only a decibel or so.
 

graz_lag

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How do you expect to hear THD of 0.05% or even 0.005% when loudspeakers are having THD of app 0.5% (above app 200Hz)?

Btw, right now I'm listening to my tube amp with THD of 0.2% and SNR of 70dB and cannot hear neither that THD nor noise when switching to my Rotel amp which has far better specs than that. How do you explain that?

Do you know these ? ;););)

1545080785381.png
 

andreasmaaan

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Nice OP @flipflop :)

@sergeauckland and others, I always tend to agree in principle that audiophile land takes distortion (especially the nebulous THD metric) far too seriously, but I do think there is pretty strong evidence of distortion audibility below 0.01%, although when I say "audible", I mean quite specific kinds of nonlinear distortion being discernible from an undistorted signal, as opposed to "sounding distorted" (and it's a whole other can of worms, but low levels of distortion seem to be preferred by a large number of test subjects across various studies).

The main study I have in mind is "Psychoacoustic Detection Threshold of Transient Intermodulation Distortion" by Petri-Larmi et al in 1980. There were two subjects in that study who, after much training and screening, were able to reliably differentiate between a signal with no additional distortion added and a signal with an average of 0.003% (averaged over 250ms) of added transient intermodulation distortion on a particular piano track.

This is the table showing the study's results, subjects two and five were the "golden ears" in this case:

1545077691421.png


Neither subject preferred the undistorted signal nor were able to say which was and which wasn't distorted btw. They were just able to discern the difference to a statistically signficant extent.

It's a bit complicated here since the distortion we're looking at was averaged over a 250ms time window with a complex signal and was no doubt very nasty being TIM, i.e. it's impossible to translate this finding into a THD or IMD figure for a sine wave.

And then there's the whole problem of THD being a more or less completely meaningless figure in itself, as the spectrum of the distortion and its relationship to the signal envelope (e.g. peaks vs zero crossings) are so much more important (hence the far greater audibility of e.g. crossover distortion vs tube saturation).

But I think it would be fair to say that some types of nonlinear distortion below 0.01% will be audible to some people on some systems.

How do you expect to hear THD of 0.05% or even 0.005% when loudspeakers are having THD of app 0.5% (above app 200Hz)?

I tend to agree, but again am hesitant to be so certain. A decent single speaker might generate 0.5% THD at 90dB RMS, but most of that distortion will be very well-masked 2nd order distortion, while most music in most homes isn't listened to as loud as 90dB RMS.

Moreover, transducer distortion tends to drop to relatively low levels as signal level decreases. 0.5% @ 90dB may translate to 0.1% or 0.2% @ 80dB, which is still moderately loud in most living rooms (if we assume two speakers, a listening distance of about 3 metres, and an Rt of about 0.5, this will likely produce about 80dB RMS at the listening position).

Moreover, as signal level decreases, so does the masking threshold for sounds higher in frequency than the masker (i.e. higher order harmonic distortion or high frequency IMD).

So if a DAC or amp is putting out 0.1% or even 0.01% distortion independently of SPL at the listening position, and particularly if the spectrum of that distortion is nastier (e.g. higher order) than the distortion spectrum of the speakers (which tends to be lower order and therefore much better masked), I can at least see an argument that that distortion might be audible.

Anyway, I still think -120dB is absurdly low even for the strict requirement. I'm not sure I understand where this figure derives from @flipflop? It doesn't seem to be mentioned in the Nwavguy article that you link; perhaps you could explain more?

Also, I'm not sure what the "lenient" requirement is supposed to represent exactly, but I think it's quite reasonable if the criterion is supposed to be "never sounding distorted" (even if certain types of distortion at that level are nevertheless discernible from an undistorted signal with certain types of music and listening levels).
 

mi-fu

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Thank you very much @flipflop!! It is very helpful for laymen like me. Much appreciated!! :D
 

amirm

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What you're saying seems intuitive, but I'll have to ask you to provide a source. Without exact numbers, it would be an estimation that I wouldn't feel comfortable making.
This is the most fundamental aspect of psychoacosutics: critical bands and simultaneous masking:

frequencyplacetransformation-83-638.jpg


The Wiki has many references and there tons more if you search: https://en.wikipedia.org/wiki/Auditory_masking

Indeed that is where the uptick is in NWAVGUY's thresholds. What he has is actually quite conservative. The 12 kHz masker is very strong and no way will you hear tones round it at low amplitudes.

1024px-Maskersameauditoryfilter1.svg.png


I can't give you an exact number for this but you can use the above graph as a guideline. Whatever you put in there, can't be a flat line.
 

sergeauckland

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What actually IS TID? It was very popular way back when, but I never understood what it actually was, why amplifiers would ever have it, and how it was measured. As far as I recall, TID involved signals totally outside what could ever be generated by a band-limited programme signal, and then only if the amplifier was heroically badly designed with poor open-loop bandwidth.
S
 

andreasmaaan

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What actually IS TID? It was very popular way back when, but I never understood what it actually was, why amplifiers would ever have it, and how it was measured. As far as I recall, TID involved signals totally outside what could ever be generated by a band-limited programme signal, and then only if the amplifier was heroically badly designed with poor open-loop bandwidth.
S

To the best of my knowledge, yes, TIM is slewing related. However, without fully understanding what causes it, it's definition and measurement are pretty well defined it seems (DIM 30 and DIM 100 Measurements per IEC 60268-3 with AP2700), and in those AP tests at least it seems to be generated by signals within the audio band. However, I'm happy to be corrected on this point by someone with greater knowledge.

In that study I posted, the distortion was simply averaged across a 250ms and compared to the signal across the same 250ms window, regardless of what caused it or how it was generated. I assume that, given that the music signals themselves were within the audio band, the "TIM distortion" was wholly generated by signals within the audio band, but again, I'm not entirely sure of this.

In any case, since the OP seemed to be interested in naming distortion thresholds that were universally applicable and took no account of the spectrum of distortion or relationship to the signal envelope, I thought it worth noting that this might mean the thresholds would need to be significantly lower than what you'd expect in % terms from a well-behaved device.
 
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flipflop

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Why would the limit not be sloping like the THD plot but remain horizontal as in the plot above over the entire power output range ?
At 1uW even a 120dB@1mW IEM headphone produces just 90dB SPL.
Even very efficient 'normal' headphones would merely produce about 70dB SPL
Why would the 'strict' line need to be 120dB all the way down to nV territory in this case ?
The same goes for the lenient line btw.
It would be safe to assume nobody on this planet can hear -30dBA let alone -50dBA.
Good questions.
If I had to draw a line for every single sensitivity rating, I might as well had posted an orange square. I assume ideal conditions / worst case scenario (depending on how you look at things) for all the thresholds. I'd be happy to use one for the power graphs, too, but I wouldn't know which sensitivity to pick, so I can't draw an appropriately sloping line.
Basically, you would have to tell me the sensitivity of the most efficient headphone before I could make an informed adjustment of the thresholds.
I think the realistic dynamic range for music reproduction is about 70dB at normal to realisticly loud levels.
I'm sure there's plenty of opinions on this :)

How do you expect to hear THD of 0.05% or even 0.005% when loudspeakers are having THD of app 0.5% (above app 200Hz)?

Btw, right now I'm listening to my tube amp with THD of 0.2% and SNR of 70dB and cannot hear neither that THD nor noise when switching to my Rotel amp which has far better specs than that. How do you explain that?
@andreasmaaan gave a more detailed explanation of what I was going to reply with, so I'll just rephrase the bottom line in my own words:
Your loudspeakers could in theory produce less audible distortion at 0.5% THD, producing mainly 2nd harmonics, than an amp producing mainly higher order harmonics at 0.005% THD.

I think some people might interpret the lenient thresholds as "anything past this point is guaranteed to be audible". They don't work like that. Far from it. I've edited the introduction to reflect that fact.

Maybe I am missing something completely, but if you are talking about audibility threshold of what we humans can hear or cannot hear, you cannot ignore masking, as that is part of the human condition and applies to all of us.
The research conducted by Fastl and Zwicker employed burst of sine waves in their testing. Correct me if I'm wrong, but I don't think masking applies to sine waves.
No offence to @amirm or @flipflop Fantastic that measurements are being made, but there does need to be some guidelines as to how one is testing an audibility threshold that means something to the average listener. Something that they can actually download and listen to which usually means music. That way folks can ABX something transient in nature, and not steady state tones... and determine their own audibility threshold...

@Ethan Winer has an artefact audibility comparisons that folks can download and try: http://ethanwiner.com/audibility.html

Measurements are meaningless if we don't know what is audible and what is not... And yah, there is a bell curve that would apply to most of us :)
None taken.
I'd be happy to implement a 3rd threshold category for what an average listener is able to detect. You would have to provide figures and sources for every measurement covered in my original post, though. If you're asking me to trawl through the entirety of Hydrogenaduio, you're asking too much.
Nothing wrong with your ideas, it just takes a lot of work to carry out. Lots of numbers to crunch ;)

Anyway, I still think -120dB is absurdly low even for the strict requirement. I'm not sure I understand where this figure derives from @flipflop? It doesn't seem to be mentioned in the Nwavguy article that you link; perhaps you could explain more?
It's based on Amir's article on dynamic range. If you can provide a source for a better figure, I wouldn't mind changing it. As far as I know, none of the measurements included in my first post have anything to do with TIM.

I can't give you an exact number for this but you can use the above graph as a guideline. Whatever you put in there, can't be a flat line.
Damned if I do, damned if I don't :(
 

Guermantes

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Thanks @flipflop, that's a good overview and I like how you have applied the thresholds to the measurement graphs in order to put them into context. It made it very accessible.

For those that are favouring music programme material for testing, I think it is very important that we understand and state what type of material we are using because that will affect the relative audibility of distortions. The table that @andreasmaaan posted from the 1980 study is indicative of this in that it appears solo piano music was more revealing of the distortions than "pop" music (I hope the original article listed the actual recordings for reference).

Yes, this all a matter of masking thresholds and audibility, but obviously if I favour using broadband material such as popular songs for testing, then I am probably going to be more tolerant of some types distortion than someone who uses solo piano or voice recordings. But then see Archimago's tests of added jitter where the broadband material was more revealing: http://archimago.blogspot.com/2018/08/demo-musings-lets-listen-to-some-jitter.html

This raises another question: is there a set of reference recordings that we would be happy to use as an industry standard (much like there is a standard set of tones for testing)? I have used the Parsons and Court Sound Check CD quite often, but is this an area where personal preference will tend to triumph over standards?
 

Sergei

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What a great original post and discussion! Not much to addd, yet still ...

Mammal hearing is very non-linear, over multiple dimensions. It evolved that way to suppress noises typically found in nature, and to extract with high temporal precision, and thus low error of direction to source, all kinds of sounds pertinent to survival.

As it relates to the just-noticeable difference between sound levels, human hearing is not very selective at the lower and upper parts of dynamic range, due to non-linear compression. Neither is it uniform over frequencies. Moreover, it varies markedly between individuals. That's why most people can only barely tell apart 110dB and 115dB SPL at 50Hz, whereas some professional musicians distinguish with 75% success rate signals played at 0.2db louder or softer at mid-range frequencies and SPL.

THD, or even TID, do not directly determine the perceived transparency. They are, however, correlated with other, more relevant, characteristics. Temporal precision is one of them, as humans can detect as low difference in the timing of arriving transient as 10 microseconds, whereas characteristic time of registering a steady tone is around 10 milliseconds. That leads to non-obvious differences in perceived quality of audio gear. For instance, as it relates to the typical amplifiers of the 1980s, with output stage made of complementary bipolar transistors, I can tell you an amusing story.

It was indeed empirically found in the early 1980s that THD of 0.003% or less at 1KHz non-clipping signal equates to sonically transparent amp of then-prevalent topology. Yet it took another decade or so to figure out that more relevant parameters, strongly correlated with THD in amps of that classic topology, are amp's slew rate and damping factor. The amusing part is that the hobbyists who built their amps back then using surplus military radar parts turned out to be right, despite seemingly unreasonable excess of having an amp that would stay stable at rated power for frequencies of up to 2,000,000 Hz (a 100x overkill).

Likewise, it could well be that the seemingly unreasonable excess of characteristics of the best modern DACs deemed transparent is correlated with other, more perceptually important, characteristics. One oft-sited characteristic is the vanishingly low level of distortions not normally found in nature, and thus very objectionable to mammal hearing. The dual of that is that seemingly awful THD measurements, especially those of transducers, are not objectionable, because they are caused by distortions of the variety that mammal hearing system evolved to perfectly cancel.
 

andreasmaaan

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The research conducted by Fastl and Zwicker employed burst of sine waves in their testing. Correct me if I'm wrong, but I don't think masking applies to sine waves.

Masking applies to all signals, but the thresholds vary somewhat depending on the type of signal (as well as duration and the temporal relationship between masker and maskee FWIW).

For example, here are some graphs from Zwicker and Fastl showing simultaneous masking thresholds for critical-band wide noise centred at 1kHz (left) vs a pure 1kHz tone (right):

1545088829035.png


As you can see, the differences between the effect of the two maskers are not as great as you might expect.
 

wiggum

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Great summary but have some questions. Here is one.
I think the realistic dynamic range for music reproduction is about 70dB at normal to realisticly loud levels.

Most of the music released now don't even have 20dB dynamic range. Classical music is usually around 30dB. I am not aware of any music that exceeds that. FM broadcast can be as low as 6dB because of dynamic range compression.
 
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flipflop

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Masking applies to all signals, but the thresholds vary somewhat depending on the type of signal (as well as duration and the temporal relationship between masker and maskee FWIW).

For example, here are some graphs from Zwicker and Fastl showing simultaneous masking thresholds for critical-band wide noise centred at 1kHz (left) vs a pure 1kHz tone (right):

View attachment 19006

As you can see, the differences between the effect of the two maskers are not as great as you might expect.

Maybe I didn't make myself clear enough or maybe I just don't understand the topic as much as I'd like. Let me try again.
If there is only one tone being played, there are no other tones to be masked, so masking doesn't apply in this case. For one tone to mask another, you would need a minimum of two different frequencies. The research I'm talking about only makes use of a single 1 kHz tone.
23.PNG
 

amirm

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If there is only one tone being played, there are no other tones to be masked, so masking doesn't apply in this case.
The signal tone masks the distortion products show in FFT. It will cast a shadow on each side of the main tone and attenuates their audibility by the same amount.
 
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flipflop

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The signal tone masks the distortion products show in FFT. It will cast a shadow on each side of the main tone and attenuates their audibility by the same amount.
Thanks, Amir. I get it now.

Getting back to @mitchco: I certainly don't want to ignore masking effects, but I can't tell you how they will affect anything either.
 

sergeauckland

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To the best of my knowledge, yes, TIM is slewing related. However, without fully understanding what causes it, it's definition and measurement are pretty well defined it seems (DIM 30 and DIM 100 Measurements per IEC 60268-3 with AP2700), and in those AP tests at least it seems to be generated by signals within the audio band. However, I'm happy to be corrected on this point by someone with greater knowledge.

In that study I posted, the distortion was simply averaged across a 250ms and compared to the signal across the same 250ms window, regardless of what caused it or how it was generated. I assume that, given that the music signals themselves were within the audio band, the "TIM distortion" was wholly generated by signals within the audio band, but again, I'm not entirely sure of this.

In any case, since the OP seemed to be interested in naming distortion thresholds that were universally applicable and took no account of the spectrum of distortion or relationship to the signal envelope, I thought it worth noting that this might mean the thresholds would need to be significantly lower than what you'd expect in % terms from a well-behaved device.
I don't think DIM and TIM are the same thing. As I understand it, TIM is what happened to a transient of greater slew rate than the amplifier can accommodate. As such, it should never happen in any amplifier if the bandwidth, both open and closed loop were correctly designed. Even if the amplifier was badly designed, a simple filter at the input would stop it. It seemed to be an issue with unfiltered preamps that had MHz bandwidths and power amps that didn't. In any event, no normal signal off an LP or tape would trigger it, and CDs are band limited. I suppose a record click or unfiltered tape recorder bias might be sufficient, as might an unfiltered NOS DAC, but frankly, why worry about badly engineered sources when there are plenty of well engineered alternatives?

I've never been convinced that TIM was ever a real problem that needed fixing, or indeed, measuring.

S
 

restorer-john

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Why would the limit not be sloping like the THD plot but remain horizontal as in the plot above over the entire power output range ?

It makes little sense to draw an arbitrary horizontal line over a THD vs Power plot. Especially measuring at 300nW and up. It's pointless- it's all residual noise until several mW and it's characterised completely differently for various topologies.
 

restorer-john

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I've never been convinced that TIM was ever a real problem that needed fixing, or indeed, measuring.

Measuring IM at high frequencies does essentially the same job.

It was coined during the DC-Daylight amplifier wars in the 1970s.

There's no doubt however that transient behaviour should be at least visualised, square wave response checked and absolute phase preservation commented upon. Surely all these Headphone-aholics would want to know if their amplifier is inverting or not? The standard single pulse or clipped sine is perfect for that.
 

mitchco

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@flipflop Thanks for getting back to me. Wrt HA, I would not expect you to go through the entire site, but a quick search through the Listening Tests section should yield some good results: https://hydrogenaud.io/index.php/board,40.0.html

Masking is a funny, but real thing... The link to Ethan's test files should give you a good idea of level of masking if you check them out.

As mentioned, if you have JRiver Media Center, you can easily and quickly test your audibility threshold with the bit depth simulator:
https://yabb.jriver.com/interact/index.php?topic=74999.0
Matt, who is one of the principals writing the software did better than I did at 13 bits, but only if he turned the volume up (cheating :) but, as folks will find out. somewhere between 12 bits and 13 bits, under "normal" or "reference" level listening conditions I mentioned in my previous posts, is typically the limit. Once an (any) artefact is below -80 dBFS, for most folks it is simply inaudible... regardless of the type of artefact...

One more point to ponder for folks performing audibility testing in a home listening environment using speakers, which also has a noise masker or noise floor. For my room it measures about 45 dB SPL broadband noise with a rise at the low frequencies. If my critical listening level is 83 dB SPL, at what level can I hear below the noise floor of my room before the noise masks the signal?
 
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