Harmonics above 20Khz - "Hi-Fi" and the limits of human hearing

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Take a piece of paper.

Draw a triangle on it.

The three points represent the listener with respect to the two speakers.

Make the speakers 10 ft apart, with the listener 10 ft back.

Now.....audiophiles have been shown to be easily able to differentiate between signals..in that 'stereoscopic sound stage' , which is strung between the speakers..where the 'image point' seems to be over, from left to right, by approximately 1 inch, and less. Now, take that 'timing' information, and then apply it to extremely rich signals, in terms of the entire note structure. Harmonics count.

Take that information,and you add it to the fact that the ear hears, for the larger part, via the leading edge of the given transient, and it's timing differentials from harmonic transients, and the level of each.


If you go through the rather simple math..you end up with a minimal requirement to satisfy the better trained audiophiles (and I POWERFULLY stress that is is BELOW the capacity of the human ear!!! ..it is merely as well as audiophiles have managed to train themselves-nothing more)..of..get this:

500Khz sampling rate with a 20 bit word length. This as a MINIMUM. This specification is only taking into account one single aspect of the human human hearing function. One we ALL express, every single day.

As for cables, this means they must be capable of not altering a signal in any way, whatsoever..from actual DC...out to approx. 1mhz, with a +10db to -70db range of loading ..this..with ZERO phase distortion or alteration of the signal..in any way, shape or form. PERIOD. I'm not talking about a clean -3db down at 500khz, but 0db down. NO phase or complex LCR issues, at ANY point in that range. Harmonics and complex note structuring take these minimums up into the low mhz range!!!!!

This is not due to the single ear's function but as a stereoscopic pair, concerning timing issues.

Which is why tube amps and turntables work. Both have extremely low inter-channel phasing issues. Totally analog. Taken to another point of analysis, it shows why digital amps are generally considered...to the more learned ear...to 'suck'.

Digital falls flat on it's face.

But the ear-brain combo can pull 'intelligence' out of a 3.5 bit deep digital signal. This does not mean that it equals hearing function, but the exact opposite. We are incredibly good at figuring out complex and dirty aural issues, but we can also 'relax' into a perfectly represented signal, as well.

This is why we can hear differences in audio equipment and wires.

I've known this simple point since 1992. Ive tired to educate the industry many times. But to no avail.

Yet..the logic and the math sit there in plain sight...like a 9000lb gorilla in the middle of the room...and are ignored.

If you go through the effort of understanding this simple point, the whole entire audiophile argument makes 110% perfect sense.
 

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audio-kraut said:

(snip)
If your hearing stops at 20kHz - what is the difference between the fundamental and the harmonics?
(snip)
I have a hard time understanding your confusion. If you can't hear it - you can't hear it.
(snip)

If I interpret percy correctly...

I think percy was trying to say that he feels that a high frequency harmonic riding on its lower frequency fundamental may be perceived differently to the high frequency if it were alone...

For example, I think he was suggesting that you may not be able to hear 24 kHz directly, but you may be able to perceive it if it is a second harmonic in the presence of its 12 kHz fundamental. In other words he is suggesting that a 12 kHz tone will sound different to a 12 kHz tone + its second harmonic, although you may not be able to directly hear the second harmonic.

Is that what you meant percy?
 
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KBK said:

...the fact that the ear hears, for the larger part, via the leading edge of the given transient, and it's timing differentials from harmonic transients, and the level of each.

You have stated that in a previous post. I find it very interesting and would like to read more on the subject. Where should I start?


KBK said:

500Khz sampling rate with a 20 bit word length. This as a MINIMUM. This specification is only taking into account one single aspect of the human human hearing function. One we ALL express, every single day.

Hang on. You mention 500 kHz sampling, which will provide a reconstituted bandwidth of 250 kHz. And then you mention a requirement for flat to 1 megaHz? You have confused me !
 
Now.....audiophiles have been shown to be easily able to differentiate between signals..in that 'stereoscopic sound stage' , which is strung between the speakers..where the 'image point' seems to be over, from left to right, by approximately 1 inch, and less.

Why are you so worried about spacial information? That is ALL you are talking about.
It might be important to you, but my concern relates to the correct reproduction of instruments or the reproduction of the human voice, the 1" be damned.

I agree that harmonics have to be able to be reproduced as they are what makes one instrument distinguishable from another. A 1 kHz sine sounds the same from one instrument to the other, only the harmonics will give you information what instrument you are hearing.

AFAIK no one has yet shown that extension of the frequency response above 20 or 22 kHz actually leads to "more" correct audio reproduction of instruments.

A short PBS test in its series "wired" had wo musicians and two studio engineers identify analog vs. mp3 music pieces via headphones. The switching between the signals was inaudible and only announced via optical cue.
The participants could not identify the source - about 50% correct.

Harmonics and complex note structuring take these minimums up into the low mhz range!!!!!

Where is your evidence - not even the guy who I linked to - and did actual measurements - proclaims such wild speculation.
Throwing wild and unsubstantiated claims around is the hallmark of the "true" audiophile - just don't be bothered abiut evidence.
 
Hi Percy,

How about a very simple experiment:

listen to sine, triangle and square wave at 14 Khz. In theory, they all should sound same if we do not hear above 20Khz (15khz in my case).

Couple caveats:

Equipment should reproduce waveforms more or less undistorted. Speakers will not do, but I think good headphones will work (with flat response up to 30Khz).

Make sure that subjective loudness is the same during listening.

I would love to do this myself, but I dont have headphones :)
 
PMA said:
It does not sound the same. I have a disc "Resolution Project" with same music recorded simultaneously with resolution and sample rate up to 24bit/192kHz. Have a look here:

http://mixonline.com/mag/audio_resolution_project/

What was the reproduction chain ? What speakers ? amp ? etc.


Gordy said:


If I interpret percy correctly...

I think percy was trying to say that he feels that a high frequency harmonic riding on its lower frequency fundamental may be perceived differently to the high frequency if it were alone...

For example, I think he was suggesting that you may not be able to hear 24 kHz directly, but you may be able to perceive it if it is a second harmonic in the presence of its 12 kHz fundamental. In other words he is suggesting that a 12 kHz tone will sound different to a 12 kHz tone + its second harmonic, although you may not be able to directly hear the second harmonic.

Is that what you meant percy?

Yes, that is exactly what I meant! Thank You!
 
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SY said:
Jan, do you find it curious that there's been no replication or follow-up, even after all these years?

Yeah, in fact this is the only paper I have been able to find on the subject (which doesn't mean there aren't any, of course. As I said, I had the feeling this paper was anyway trying to legalise the case for 96/192kHz sampling, so it may well have been a single shot. I was hoping someone else might have some more info on it.

Jan Didden
 
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percy said:
So it looks like there is no disagreement that musical instruments do have harmonic content well over 20Khz.

What remains now to be found is whether it would sound the same to the human ear if the harmonics over 20Khz were removed v/s all harmonics retained just like in the original signal.
Which I'd imagine shouldn't be too hard to experiment today which the availibity of extended range tweeters and amplifiers.

Here's what I think about all this -
In terms of human hearing capability, a higher order harmonic is not the same way as a fundamental of the same frequency. i.e. the 29th harmonic at 30Khz is not the same as a 30Khz fundamental. It is intuitive to think that since you cant hear 16Khz so obviously you can't hear 30Khz, but I doubt its as simple as that.


It is well known (and exploited by speaker builders as well as musicians) that if we hear two tones of, say, 2000Hz and 3000Hz our brain synthesises the fundamental and we 'hear' a pitch of 1000Hz with some 'timbre' caused by the two harmonics.

I don't know how high in frequency this goes on, though.

Jan Didden
 
Take a piece of paper.

Draw a triangle on it.

How was it determined that this differentiation was due to timing differences and not amplitude (volume) differences as the virtual image moved across? (Got a reference on this study, by the way, it would be interesting to get more details on how it was done?)

How does the time of arrival theory square with the fact that the wavelength of a 250kHz tone in air is only 54 thousandths of an inch? Did the listener keep his head THAT steady during the test (both left to right and forward/backward), or did they use a head vice? The simple math seems pretty suspicious, I think. More backup, please.
 
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Irakli makes a very valid point. I have tried this many times using a function generator and above about 4.8 Khz sine/square & triangle waveforms sound identical.Starting at say 2 Khz with a square wave and slowly increasing frequency all hint of the harmonic structure disappears around 4.8 Khz. This is on a pair of very poor quality H/phones, however using these on a pure (sine) tone I can hear to 15+ Khz.
Apply 5Khz square wave to line inputs on a digital recorder (MiniDisc etc) and monitor on a 'scope the line output.It will bear no resemblance due to the 20Khz ABSOLUTE upper limit filtering removing the higher harmonics.Using an analogue audio source (Any C.D. will already be bandwidth limited) I wonder if any listeners can tell the upper harmonics are missing when the recorder is in the loop.
Karl
 
percy said:
thanks for asking - it reminded me to mention a point about this -

This measurement was done using the ECM 8000. Yes it has fast rolloff after 20Khz. Point is that if the ecm 8000 could capture the harmonics, it indicates that those are indeed significant harmonics. With a mc having reasonable response up to that range, the spectrum would really be a whole different "picture".

The pre-amp (UB802) and soundcard (ESI Juli@) have good response over 40Khz+.
One thing I was wondering, how does one distinguish whether the harmonics is from the signal source or the mic itself?
 
Nice thread.

was it confirmed that this mic could reproduce those high freq. accurately?
i would think that a lot of the freq. above 20k is probably system noise.
and the whole analog to digital conversion, and depending on the system used, clock jitter etc. above 20k is gonna be tainted. right?
was dither introduced before spectral analysis?

you got to be a bona fide mad scientist to do the math for this test! and even then how does one tell the ear to subtract the noise from the output gear? Oh my god i need to stop thinking about this cause i see no end. :xeye:

but all in all it doesnt take numbers or a spectral graph to prove to me that freq. above or below human hearing affects what we hear.
a synthesizer proved that to me long ago.
 
Take two of the same passage but different sample rate, do a difference on them using the difference software at the Praxis site or any other software, then see what the spectral content is.

Yes, do, but rather than just looking at spectrum (which does show a difference, of course, which could even be noise), LISTEN to the difference. I've done it subtracting 96kHz wav files and from 44.1kHz wav files that had been sample-rate converted to 96kHz. I had to turn the difference level up about 30dB to be able to hear anything at all; but others' ears might be better at that than mine and recordings of different music made with different mics might show more of a change. But the lack of difference in that one test was rather stunning.
 
bwaslo said:


Yes, do, but rather than just looking at spectrum (which does show a difference, of course, which could even be noise), LISTEN to the difference. I've done it subtracting 96kHz wav files and from 44.1kHz wav files that had been sample-rate converted to 96kHz. I had to turn the difference level up about 30dB to be able to hear anything at all; but others' ears might be better at that than mine and recordings of different music made with different mics might show more of a change. But the lack of difference in that one test was rather stunning.
Yes, we have to listen. But in order to figure out what makes the differences, it is not only necessary to look at the spectrum content, but also look at all three tracks on the same time scale.
 
soongsc said:
Take two of the same passage but different sample rate, do a difference on them using the difference software at the Praxis site or any other software, then see what the spectral content is.

I am not quite sure about this test. Are you saying record a passage at two different sample rates and do a difference ?
If the content really has harmonics in the spectrum above the frequency of the lower sampling rate you will always see a difference.

Its the same as recording just at the higher sampling rate and looking at the spectrum beyond the Fs/2 point of the lower sampling rate. Unless I am missing something.


bwaslo said:


I've done it subtracting 96kHz wav files and from 44.1kHz wav files that had been sample-rate converted to 96kHz.

Did you say you converted the 44.1Khz to 96Khz ? If so, thats an invalid test. You need an 'original' 96Khz file recorded at true 96Khz.
 
bwaslo said:




How was it determined that this differentiation was due to timing differences and not amplitude (volume) differences as the virtual image moved across? (Got a reference on this study, by the way, it would be interesting to get more details on how it was done?)

How does the time of arrival theory square with the fact that the wavelength of a 250kHz tone in air is only 54 thousandths of an inch? Did the listener keep his head THAT steady during the test (both left to right and forward/backward), or did they use a head vice? The simple math seems pretty suspicious, I think. More backup, please.


It is both amplitiude and timing. Which really loads up the level of complexity, and thus the amount of information that needs to come through the given chain of electronics unimpeded, is larger than most think. The study I read at the time, stated equal amplitude - timing variations. Back in 1992-93? Couldn't tell you where it came from, today. Not a freaking clue.

The experiment can be done with a small bell and someone walking or moving it. Then it becomes strictly a timing issue.


Suffice it to say, the information is right there in front of you..in front of any stereo system, by sitting in the listening chair. Go through the logic of it, YOU are the 'cutting edge' study at that point. There isn't much in the way of academia on this one, it's all too restricted in terms of knowledge desired for a given point in research. We are the research at this point in time, as in normal acedemia this particular point does not apply too darned often..thus..no studies on the subject other that what I've posted here. At least, as far as I am aware of things.

A pocket calculator, a sheet of paper and a pen..and a brain. Not much more to it that that. The point I made does become quite obvious, when the few minutes are spent to go through it.

It has nothing to do with the frequency. It specifically has to do with timing of arrival and intermixing of any given harmonics. All turn out to be excruciatingly critical. Amplitude, timing, and harmonics. Under that point of analysis, the specs on a given amp or cable catapult into the critical. Two analog amplifier channels at 20khz (0db down) have, relatively speaking..between them...ZERO phase issues, in terms of being able to deliver signals on one channel...and the next channel recieving and sending out the same signal 1 micro-second later.

Even a pair of 1955 tube monoblocks that start rolling off at 17khz and with power and phase issues can (and do) easily excel at this task.

A digital system cannot.

Which is why I have a highly regarded $3.5k+ digital crossover (modded out to retail at about $12k), running at 96khz..and I say: I think it bites the big one. Sucks, it does.

You can't say I haven't given digital a chance (just being defensive for digital-or-analog's sake). I've done the same since digital was introduced, back in the early-mid 80's. I do my homework, and I put myself in the other guy's shoes.
 
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