are you sick of that digital sound?

[John Eppstein]

Originally Posted by theblue1

There seems to be a distinct difference of opinion about whether or not real world DSD is superior to conventional PCM, particularly in light of contemporary sampling design considerations. I'm agnostic on it. And definitely not ready to wade into some of the detailed debate. I have to admit that, in my gut [highly intuitive and completely subjective nature of same duly noted, I hope], I lean toward skepticism about DSD. Some folks considered generally authoritative can make a very good sounding case for the downside of DSD, but there are some respected advocates, as well, I think. Still, my starting place for any 'new' technology is definitely skepticism, as it was with digital a quarter century ago.

Well, in this case hearing is believing. Don't take my word for it, listen for yourself.thumbsup

[John Eppstein]

Originally Posted by Mr.HOLMES

There I found it have searched a long time for it.

So this Graph shows in how many countries over the world sound engineers are sick of digital since 1967. A slow dip was in 2003 and 2007.

Ha! Interesting..... Perhaps we had a large influx of newbies in '03 and '07 to account for the anomalies? No, I don't mean anybody here......

[norman_nomad]

Originally Posted by John Eppstein

Sure, but that has nothing to do with what I'm saying - in fact, it supports my argument. He's why - with a mechanical drawing aid (a compass) you can use 2 dots to "define" a circle. With a similarly artificial aid - a smoothing algorithm - you can use two points to "define" a sine wave. HOWEVER if I put two dots on a piece of paper, hand you a compass, and ask you to draw me a square, can you do it? No. The tool you have presupposes that anything defined by those two points is going to be a circle, not a square, triangle, or, god forbid, a complex polygon. BY the same token, your algorithm that allows you to "define" a sine wave with two points presupposes that any two points you give it lie on a sine wave - if those points happen to instead be part of a square, triangle, or complex waveform the algorithm fails to reproduce the original result. It's a case of the design of the tool presupposing the form of the output, with no regard to the actual form of the input. In essence, all harmonic content is lost by the artificial constraints of the tool, which is based on the assumption that, although two points actually mathematically define a straight line (the side of a triangle wave) since the waveform might actually not have been a triangle wave it's better to through out all the potentially spurious harmonic content and make it a nice safe sine wave with no harmonic content at all. Thus we lose detail.

The problem here is the use of the word "define". Two points actually can only define a straight line. If the points are equidistant in time, as set by a digital clock, the straight line therefore define, in the absolute, rigorous sense, a triangle wave. Get a piece of graph paper and a ruler. Place dots on the graph and connect them - you get triangles, or shapes made up of triangles. THERE ARE NO CURVES. Curves only come in if you use a tool for making curves, say a Bezier Curve drawing aid. Take another piece of graph paper. This time use 4 different colored pens. With one, draw a complex wave with lots of squiggles between the lines of the graph paper. Then take another pen and plot points wherever the complex curve crosses the vertical lines. These are your sampling points. Next that pen #3 and a ruler and draw lines between the dots. This would be you unsmoothed output waveform. Finally take pen #4 and your Bezier curve and plot the smoothest curve that will join your dots. Still doesn't look a whole lot like your original waveform, does it? The Bezier curve is a tool for plotting sine based curves, just like your smoothing algorithm and it has pretty much the same effect on the data.

Smoothing algorithms make assumptions about the data that are not true. The only way you can "define" a sine wave with two points (which actually define a line, not a curve) is with such artificial tools. It takes a minimum of 3 points to define a curve, and even then, any data between those points will be lost - you only get a greatly simplifified generalization of the original shape.

Once you lose it in the sampling process it's gone - you can't get it back. You may be able to use mathematical trickery to get something less obnoxious than your raw sampled data (the graph made with the ruler), but you can never recover the complexity of the original waveform.

Q.E.D.

'Mathmatical trickery'

I'm going to copy and paste my comments from another thread... maybe you'll get something from it, maybe you won't. Enjoy!

*********************

Let's use an example to think about this.

You have a white noise generator and you're recording it's output through your a/d converter's input.

What is the full spectral content of white noise? White noise has equal spectral power density in any band.

What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz.

So with your white noise there is a combination of all of these randomized sine waves playing all at once. The smallest variation in this chaotic wave that we're interested in capturing is the wave of a 20khz signal, right? Any wave shorter than that of a 20khz wave would be higher in frequency than 20khz and thus outside of the range of most human ears. Square or triangle waves at 20khz are just regular multiples of the frequency of the sine wave. So if we can capture the 20khz signal accurately due to the frequency rate that our converter samples the sound, then we can easily capture longer, lower frequency sine waves with less frequent peaks and troughs.

So you see, any complex combination of frequencies between 20hz and 20khz can be captured perfectly with 44.1k.

The difference is in the converter design.. getting the analog components to best carry out this task without error or unintended variation.


************************

noolness says....



"However, not all signals can be represented accurately by a set of sine waves below 20kHz. In particular, sawtooth waves (also known as triangular waves) and square waves can only be represented by an infinite set of sine waves with frequencies extending all the way to infinity. When you capture either sawtooth waves or sine waves digitally, you don't get back a perfect waveform when you play it back due to filtering."

So technically you can only accurately recreated a sawtooth or square wave digitally by having an infinite sample rate.

norman_nomad:

This is true! A 20khz square wave captured at 44.1k will not capture the harmonic content created much further past the 20khz fundamental.

The question you have to ask yourself is: Do you care and does it matter?

For most of us, the answer is: No, it doesn't.

You (at least I can't) hear past 20khz. So any harmonic content created above this range due to a square or triangle wave, whether captured by your converter or not, does not and should matter to us because we wouldn't be able to hear it anyways.

An example to think about:

If a 1khz square wave is generated by an imaginary synth with infinite bandwidth played by a speaker of infinite bandwidth we would hear the 1khz fundamental along with all of the increasingly diminishing harmonics up to 20khz after which harmonics would exist, but we would not be able to hear them due to the limitations of our physical hearing.

For that same reason, a converter only needs to capture spectral content up to the threshold of human capacity, past which point there is a dubious return in utility.

This is why a 44.1khz sampling rate is considered to be sufficient - it covers the entire range of human hearing.

There are some that will argue that harmonics past the point of human hearing have some effect on the sounds we can hear. They may be right. I haven't done enough research to know if there is any merit to this or not... but before you tread down this path, consider the bandwidth limitations of your microphones and your speakers/headphones. Many of these devices are not capable of capturing or playing back much usable content past 25khz...

Also consider this: Any interaction that happens with an acoustic instrument due to harmonics past 20khz is happening in the air during the recording and thus you, in essence, record those interaction as they manifest in the 20khz and under frequency range (in other words, in the range you actually hear). You won't loose the effects of the ultra high frequencies by excluding them from the digital capture - they've already done their work in the air during the recording and their effect will be maintained on playback. Make sense?

*********************************

Idiophonic says...

I still can't help but feel that the amplitude issue exists at the lower end of sample rates because, as you indicated, the chance that your 2 samples hit the peaks is small. It seems that even with 2.2 samples (only fractionally more!) you are still in danger of under-representing the amplitude of the upper frequencies...4.4 samples would have a better chance of being more accurate in this respect, yes?

Norman_nomad:


Hey Idiophonic,

The samples do not need to be at the peak of the sample to represent the frequency accurately.

From the link that noolness posted:



"How is this possible? How does the DAC know how to "plot" the signal in between sample points? ...

How can removing frequencies above Nyquist restore the correct peak levels (which are higher than any individual sample)? This is hard to explain without resorting to mathematics, but essentially Fourier Theory postulates that any complex continuously varying signal can be represented by a set of sine waves of varying frequencies and amplitudes. When you sum all these sine waves, you get the original signal.

In the case of Figure 4, if you draw a set of straight lines between sample points, you are plotting a signal composed of many sine waves summed together. These sine waves "modify" the original sine wave and lower the actual peaks of the waveforms. When these extraneous sine waves are removed, the peaks of the sine wave between sample points are restored.


If you still find this difficult to swallow, try thinking of it in a different way. The reason a perfect sine wave is output even though the samples did not capture the peaks is that a 19997Hz sine wave is the only possible plot that you can draw that passes through all the sample points but does not contain frequencies higher than Nyquist. This can actually be proven mathematically, but I will spare you the calculations."


So to sum it up:

If you sample a twice the rate of the highest frequency you wish to capture you will able to capture that frequency accurately and reconstruct it without anomalies using a theoretically perfect analog circuit. Because there is no such thing as a perfect analog circuit, each converter will handle this task with more or less grace. The samples don't need to catch the peaks of the frequency to know how to redraw them because there is only ONE POSSIBLE PLOT THAT CAN BE DRAWN after filtering.

[John Eppstein]

Originally Posted by theblue1

You're talking about efficacy metrics of clinical treament of psychological disorders and apparently trying to equate that with the design of psychometric perceptual testing, which is a branch of cognitive research and neuroscience..

That's just nutty, if you'll pardon the witticism.


Here's info on experimental design in the field of psychology that should give you important insight into the differences: Experimental design - Psychology Wiki


And here's a general article on experimental design: Design of experiments - Wikipedia, the free encyclopedia

________

Now... I'm about to take that ol' aforementioned gitbox out into that nice spring day out there and... drink more coffee at my favorite sidewalk cafe.

So I'm counting on you to have this all sorted out when I get back and to have arrived at a consensus you can all live with...

Well some might argue that involvement in music production is per se a psychological disorder.....<grin>

[John Eppstein]

Originally Posted by norman_nomad

'Mathmatical trickery'

I'm going to copy and paste my comments from another thread... maybe you'll get something from it, maybe you won't. Enjoy!

*********************

Let's use an example to think about this.

You have a white noise generator and you're recording it's output through your a/d converter's input.

What is the full spectral content of white noise? White noise has equal spectral power density in any band.

What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz.

So with your white noise there is a combination of all of these randomized sine waves playing all at once. The smallest variation in this chaotic wave that we're interested in capturing is the wave of a 20khz signal, right? Any wave shorter than that of a 20khz wave would be higher in frequency than 20khz and thus outside of the range of most human ears. Square or triangle waves at 20khz are just regular multiples of the frequency of the sine wave. So if we can capture the 20khz signal accurately due to the frequency rate that our converter samples the sound, then we can easily capture longer, lower frequency sine waves with less frequent peaks and troughs.

So you see, any complex combination of frequencies between 20hz and 20khz can be captured perfectly with 44.1k.

The difference is in the converter design.. getting the analog components to best carry out this task without error or unintended variation.


************************

noolness says....



"However, not all signals can be represented accurately by a set of sine waves below 20kHz. In particular, sawtooth waves (also known as triangular waves) and square waves can only be represented by an infinite set of sine waves with frequencies extending all the way to infinity. When you capture either sawtooth waves or sine waves digitally, you don't get back a perfect waveform when you play it back due to filtering."

So technically you can only accurately recreated a sawtooth or square wave digitally by having an infinite sample rate.

norman_nomad:

This is true! A 20khz square wave captured at 44.1k will not capture the harmonic content created much further past the 20khz fundamental.

The question you have to ask yourself is: Do you care and does it matter?

For most of us, the answer is: No, it doesn't.

You (at least I can't) hear past 20khz. So any harmonic content created above this range due to a square or triangle wave, whether captured by your converter or not, does not and should matter to us because we wouldn't be able to hear it anyways.

An example to think about:

If a 1khz square wave is generated by an imaginary synth with infinite bandwidth played by a speaker of infinite bandwidth we would hear the 1khz fundamental along with all of the increasingly diminishing harmonics up to 20khz after which harmonics would exist, but we would not be able to hear them due to the limitations of our physical hearing.

For that same reason, a converter only needs to capture spectral content up to the threshold of human capacity, past which point there is a dubious return in utility.

This is why a 44.1khz sampling rate is considered to be sufficient - it covers the entire range of human hearing.

There are some that will argue that harmonics past the point of human hearing have some effect on the sounds we can hear. They may be right. I haven't done enough research to know if there is any merit to this or not... but before you tread down this path, consider the bandwidth limitations of your microphones and your speakers/headphones. Many of these devices are not capable of capturing or playing back much usable content past 25khz...

Also consider this: Any interaction that happens with an acoustic instrument due to harmonics past 20khz is happening in the air during the recording and thus you, in essence, record those interaction as they manifest in the 20khz and under frequency range (in other words, in the range you actually hear). You won't loose the effects of the ultra high frequencies by excluding them from the digital capture - they've already done their work in the air during the recording and their effect will be maintained on playback. Make sense?

*********************************

Idiophonic says...

I still can't help but feel that the amplitude issue exists at the lower end of sample rates because, as you indicated, the chance that your 2 samples hit the peaks is small. It seems that even with 2.2 samples (only fractionally more!) you are still in danger of under-representing the amplitude of the upper frequencies...4.4 samples would have a better chance of being more accurate in this respect, yes?

Norman_nomad:


Hey Idiophonic,

The samples do not need to be at the peak of the sample to represent the frequency accurately.

From the link that noolness posted:



"How is this possible? How does the DAC know how to "plot" the signal in between sample points? ...

How can removing frequencies above Nyquist restore the correct peak levels (which are higher than any individual sample)? This is hard to explain without resorting to mathematics, but essentially Fourier Theory postulates that any complex continuously varying signal can be represented by a set of sine waves of varying frequencies and amplitudes. When you sum all these sine waves, you get the original signal.

In the case of Figure 4, if you draw a set of straight lines between sample points, you are plotting a signal composed of many sine waves summed together. These sine waves "modify" the original sine wave and lower the actual peaks of the waveforms. When these extraneous sine waves are removed, the peaks of the sine wave between sample points are restored.


If you still find this difficult to swallow, try thinking of it in a different way. The reason a perfect sine wave is output even though the samples did not capture the peaks is that a 19997Hz sine wave is the only possible plot that you can draw that passes through all the sample points but does not contain frequencies higher than Nyquist. This can actually be proven mathematically, but I will spare you the calculations."


So to sum it up:

If you sample a twice the rate of the highest frequency you wish to capture you will able to capture that frequency accurately and reconstruct it without anomalies using a theoretically perfect analog circuit. Because there is no such thing as a perfect analog circuit, each converter will handle this task with more or less grace. The samples don't need to catch the peaks of the frequency to know how to redraw them because there is only ONE POSSIBLE PLOT THAT CAN BE DRAWN after filtering.

"What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz."

STOP RIGHT THERE!!!!

You're making erroneous assumptions again. Please reread my posts again, and pay attention this time.

The assumption that 20KHz is the highest frequency of significance is wrong and has been outmoded for some time - at least 20 years.

PLEASE read carefully what I've been saying - I'm getting extremely tired of repeating myself and when I get tired I get cranky - and then I start making jokes....... rather pointed ones.

[Mr.HOLMES]

Originally Posted by John Eppstein

Ha! Interesting..... Perhaps we had a large influx of newbies in '03 and '07 to account for the anomalies? No, I don't mean anybody hear......

Thats totally right John the dips came from that new home-recordists start out with an G-SSL-Console 48 Ch. as well with two 24 track Studers and at least five UA-1176 and a Lexicon 960 L reverberator.

Not to mention perfect acoustic treatment and 3500 sqf tracking room.

You know that as well in 2003 and 2007 there was no other way to produce a good sounding album.

I also found a new graph which shows significant sells off DAWs at e-bay since 1999:



The next graph shows that SSL sold more consoles than ever since this time when e-bay nearly collapsed because of the DAW selling's in 1999.
This graph is in Bil. Dollars!!!

[norman_nomad]

Originally Posted by John Eppstein

"What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz."

STOP RIGHT THERE!!!!

You're making erroneous assumptions again. Please reread my posts again, and pay attention this time.

The assumption that 20KHz is the highest frequency of significance is wrong and has been outmoded for some time - at least 20 years.

PLEASE read carefully what I've been saying - I'm getting extremely tired of repeating myself and when I get tired I get cranky - and then I start making jokes....... rather pointed ones.

Where are the studies supporting such a claim? There seem to be many more in the 20hz - 20khz camp.

Always open to new ideas through good science however if you can provide it....

[dkelley]

Originally Posted by theblue1

This is the position/understanding I've slowly come to.

When I first moved to digital tracking in late '92 or early '93, one of the first things I noticed was how "clean" everything was -- and I quickly came to the conclusion it was "too clean" -- I remember writing at the time that I thought that the next big product sector would be what I called at the time "dirt boxes" or "warm boxes" (I figured "dirt box" wouldn't have much marketing cachet ).

I went looking to replace tape saturation with various tube and FET based preamps, DBs, and compressors...

And then I began realizing just how little I really understood about artfully using compression. When I came up, I mostly learned how to use compression under fire, in the middle of sessions, twisting knobs until I got what I thought I wanted. I mean, I knew what the parameters were but each compressor I used seemed so very different from the previous that until I had a few full control compressors of my own to live with every day and toy with on my own time, I never really got it, completely.


Now, don't get me wrong -- I am absolutely not saying that compression can achieve special magic of "that tape sound" that many love.* The best, most direct, quite likely only, way to get that, obviously, is by using analog tape.

But, for me, really starting to learn and understand compression (and I feel like I'm still learning) was one of the most important keys to me finally beginning to develop an approach to digital recording that didn't look backwards and try to recreate the particulars of the analog tape sound.


* Back in the day I worked with more than a couple of artists and producers new to studio recording. It was a pretty common thing for a singer or producer to sit on the CR couch during live tracking or getting sounds and say, "Gee, is it going to sound this way on tape? It sounds really weird. Are you sure you're doing everything right? This doesn't sound at all like I expected." Standard reply: "Don't worry. Once we hit tape, it's going to sound a lot more like what you expect. And once we've got the compressors and effects on in the mix, it'll sound just like a record." Well... that's what we told 'em.

sorry, having a hard time keeping up with this thread's rapid posting!

anyway, yes! well said, I agree with your specific points too about compression.

and no matter how long I do this, I'm always learning too. and changing my mind. what I used to love I hate now and vice versa.

getting old, that's what my wife says. hell I'm only 40. that's what I get for marrying someone younger than myself :-)

cheers,
Don

[audiovisceral]

Originally Posted by norman_nomad

Where are the studies supporting such a claim? There seem to be many more in the 20hz - 20khz camp.

Always open to new ideas through good science however if you can provide it....

Just curious - what are your thoughts on the square-sine dilemma as described ITT?

I imagine one of two possibilities. The volume matched 12khz sine and square can sound different because:

- Differing error is introduced in differing signal generation and it is this error which is heard.
- Sounds above 20 khz can have musically significant interactions with sounds below 20 khz.

I have no idea. Never heard this test. But I find it interesting whatever the case may be.

Also, why in your opinion does DSD sound better to many than say 88.2 khz?

[John Eppstein]

Originally Posted by norman_nomad

Where are the studies supporting such a claim? There seem to be many more in the 20hz - 20khz camp.

Always open to new ideas through good science however if you can provide it....

read the posts. I gave a simple experiment that you can try for yourself.... One which, I'm now told, is also promoted by guy guy called, uh, "Neve", I think it was?....... I dunno, I came up with it on my own......

[G4Jet]

Originally Posted by Soulbrother

It seems to be the case nowadays that we are so hammered with hype about analog warmth this, tape that and tube the other, that some people have begun to think this elusive Analog Warmth is far more important than it actually is.

Beleive me , if your mixes are sounding harsh, it isnt because you are using digital. Digital is neither harsh nor brittle or any of the negative adjectives being thrown at it. Its just, digital, it sounds like whats going into it and little else. You can eaily make a lovely fat warm, recording using nothing but digital equipment. If its harsh, its your mixing skills, your crappy mics possibly, your arrangements or something else.

Secondly, are you sure you actually know what this so-called Analog Warmth your after actually sounds like? It seems to be an almost magical quality on here, an elusive and indefinable 'isness' that seems almost occult in nature.

My feeling is that what people think is Analog Warmth is actually a combination of many factors:

(1) Records being recorded with the whole band in the same room (as was done before the 80s) - nice sloppy backing vocals.

(2) Springs/Plates and echo chambers, or ambient micing rather than algorymthmic reverbs.

(3) Records that have mistakes and out of tune singing on them, rhtmys that push and pull rather than records that are sliced and diced to the grid, and autotuned to death.

(4) Records where the eq is largely subtractive.

(5) Records where compression is used on the Lead Vocal and maybe the bass, not on every one of its 100 plus tracks and the 2 Buss.

And many other factors. But the contribution of tubes, tapes and transformers to all of this is a good bit subtler than the factors I mentioned above.

Ever noticed how when people talk about "Analog Warmth" they always reference records made in the 60s and 70s, but never the 80s - even though the 80s was still all about analog tape and analog mixing - yet plenty of those 80s analog recordings sound 'cold' now - largely becuase of the invention of drum machines, Lexicons, the dreaded DX7 and shiny EQ on everything. But they were still 'analog' records for the most part.

Tape is just a recording medium, it isnt a magical tool that'll turn your quantised tune made with vsti's and loops into a dusty, down and dirty Swamp Rock gem from the 70s. Thats not how it works.

I agree with this. poeple are manipulated by the old days!! Move to the future.

[Mr.HOLMES]

Originally Posted by John Eppstein

read the posts. I gave a simple experiment that you can try for yourself.... One which, I'm now told, is also promoted by guy guy called, uh, "Neve", I think it was?....... I dunno, I came up with it on my own......

That guy <Neve> dangerous!! Too much analogue you know we do not want to throw out the baby with the bath water....

[A-List]

I love that digital sound.

[norman_nomad]

Originally Posted by John Eppstein

read the posts. I gave a simple experiment that you can try for yourself.... One which, I'm now told, is also promoted by guy guy called, uh, "Neve", I think it was?....... I dunno, I came up with it on my own......

I'm sorry, I don't see the experiment that proves we can hear past 20khz. Would you mind reposting it so I can try it?

[DamnYankee]

Originally Posted by Mr.HOLMES

I wrote the same with my words but no one is listening now they discuss science I guess.

Again buy a nice mic pre with transformers a nice tube unit or a tape machine or all three combinations.... see how far you can get....

No one in this world can tell you in the end that it not has be mixed on a console.

We do not need to discuss gear we need to discuss know how.

Nice pres/transformers isn't the topic of the discussion. There was an issue from one of the posters regarding a difference in sound with two samples when he attempted to double track. Specifically, part of the bass frequencies dropped out of the original sample. I responded with some Tom Scholz articles talking about this phase angle distortion issue which occurs with his ProTools software but doesn't occur with his 24 track 3M M79. Not only does the bass drop out, but Scholz states the highs drop out too. This is a distinct and separate discussion than Latency. So...the acoustic experts are hashing this out and this has to be one of the best threads I've read in here. I only wish Mr Scholz could weigh in with his MIT-trained engineering expertise.

[norman_nomad]

Originally Posted by audiovisceral

Just curious - what are your thoughts on the square-sine dilemma as described ITT?

I imagine one of two possibilities. The volume matched 12khz sine and square can sound different because:

- Differing error is introduced in differing signal generation and it is this error which is heard.
- Sounds above 20 khz can have musically significant interactions with sounds below 20 khz.

I have no idea. Never heard this test. But I find it interesting whatever the case may be.

Also, why in your opinion does DSD sound better to many than say 88.2 khz?

This was already answered by Alcohol earlier:

"There are less-formal experiments that purport to show that we can hear above 20 kHz, and perhaps the best known of these is the one that Rupert Neve — whom I have a tremendous amount of admiration for, although I think he's completely wrong on this — does. He plays his audience a 10kHz sine wave and then a 10kHz square wave, and everyone in the place agrees that the two waves sound different. Therefore, he concludes, because the lowest harmonic above the fundamental in a square wave is the third, we are hearing 30 kHz!

Of course this is, as the English say, “tosh,” and many before me have pointed this out. There are a lot of reasons why we can hear the difference between those two tones, none of which have anything to do with ultrasonic sensitivity. One is simply that the energy of a square wave is higher than a sine wave at the same nominal amplitude, so the square wave sounds louder. Another is that any transformers in the signal path, unless they are exquisitely designed and constructed for passing such high frequencies, will introduce slewing and intermodulation distortion from the square wave — not only from the third harmonic, but from all the odd harmonics above it — that will have products well inside the audible range. And, if somehow a perfectly amplified 10kHz square wave were to make it all the way to the speakers, then the speakers would create their own distortion, which would be quite different from the distortion a sine wave would make"

Here's the crux of it - I've seen no reliable evidence/studies that suggest humans respond to ultrasonic frequencies (maybe there are some, I'd like to see them). There is the argument that ultrasonic frequencies interact with sounds in the audible domain and that we're able to detect these interactions. Cut our bandwidth at 20khz and we loose those interactions. There's a fundamental flaw with that line of reasoning however.

A narrative:

A tale of the romanticist and the scientist

Scientist: What are you doing?

Romanticist: Recording a flutists. The higher pitched notes are creating harmonics exceeding 20khz.

Scientist: Why do you even bother to mention that, we can't hear beyond 20khz? I have a bookshelf full of audiometric exams to prove it.

Romanticist: The harmonics above 20khz actually interact with the sound below that frequency range. This is why I'm sampling at 192khz. It's important that we capture them.

Scientist: Important that you capture the ultrasonics or their affect?

Romanticist: What do you mean?

Scientist: Well any interaction that happens with harmonics over 20khz that affects the audible range must be happening in the air as the flutist plays; otherwise we would not hear them.

Romanticist: So?

Scientist: Well I imagine you could lower your sampling rate. Your ultrasonic interactions are only perceivable in the audible range. As long as you capture what relevant to the human perceptual system, you should also be capturing the affect of the interactions. In fact capturing the ultrasonics which, according to you, affects the sound in the audible range might even be detrimental in that you'd be folding those same harmonics back on the music during playback on your stereo, creating even more 'interactions'.

Romanticist: Get the f*ck out of here.

The end.

So you see, if we use a capturing mechanism which meets our exceeds our own physical bandwidth limitations (the ears) then we're capturing all of the sounds relevant to a human's sensory system. There's no mysticism to this; no religion.

[DamnYankee]

Originally Posted by John Eppstein

&quot;What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz.&quot;

STOP RIGHT THERE!!!!

You're making erroneous assumptions again. Please reread my posts again, and pay attention this time.

The assumption that 20KHz is the highest frequency of significance is wrong and has been outmoded for some time - at least 20 years.

PLEASE read carefully what I've been saying - I'm getting extremely tired of repeating myself and when I get tired I get cranky - and then I start making jokes....... rather pointed ones.

I read Rupert Neve demonstrated the human ear hears above 20 kHz. I also read he designed some of his gear to hit the 100 kHz range as he believes the higher frequencies we can't hear affects the [timbre for the lack of a better word] highest frequencies we can hear.

[norman_nomad]

Here's another test you could do.

Set up two tracks.

Play a 12k sine on one
Play a 24k sine on two

Mute and unmute track two...does the sound change?

[audiovisceral]

Originally Posted by norman_nomad

So you see, if we use a capturing mechanism which meets our exceeds our own physical bandwidth limitations (the ears) then we're capturing all of the sounds relevant to a human's sensory system.

I agree.

But then why do you suppose many find 5644.8 kHz or 2822.4 kHz DSD sounds superior to say 88.2 kHz PCM, when Nyquist only theoretically requires 40 kHz PCM?

[norman_nomad]

Originally Posted by audiovisceral

I agree.

But then why do you suppose many find 2800 khz DSD sounds superior to say 88.2 khz, when Nyquist only theoretically requires 40 khz?

Don't know. Never heard DSD, so I can't comment personally on the matter.

There are many factors involved including circuitry, layout, implementation - all of which can affect sonics.

Also, 88.2khz on what converter?

[vincentvangogo]

Originally Posted by norman_nomad

'Mathmatical trickery'

I'm going to copy and paste my comments from another thread... maybe you'll get something from it, maybe you won't. Enjoy!

*********************

Let's use an example to think about this.

You have a white noise generator and you're recording it's output through your a/d converter's input.

What is the full spectral content of white noise? White noise has equal spectral power density in any band.

What is the highest frequency band that is of relevance when taking into account the capacity of human hearing. For most of us, that would be 20khz.

So with your white noise there is a combination of all of these randomized sine waves playing all at once. The smallest variation in this chaotic wave that we're interested in capturing is the wave of a 20khz signal, right? Any wave shorter than that of a 20khz wave would be higher in frequency than 20khz and thus outside of the range of most human ears. Square or triangle waves at 20khz are just regular multiples of the frequency of the sine wave. So if we can capture the 20khz signal accurately due to the frequency rate that our converter samples the sound, then we can easily capture longer, lower frequency sine waves with less frequent peaks and troughs.

So you see, any complex combination of frequencies between 20hz and 20khz can be captured perfectly with 44.1k.

The difference is in the converter design.. getting the analog components to best carry out this task without error or unintended variation.


************************

noolness says....



"However, not all signals can be represented accurately by a set of sine waves below 20kHz. In particular, sawtooth waves (also known as triangular waves) and square waves can only be represented by an infinite set of sine waves with frequencies extending all the way to infinity. When you capture either sawtooth waves or sine waves digitally, you don't get back a perfect waveform when you play it back due to filtering."

So technically you can only accurately recreated a sawtooth or square wave digitally by having an infinite sample rate.

norman_nomad:

This is true! A 20khz square wave captured at 44.1k will not capture the harmonic content created much further past the 20khz fundamental.

The question you have to ask yourself is: Do you care and does it matter?

For most of us, the answer is: No, it doesn't.

You (at least I can't) hear past 20khz. So any harmonic content created above this range due to a square or triangle wave, whether captured by your converter or not, does not and should matter to us because we wouldn't be able to hear it anyways.

An example to think about:

If a 1khz square wave is generated by an imaginary synth with infinite bandwidth played by a speaker of infinite bandwidth we would hear the 1khz fundamental along with all of the increasingly diminishing harmonics up to 20khz after which harmonics would exist, but we would not be able to hear them due to the limitations of our physical hearing.

For that same reason, a converter only needs to capture spectral content up to the threshold of human capacity, past which point there is a dubious return in utility.

This is why a 44.1khz sampling rate is considered to be sufficient - it covers the entire range of human hearing.

There are some that will argue that harmonics past the point of human hearing have some effect on the sounds we can hear. They may be right. I haven't done enough research to know if there is any merit to this or not... but before you tread down this path, consider the bandwidth limitations of your microphones and your speakers/headphones. Many of these devices are not capable of capturing or playing back much usable content past 25khz...

Also consider this: Any interaction that happens with an acoustic instrument due to harmonics past 20khz is happening in the air during the recording and thus you, in essence, record those interaction as they manifest in the 20khz and under frequency range (in other words, in the range you actually hear). You won't loose the effects of the ultra high frequencies by excluding them from the digital capture - they've already done their work in the air during the recording and their effect will be maintained on playback. Make sense?

*********************************

Idiophonic says...

I still can't help but feel that the amplitude issue exists at the lower end of sample rates because, as you indicated, the chance that your 2 samples hit the peaks is small. It seems that even with 2.2 samples (only fractionally more!) you are still in danger of under-representing the amplitude of the upper frequencies...4.4 samples would have a better chance of being more accurate in this respect, yes?

Norman_nomad:


Hey Idiophonic,

The samples do not need to be at the peak of the sample to represent the frequency accurately.

From the link that noolness posted:



"How is this possible? How does the DAC know how to "plot" the signal in between sample points? ...

How can removing frequencies above Nyquist restore the correct peak levels (which are higher than any individual sample)? This is hard to explain without resorting to mathematics, but essentially Fourier Theory postulates that any complex continuously varying signal can be represented by a set of sine waves of varying frequencies and amplitudes. When you sum all these sine waves, you get the original signal.

In the case of Figure 4, if you draw a set of straight lines between sample points, you are plotting a signal composed of many sine waves summed together. These sine waves "modify" the original sine wave and lower the actual peaks of the waveforms. When these extraneous sine waves are removed, the peaks of the sine wave between sample points are restored.


If you still find this difficult to swallow, try thinking of it in a different way. The reason a perfect sine wave is output even though the samples did not capture the peaks is that a 19997Hz sine wave is the only possible plot that you can draw that passes through all the sample points but does not contain frequencies higher than Nyquist. This can actually be proven mathematically, but I will spare you the calculations."


So to sum it up:

If you sample a twice the rate of the highest frequency you wish to capture you will able to capture that frequency accurately and reconstruct it without anomalies using a theoretically perfect analog circuit. Because there is no such thing as a perfect analog circuit, each converter will handle this task with more or less grace. The samples don't need to catch the peaks of the frequency to know how to redraw them because there is only ONE POSSIBLE PLOT THAT CAN BE DRAWN after filtering.

So why does digital continue to suck?

[John Eppstein]

Originally Posted by norman_nomad

This was already answered by Alcohol earlier:

"There are less-formal experiments that purport to show that we can hear above 20 kHz, and perhaps the best known of these is the one that Rupert Neve — whom I have a tremendous amount of admiration for, although I think he's completely wrong on this — does. He plays his audience a 10kHz sine wave and then a 10kHz square wave, and everyone in the place agrees that the two waves sound different. Therefore, he concludes, because the lowest harmonic above the fundamental in a square wave is the third, we are hearing 30 kHz!

Of course this is, as the English say, “tosh,” and many before me have pointed this out. There are a lot of reasons why we can hear the difference between those two tones, none of which have anything to do with ultrasonic sensitivity. One is simply that the energy of a square wave is higher than a sine wave at the same nominal amplitude, so the square wave sounds louder. Another is that any transformers in the signal path, unless they are exquisitely designed and constructed for passing such high frequencies, will introduce slewing and intermodulation distortion from the square wave — not only from the third harmonic, but from all the odd harmonics above it — that will have products well inside the audible range. And, if somehow a perfectly amplified 10kHz square wave were to make it all the way to the speakers, then the speakers would create their own distortion, which would be quite different from the distortion a sine wave would make"

Here's the crux of it - I've seen no reliable evidence/studies that suggest humans respond to ultrasonic frequencies (maybe there are some, I'd like to see them). There is the argument that ultrasonic frequencies interact with sounds in the audible domain and that we're able to detect these interactions. Cut our bandwidth at 20khz and we loose those interactions. There's a fundamental flaw with that line of reasoning however.

A narrative:

A tale of the romanticist and the scientist

Scientist: What are you doing?

Romanticist: Recording a flutists. The higher pitched notes are creating harmonics exceeding 20khz.

Scientist: Why do you even bother to mention that, we can't hear beyond 20khz? I have a bookshelf full of audiometric exams to prove it.

Romanticist: The harmonics above 20khz actually interact with the sound below that frequency range. This is why I'm sampling at 192khz. It's important that we capture them.

Scientist: Important that you capture the ultrasonics or their affect?

Romanticist: What do you mean?

Scientist: Well any interaction that happens with harmonics over 20khz that affects the audible range must be happening in the air as the flutist plays; otherwise we would not hear them.

Romanticist: So?

Scientist: Well I imagine you could lower your sampling rate. Your ultrasonic interactions are only perceivable in the audible range. As long as you capture what relevant to the human perceptual system, you should also be capturing the affect of the interactions. In fact capturing the ultrasonics which, according to you, affects the sound in the audible range might even be detrimental in that you'd be folding those same harmonics back on the music during playback on your stereo, creating even more 'interactions'.

Romanticist: Get the f*ck out of here.

The end.

So you see, if we use a capturing mechanism which meets our exceeds our own physical bandwidth limitations (the ears) then we're capturing all of the sounds relevant to a human's sensory system. There's no mysticism to this; no religion.

Norman, have you ACTUALLY TRIED THE EXPERIMENT?

Really, this one is a no-brainer for anyone who has actually spent any amount of time working with an audio generator and a scope.

If you have not tried it, do so. Until then you have no possible argument. If I feel like it, a bit later I may relate some of my experiences as an audio amp tech than suopport the fact that our perception is affected by frequencies WELL above 20K. Really, the whole question is silly to anyone who has actually worked in the field. (I don't mean recording, I mean audio equipment service.)

Btw, that's an amusing story, but it's utter nonsense.

[kats]

Originally Posted by norman_nomad

Where are the studies supporting such a claim? There seem to be many more in the 20hz - 20khz camp.

Always open to new ideas through good science however if you can provide it....

Hey fellas, back again. Nope can't prove it. I can't prove that we know everything either. But I'll leave you with an interesting anecdote.

You all have heard the Geoff Emerick/Rupert Neve story?

Here's part of it:

Fletcher: There has been some measure of debate about bandwidth including frequencies above 20kHz, can we hear them, do they make a difference, etc.

Rupert: OK, Fletch, pin your ears back...back in 1977, just after I had sold the company, George Martin called me to say that Air Studios had taken delivery of a Neve Console which did not seem to be giving satisfaction to Geoff Emmerick. In fact, he said that Geoff is unhappy.... engineers from the company, bear in mind that at this point I was not primarily involved, had visited the studio and reported that nothing was wrong. They said that the customer is mad and that the problem will go away if we ignore it long enough.
Well I visited the studio and after careful listening with Geoff, I agreed with him that three panels on this 48 panel console sounded slightly different. We discovered that there was a 3 dB peak at 54kHz Geoff's golden ears had perceived that there was a difference. We found that 3 transformers had been incorrectly wired and it was a matter of minutes to correct this. After which Geoff was happy. And I mean that he relaxed and there was a big smile on his face.
As you can imagine a lot of theories were put forward, but even today I couldn't tell you how an experienced listener can perceive frequencies of the normal range of hearing.

Here's something else to ponder:

Could you hear the difference between a sine wave at 10k (not too high, eh?) and a triangle wave at 10k? I can. Most people can.

Since this is a single wave, no interaction (hetereodyning) is present.

However, theoretically, the one component that makes a sine into a triangle is a 30k harmonic that we "should not be able to hear". If you filter out the harmonics over a 100Hz wave, you would hear just the fundamental (as your ear structure SHOULD filter out things over 20k). - Brian Kehew

But back to Emerick, Eric Bridenbaker over at PSW posted a neat trick a few years ago as a possible answer to the Emerick/Neve dilemma where he was pumping a 56k sine wave through his speakers which produced, well nothing audible. Then he blended a 57k sine wave in and:

the "beat" created between these two ultrasonic tones is equal to 1Khz (57K - 56K), which is a frequency right in the middle of the human hearing range and reproducible on pretty much any speaker...There is a mathematical propensity for harmonics to converge about three and a half octaves above the fundamental

Why do I post all this? Just to point out that this is a pretty complicated issue in the real world and we shouldn't hold onto white papers as gospel. Ultimately, as blue1 says, trust your own ears and go with it (and that's where I agree with him 100%).

Oh and for fun, here's some more interesting stuff Eric provided us:

A similar idea was explored in the late 1800's by a rather controversial figure named John W. Keely. He was a contemporary of Tesla and developed a field of research which he termed "Sympathetic Vibratory Physics". Residing somewhere in between physics and metaphysics, his work has generated much debunking, debating, and general interest since.

He proposed a theory for "beat harmonics", which tried to explain how the higher overtones can combine to create audible resonances at the fundamental frequency. As part of the theory, he indicated that recursive harmonics will converge at the twelfth harmonic, which is about three and a half octaves higher than the fundamental. He made some rather bold claims as to the relative intensities of these overtones, nonetheless the concept seems to have some ballast.

http://www.svpvril.com/Fig_11.html<b...his site well.

I've posted a simple math exercise involving recursive harmonics to show that indeed, there should be a convergence at the twelfth
here.

Link

As a kid I always wondered why turning up the treble made it seem like there was more bass... After some basic audio theory, the Fletcher-Munson curves provided an explanation. Perhaps this proposed harmonic interaction is related to the effect.

Cheers,
Eric

20hz-20khz might not explain the whole picture.

[norman_nomad]

Originally Posted by John Eppstein

Norman, have you ACTUALLY TRIED THE EXPERIMENT?

I have. Have you tried mine?

Originally Posted by John Eppstein

Until then you have no possible argument. .

And this here is the crux of the problem. You equate your interpretation of reality with an absolute reality. I don't need to punch in 2+2=4 into the calculator to know the answer is 4. I don't need to experience 4 to know it. I can know it though deduction.

You have an experience and then invent a rational that makes sense to you, but may have nothing to do with the way things actually work.

Trust your ears as little artists on the side of your head, not as little scientists. Anyone who's watched a game of 3 card monte on the street knows that the senses can easily misinterpret reality with absolute certainty. I'd put money on that.

For the record I often prefer the 'sound' of analog tape. I own an Ampex 2" machine; it's a pain in the ass to use and maintain but it sounds great. I'm able to love analog without hating digital. I see no need to polarize my preferences to justify them. I don't think digital is fundamentally 'flawed', i just think it's accurate to a fault. It can be boring and vanilla. And when there's distortion in the digital domain, it's ugly. Digital done well sounds good but requires disciplines and a different approach than traditional analog recordings.

Originally Posted by John Eppstein

If I feel like it, a bit later I may relate some of my experiences as an audio amp tech than suopport the fact that our perception is affected by frequencies WELL above 20K.

I'd love to hear them. Especially tests that prove we can hear and experience sonics above 20k.

Originally Posted by John Eppstein

Btw, that's an amusing story, but it's utter nonsense.

Calling my little story nonsense isn't an argument. But you knew that. Awaiting your tests with open ears.

[audiovisceral]

Originally Posted by norman_nomad

I don't need to punch in 2+2=4 into the calculator to know the answer is 4. I don't need to experience 4 to know it. I can know it though deduction.

If that was true we'd record at 44.1 khz.

[norman_nomad]

Originally Posted by vincentvangogo

So why does digital continue to suck?

ehe...

A few reasons maybe:

A) Pragmatic: The people using it suck

B) Provocative: It doesn't suck it's just different

C) Philosophical/Romantic:

Digital removes the mystery. Capturing art to less accurate mediums like tape is appealing because of the subtle loss of detail that occurs - a loss which has the effect of inviting the listener to insert their own interpretations of what is missing. There is an implied dialog between music and listener that emerges in the analog domain that does not always surface in the flawlessness of newer digital recordings. This 'mystery' is part of the allure, it's integral to the process of making art.

[norman_nomad]

Originally Posted by audiovisceral

If that was true we'd record at 44.1 khz.

A lot of people do? Some manufacturers do a better job at making the filter invisible at 44.1 than others. I like Apogee AD16x's at 44.1. I run my Lynx at 96k b/c I think it sounds slightly more open.

[audiovisceral]

Originally Posted by norman_nomad

A lot of people do? Some manufacturers do a better job at making the filter invisible at 44.1 than others. I like Apogee AD16x's at 44.1. I run my Lynx at 96k b/c I think it sounds slightly more open.

Isn't that the point here? Practice is more complex than theory?

According to Nyquist, a chip should sound no different at 44 or 96 (or 192). Due to filtering problems (or other issues no one has yet pinpointed), however, this is not the reality we find.

You could not deduce your Apogee would sound better at 96. You had to listen.

[audiovisceral]

Originally Posted by norman_nomad

C) Philosophical/Romantic:

Digital removes the mystery. Capturing art to less accurate mediums like tape is appealing because of the subtle loss of detail that occurs - a loss which has the effect of inviting the listener to insert their own interpretations of what is missing. There is an implied dialog between music and listener that emerges in the analog domain that does not always surface in the flawlessness of newer digital recordings. This 'mystery' is part of the allure, it's integral to the process of making art.

If we are getting to the point where we can recognize sampling theory cannot stand up 100% in practical application, why is it still so inconceivable to some that digital is introducing its own unique artifacts and is not in any way even remotely flawless?

As an example, jitter is one clearly documented source of digital error. As discussed in this thread, imperfect filtering is another.

[norman_nomad]

Originally Posted by audiovisceral

Isn't that the point here? Practice is more complex than theory?

According to Nyquist, a chip should sound no different at 44 or 96 (or 192). Due to filtering problems (or other issues no one has yet pinpointed), however, this is not the reality we find.

You could not deduce your Apogee would sound better at 96. You had to listen.

Practice is art, theory is science.

As an audio engineer, practice is king.

Look... when it comes to making record. I could give sh!t about theories or the rules or whatever... I search for sounds... I'm a detective for cool sounds. I experiment. I do everything 'wrong' if it sounds 'right'. I think that's how most engineers work.

To me this whole thing is just left brain nerding out... figuring out WHY we like what we like...