[71 dB]

At least one experiment (sorry, don't have the link right now) seems to have indicated, however, that the human ability to distinguish two clicks might be finer than 0.02 miliseconds, i.e. one sample at 44.1Khz. Or in other words, perceptible phase/timing information from (some magical, ideal) recordings might be lost at normal sampling rates.

This red part is not true! Sampling frequency limits bandwidth, not phase or timing resolution, which is "infinite" no matter what the sampling frequency is. It's not that we have to move the waveform in time steps of 1/44100 seconds. If the signal is delayed say 0.01 milliseconds, it means every sample value changes a little bit, since the the value of the signal at every point in time sample values are taken is different.

Limited time resolution in digital audio is a common misunderstanding. There is no limits. Timing/phase resolution is "infinite".

 

[Zapp_Fan]

This red part is not true! Sampling frequency limits bandwidth, not phase or timing resolution, which is "infinite" no matter what the sampling frequency is. It's not that we have to move the waveform in time steps of 1/44100 seconds. If the signal is delayed say 0.01 milliseconds, it means every sample value changes a little bit, since the the value of the signal at every point in time sample values are taken is different.

Limited time resolution in digital audio is a common misunderstanding. There is no limits. Timing/phase resolution is "infinite".

Oh, that is a good point, I see what you mean. Still, If you consider that a person *could in theory* distinguish two sonic events (in experiments, a click/impluse ) happening with a delay/spacing of less than 1 sample at 44.1Khz, you will also require ultrasonics to reproduce all audible information, since such a waveform can't be reproduced without ultrasonics. In practice I'm struggling to think of what might occur in a musical recording that would really be affected by this, (maybe some timbre-related issues with certain string instruments??) but hey.

 

[pinnahertz]

Not to gravebump, but this is something I have been thinking about a bit in the past, and never got a satisfactory resolution to it.

High sample rates are often derided because nobody can hear ultrasonics so why bother?

However, that is only considering the problem in the frequency domain. At least one experiment (sorry, don't have the link right now) seems to have indicated, however, that the human ability to distinguish two clicks might be finer than 0.02 miliseconds, i.e. one sample at 44.1Khz. Or in other words, perceptible phase/timing information from (some magical, ideal) recordings might be lost at normal sampling rates.

As 71 dB clarified, the Nyquist frequency is a frequency bandwidth limit. Sub-sample timing difference are still preserved.

Now, when you consider that even if a studio does all their recording, mixing and mastering at 192Khz, some piece of gear or processing step is likely to obscure that phase information anyway...

If a studio were to do all recording and post at 192kHz, and processed everything "in the box", then the full spectrum (apart from deliberate changes) would be preserved. We can circle back to "phase information" later.

And, many mastering engineers will as a matter of course lowpass their recordings at 20Khz or so, just as a safety measure, unless they're specifically working on a high-res master... leaving no music above 20khz at all...

Wow. Where did that one come from? The 20kHz limit (or about) is there because of working in 44.1 or 48kHz. What possible "safety measure" would that be? And what filter would they use? Answer: they don't.

and most microphones are not designed to capture any content above 20khz in the first place... and most studio gear regardless of function is not rated above 20khz...

That's a very black/white view. Response above 20kHz in mics and analog gear is not an on/off thing, it's a slow roll-off, like flat to 20kHz then falling at 6dB/octave. And the 20kHz figure isn't even firm. That doesn't mean there is music above 20kHz, but lots of stuff will pass 20+kHz albeit attenuated.

well, it seems hopeless, I guess. There are usually a lot of obstacles in preserving ultrasonics from the recording session all the way to your living room. Gear that's flat "from DC to daylight" certainly exists, but I'd wager it's a rare master that doesn't touch any gear less capable than that.

Don't blame the gear! And it's not that it's a choice. 20+kHz in music is more than 40dB below the fundamental at best, very best, typically 60dB or more. You're not missing anything. People worry about this artificial high end cut-of, but it's not there to begin with. And, HF response isn't the point of high sampling frequency, other that the fictional view.

But still - I am not convinced that there is literally nothing to be gained at least in theory, from high sampling rates. Anyone else looked into this?

Yes, extensively.

Problem 1 is you can't actually deliver 20+kHz to the ear. Speakers that can do it beam like crazy. Reflective room surfaces all become absorbers above 20k. The chances you'll get it to your ears are practically nil, even if it is there.

But I'm convinced that the entire issue is not about bandwidth or resolution, but rather about complex intermodulation of high frequency components from 8kHz and up to slightly above 20kHz. IMD products "fold" downward and upward. Some very early tests on this were done in the late 1980s, and a test method devised. The AES paper is "Measuring Spectral Contamination" by Deane Jensen (Jensen Transformers) and Gary Sokolich, presented at the November 1988 AES. They didn't accomplish much in terms of audible correlation, but they sure did find some problems. However, it isn't about simple bandwidth, it's about intermodulation distortion, which happens many times to be better in devices without severe bandwidth limitations. That would be the only reason to go with higher bandwidth. And the simple fact is, if you fix the IMD issue, then bandwidth isn't a factor.

Otherwise, efforts to show a difference between hi-res and CD-res files have been largely inconclusive.

 

[bigshot]

Alex, the problem with what you're worrying about here is simple... There's absolutely nothing in music that would come anywhere close to having a transient of .02 milliseconds, and samples aren't stair steps. They are aliased to be a smooth waveform. Nyquist says that a waveform is perfectly reproduced by two samples. You can add more samples, but it doesn't get any more perfect than perfect. You can't hear above 20kHz and there is almost nothing in music above that unless you're listening to gamelan gongs. Even then, the upper harmonics are going to be VERY quiet compared to the fundamental.

So for the purposes of listening to recorded music in the home, higher sampling rates are about as useful as teats on a bull hog.

 

[pinnahertz]

Alex, the problem with what you're worrying about here is simple... There's absolutely nothing in music that would come anywhere close to having a transient of .02 milliseconds, and samples aren't stair steps. 1. They are aliased to be a smooth waveform. 2. Nyquist says that a waveform is perfectly reproduced by two samples. 3. You can add more samples, but it doesn't get any more perfect than perfect. You can't hear above 20kHz and there is almost nothing in music above that unless you're listening to gamelan gongs. Even then, the upper harmonics are going to be VERY quiet compared to the fundamental.

So for the purposes of listening to recorded music in the home, higher sampling rates are about as useful as teats on a bull hog.

1. Change "aliased" to "reconstructed". Aliasing is a form of distortion (bad).
2. Nyquist doesn't say that at all. He does say that a sampling frequency can be sufficient for perfect reconstruction of band-limited signals if it is twice the highest frequency in the band, (which would result in 2 samples for the highest frequency in the band). For all other signals in band there are many, many more samples.
3. For frequencies below Nyquist you must and will add more samples to be "perfect".

 

[spruce music]

Yes, the actual timing resolution with 16 bit 44khz is 56 picoseconds if you don't use dither. If you use dither the timing resolution is pushed even lower. BTW, the timing resolution with human hearing over a restricted bandwidth and test tones is somewhere around 10 microseconds. That latter is more than 150,000 times longer than 56 picoseconds.

 

[danadam]

There's some discussion about time resolution in this hydrogenaudio thread. There is a formula somewhere below there for minimum possible delay:

1 / (2 * pi * bandwidth * number_of_levels)

There are also some files for ABXing, which had N-sample delays between channels @ 192 kHz and then they were downsampled to 44.1 kHz. Apparently one guy was able to ABX the file with 4-sample delay, which is 20.8 uSec.

 

[bigshot]

Anyone have some stats on the efficacy of teats on a bull hog?

 

[Zapp_Fan]

There's absolutely nothing in music that would come anywhere close to having a transient of .02 milliseconds,

This is simply not true, at least in theory. All impulses (specifically - electronically generated ones) have, in theory, an infinitely short transient, and therefore, an infinite series of ultrasonic partials. So pretty much any electronic music could, in theory, have such transients. Even a real-world (hard) cymbal strike might be expected to have a transient fast/sharp enough to require ultrasonics to reproduce fully. Now, is any of that really audible, or what, I don't know.

But I'm not really worried about what actually occurs in music or how often. The conclusion of almost every debate on this subject is "humans can't hear anything that 16/44.1 (or sometimes 24/48, whatever) can't reproduce", and the point I'm getting at is that there is some experimental evidence that this is not true.

For example, if you actually wanted to repeat this two-click threshold test done in the 70s (I found the link) http://asa.scitation.org/doi/abs/10.1121/1.1912374 you would not be able to do so with digital equipment running at 44.1Khz. The shortest click you can represent at that sampling rate is... 22 us.

If there is some audible difference between clicks lasting 20 and 10 microseconds, then we must conclude that people CAN hear (under specific circumstances) more than 44.1 can reproduce. I won't argue that this really matters for music, but if we want a standard that theoretically exhausts human ability, we may want to consider that 16/44.1 isn't it.

Again, just to be clear, I am not arguing that there is anything really pertinent to real-world-music-listening at higher sampling rates, just that maybe it's technically possible to hear something that 44.1 can't do.

@pinnahertz: When I was talking about rolling off inaudible frequencies for safety, this is often done to the mix (sometimes in several places) to remove residual content that might throw off a compression or limiting stage. I'm sure I read it in a mixing handbook somewhere... anyway, I can vouch that it's a useful technique as long as you know that you're mixing for 44.1. It's a lot more important to do on the low end, but if you want to be a boy scout about your dynamics you might roll off over 20Khz too.

And, I am not suggesting that mics and other gear won't pass / reproduce ultrasonics ... just that they're not usually designed for it, and so there is no assurance of fidelity at all, once you pass 20Khz, usually.

 

[spruce music]

Anyone have some stats on the efficacy of teats on a bull hog?

Amidst the current fashion of various gender issues my guess is the answer is yes.

 

[Zapp_Fan]

Yes, the actual timing resolution with 16 bit 44khz is 56 picoseconds if you don't use dither.

Huh?

 

[spruce music]

This is simply not true, at least in theory. All impulses (specifically - electronically generated ones) have, in theory, an infinitely short transient, and therefore, an infinite series of ultrasonic partials. So pretty much any electronic music could, in theory, have such transients. Even a real-world (hard) cymbal strike might be expected to have a transient fast/sharp enough to require ultrasonics to reproduce fully. Now, is any of that really audible, or what, I don't know.

But I'm not really worried about what actually occurs in music or how often. The conclusion of almost every debate on this subject is "humans can't hear anything that 16/44.1 (or sometimes 24/48, whatever) can't reproduce", and the point I'm getting at is that there is some experimental evidence that this is not true.

For example, if you actually wanted to repeat this two-click threshold test done in the 70s (I found the link) http://asa.scitation.org/doi/abs/10.1121/1.1912374 you would not be able to do so with digital equipment running at 44.1Khz. The shortest click you can represent at that sampling rate is... 22 us.

If there is some audible difference between clicks lasting 20 and 10 microseconds, then we must conclude that people CAN hear (under specific circumstances) more than 44.1 can reproduce. I won't argue that this really matters for music, but if we want a standard that theoretically exhausts human ability, we may want to consider that 16/44.1 isn't it.

Again, just to be clear, I am not arguing that there is anything really pertinent to real-world-music-listening at higher sampling rates, just that maybe it's technically possible to hear something that 44.1 can't do.

@pinnahertz: When I was talking about rolling off inaudible frequencies for safety, this is often done to the mix (sometimes in several places) to remove residual content that might throw off a compression or limiting stage. I'm sure I read it in a mixing handbook somewhere... anyway, I can vouch that it's a useful technique as long as you know that you're mixing for 44.1. It's a lot more important to do on the low end, but if you want to be a boy scout about your dynamics you might roll off over 20Khz too.

And, I am not suggesting that mics and other gear won't pass / reproduce ultrasonics ... just that they're not usually designed for it, and so there is no assurance of fidelity at all, once you pass 20Khz, usually.

You should watch the video in Bigshots signature. The one from xiph.org as it answers so many questions and has so many actual examples of what happens using very high quality totally analog wide bandwidth instruments to show what digital does and does not do.

The single sample impulse while possible in software is an illegal signal. Nyquist-Shannon shows a bandwidth limited signal can be fully reconstructed thru and AD/DA stage. A single sample pulse represents infinite bandwidth in infinitely short time. Such a signal would be filtered in AD which would allow correct reproduction of all parts below 20 khz at the DA stage.

Also, don't have it handy, but could find it, a drummer recorded with wide bandwidth mics at 24/96 nearly all available drum cymbals. Most have some resonance at 9-13 khz which is the peak of response and ends up being the steepest transient in the signal. One easily managed by 44 khz sampling. You have to remember steepest transients are more than just frequency. A high amplitude 10 khz signal is much steeper than a low amplitude 50 khz signal. Most music, very nearly 100% of it has no high amplitude high frequency signal. Yes I am sure there is an example of it somewhere once or twice, but mostly it just isn't in the music.

 

[spruce music]

Huh?

The formula already given by Danadam determines timing accuracy. I do believe instead of bandwidth it should be sample rate however.

1 / (2 * pi * bandwidth * number_of_levels)

Notice it involves number of levels. Timing accuracy of 24 bits is more than 16 bits because there are more levels. Dither allows recording information below the hard noise floor of the lowest bit. Which means it acts much like having more than 65k levels. Which means timing accuracy can actually be lower than 56 picoseconds of 44/16 if dither is applied. Without dither.

1/(2x 3.14 x 44100hz x 65,535 sample value levels)=55 picoseconds.

 

[bigshot]

This is simply not true, at least in theory.

I'm not talking about theory. I'm talking about the real world. There is absolutely nothing in music that even approaches a transient that doesn't span dozens and dozens of samples if not hundreds. It's important to have a general idea of what numbers represent. Use horse sense- just ballpark it and conceive of the time in your head- divide a second into 44,100 parts. Now find something in music that is faster than the fastest shutter speed on a camera. Not with acoustic instruments for sure. Even electronic instruments is unlikely. Now find something an order of magnitude faster that and you'd be talking about a one sample transient. Good luck!

 

[Zapp_Fan]

You should watch the video in Bigshots signature. The one from xiph.org as it answers so many questions and has so many actual examples of what happens using very high quality totally analog wide bandwidth instruments to show what digital does and does not do.

The single sample impulse while possible in software is an illegal signal. Nyquist-Shannon shows a bandwidth limited signal can be fully reconstructed thru and AD/DA stage. A single sample pulse represents infinite bandwidth in infinitely short time. Such a signal would be filtered in AD which would allow correct reproduction of all parts below 20 khz at the DA stage.

Also, don't have it handy, but could find it, a drummer recorded with wide bandwidth mics at 24/96 nearly all available drum cymbals. Most have some resonance at 9-13 khz which is the peak of response and ends up being the steepest transient in the signal. One easily managed by 44 khz sampling. You have to remember steepest transients are more than just frequency. A high amplitude 10 khz signal is much steeper than a low amplitude 50 khz signal. Most music, very nearly 100% of it has no high amplitude high frequency signal. Yes I am sure there is an example of it somewhere once or twice, but mostly it just isn't in the music.

Don't really dispute any of the above. However, I'm really just interested in whether the familiar arguments about 16/44.1 are actually 100% true. It's always asserted with such finality that I could not help but wonder if there was some small exception. And, since the argument (for me anyway) actually is about digital representations and not reproduction (which, at that point, just forget it... I can't afford speakers that are flat to 40Khz anyway), it's pertinent to consider impulses. Side note: A lot of electronic drum samples, actually, include what amounts to a single sample impulse.