High resolution audio. The science, or lack of...?

[steve_1979]

It is an opinion - you have stated :

It's a fact that 16/44.1 can sound identical to 24/96. This has been proven many times (including in this thread by fr0g).

This thread has not proved it, and you used the word can - which is not absolute.

16.44.1 can sound different to 24/96. But if a 24/96 file is converted into 16/44.1 using any compentent software that does the job properly then it will sound identical.

As I said to lemon: "The differences between 16/44.1 and 24/96 are less than -80dB down in volume or occur at ultrasonic frequencies over 20kHz." Unless you can hear noise that is less than -80dB below the music volume or can hear ultrasonic frequencies they do sound the same.

I asked fr0g whether he believed that cables sound different or not.

Cables can sound different.

But all cables that meet the necessary specification do sound identical.

p.s. If anyone wants to discuss whether cables sound the same or not I respectfully ask that you start a new thread rather than take this one of topic.

 

[shadders]

It is an opinion - you have stated :

It's a fact that 16/44.1 can sound identical to 24/96. This has been proven many times (including in this thread by fr0g).

This thread has not proved it, and you used the word can - which is not absolute.

16.44.1 can sound different to 24/96. But if a 24/96 file is converted into 16/44.1 using any compentent software that does the job properly then it will sound identical.

As I said to lemon: "The differences between 16/44.1 and 24/96 are less than -80dB down in volume or occur at ultrasonic frequencies over 20kHz." Unless you can hear noise that is less than -80dB below the music volume or can hear ultrasonic frequencies they do sound the same.

I asked fr0g whether he believed that cables sound different or not.

Cables can sound different.

But all cables that meet the necessary specification do sound identical.

p.s. If anyone wants to discuss whether cables sound the same or not I respectfully ask that you start a new thread rather than take this one of topic.

Hi,

The point is that if a person states that difference sounds below -65dB cannot be heard, and cables difference are below this threshold, the cables do not sound different. My analysis shows this based on fr0g statement that differences below -65dB cannot be heard.

As such, you cannot state that differences below -65dB cannot be heard, i provide analysis that two cables have a difference below this threshold, and then state that cables do indeed sound different.

fr0g has not detailed his process - hence the process, analysis and results cannot be investigated.

Performing a test and only sharing some of the process and results is insufficient to believe the results and conclusions.

The fact that fr0g cannot hear the difference means just that - fr0g cannot hear the difference - there are many other people who may be able to hear the difference.

Regads,

Shadders

 

[altruistic.lemon]

And fake BenLaws too - remember LenBaw ?

No, who was that?

Our mate Max, I'm guessing. It's a few pages back.

 

[steve_1979]

Aww, come on Clare, everyone knows those spaceships can't make those whooshing noises while they're flying in space

In science fiction movies like Star Wars people use laser guns to shoot robots and make them explode. But in real life high powered laser beams only cause a small area of increased temperature where it hits. So wouldn't it be more realistic to use a laser like a long distance welding torch to melt the movable joints in a robots limbs to disable them?

(I'm not really sure why I'm posting this on a hifi forum but it is interesting :roll: )

 

[steve_1979]

Hi,

The point is that if a person states that difference sounds below -65dB cannot be heard, and cables difference are below this threshold, the cables do not sound different. My analysis shows this based on fr0g statement that differences below -65dB cannot be heard.

As such, you cannot state that differences below -65dB cannot be heard, i provide analysis that two cables have a difference below this threshold, and then state that cables do indeed sound different.

fr0g has not detailed his process - hence the process, analysis and results cannot be investigated.

Performing a test and only sharing some of the process and results is insufficient to believe the results and conclusions.

The fact that fr0g cannot hear the difference means just that - fr0g cannot hear the difference - there are many other people who may be able to hear the difference.

Regads,

Shadders

That's a fair point as far as the scientific method and wording are concerned.

I should have used the phrase "They do sound the same as far a humans hearing can tell". But if anyone can hear anything which is less than -80dB down or at ultrasonic frequencies then they must have bloody good hearing.

 

[BenLaw]

And fake BenLaws too - remember LenBaw ?

No, who was that?

Our mate Max, I'm guessing. It's a few pages back.

Ah, I see. I'm flattered. Although I guess it was a bit easier than laltruistic emon.

 

[John Duncan]

It was not Max.

 

[jcbrum]

We know that the analogue signal up to 20 KHz can be reformed perfectly. We know we can't hear sounds above that frequency. I now know that a null plot between HD and downsampled produces a flat signal only differing by less than is humanly audible.

Hi,

This is incorrect - it is an approximation. The use of higher bit rates and higher sampling rates reduces the error introduced by the analogue filter stage used to interpolate the signal - or by the digital filter in the DAC.

Regards,

Shadders.

Er, no, it's not an approximation, it's an exact reconstruction but with added noise.

Go and re-examine your Shannon-Nyquist theory. There is only one curve which resolves.

Don't forget that noise and distortion are the same thing.

As long as noise is kept below the perception level of human hearing it becomes irrelevant.

JC

 

[jcbrum]

Some amplifiers buzz and hiss quietly, others appear to be silent.

All amplifiers are noisy (molecular, electron noise, component noise etc), but some are so quiet you can't hear it.

JC

 

[Paul.]

Why in films can you see the light moving when a laser is fired? And why do they make a 'dewsh dewsh' noise? (Sorry for the off topic posts)

In science fiction movies like Star Wars people use laser guns to shoot robots and make them explode. But in real life high powered laser beams only cause a small area of increased temperature where it hits. So wouldn't it be more realistic to use a laser like a long distance welding torch to melt the movable joints in a robots limbs to disable them?

A Phaser/disruptor is not a laser, its a directed energy weapon. Charged particle beams. No idea what noise they would make

 

[fr0g]

It is an opinion - you have stated :

It's a fact that 16/44.1 can sound identical to 24/96. This has been proven many times (including in this thread by fr0g).

This thread has not proved it, and you used the word can - which is not absolute.

16.44.1 can sound different to 24/96. But if a 24/96 file is converted into 16/44.1 using any compentent software that does the job properly then it will sound identical.

As I said to lemon: "The differences between 16/44.1 and 24/96 are less than -80dB down in volume or occur at ultrasonic frequencies over 20kHz." Unless you can hear noise that is less than -80dB below the music volume or can hear ultrasonic frequencies they do sound the same.

I asked fr0g whether he believed that cables sound different or not.

Cables can sound different.

But all cables that meet the necessary specification do sound identical.

p.s. If anyone wants to discuss whether cables sound the same or not I respectfully ask that you start a new thread rather than take this one of topic.

Hi,

The point is that if a person states that difference sounds below -65dB cannot be heard, and cables difference are below this threshold, the cables do not sound different. My analysis shows this based on fr0g statement that differences below -65dB cannot be heard.

As such, you cannot state that differences below -65dB cannot be heard, i provide analysis that two cables have a difference below this threshold, and then state that cables do indeed sound different.

fr0g has not detailed his process - hence the process, analysis and results cannot be investigated.

Performing a test and only sharing some of the process and results is insufficient to believe the results and conclusions.

The fact that fr0g cannot hear the difference means just that - fr0g cannot hear the difference - there are many other people who may be able to hear the difference.

Regads,

Shadders

I don't think I said that about -65 dB. (I do think it is still the case, but I didn't say it).

I mentioned 65 dB in a purely hyperthetical example as to the difference between the volume of a "silent" room at 25 dB and a "loud" listening volume at 90 dB

As for the cable question, very off-topic, but I don't mind answering.

I am not sure.

There is definitely a difference if you swap a cable that is too thin or resistive, for one that isn't.

I "think" I have heard differences, albeit subtle, between analogue cables...but I doubt I could ABX them. Moving your head 1cm makes more of a difference to the sound. My opinion is that any reasonably built multistrand copper cable will sound identical to most people. I have a selection of interconnects from before I actually tested myself, nothing too expensive, but between £5 and £100 per metre. They sound the same. So much so I will happily use the freebie black cables that come with some kit. It is the equal of the £100 a metre stuff. And I would literally bet my house that nobody could prove me wrong in a blind test.

Digital cables, within spec, sound identical, or rather, they don't have a sound, they transfer digital data. Audiophile USB, HDMI,optical, CAT5+ etc are without doubt a complete con.

 

[fr0g]

No, not "End of", do you think you own the forum? You are missing the point ENTIRELY. (Which seems quite usual for you).

The point is, the HD version "doesn't need" to sound better. If it does it isn't because of the format, it is despite it. And that to me is subterfuge and is dishonest.

There's no need to start getting personal. It's a weak tactic and liable to lessen the force of an argument.

Yes, you are right. I am trying my best. Sometimes my best isn't good enough.

Although I am reminded of the 1st of the Satanic version of the deadly sins...which is bang on.

 

[shadders]

We know that the analogue signal up to 20 KHz can be reformed perfectly. We know we can't hear sounds above that frequency. I now know that a null plot between HD and downsampled produces a flat signal only differing by less than is humanly audible.

Hi,

This is incorrect - it is an approximation. The use of higher bit rates and higher sampling rates reduces the error introduced by the analogue filter stage used to interpolate the signal - or by the digital filter in the DAC.

Regards,

Shadders.

Er, no, it's not an approximation, it's an exact reconstruction but with added noise.

Go and re-examine your Shannon-Nyquist theory. There is only one curve which resolves.

Don't forget that noise and distortion are the same thing.

As long as noise is kept below the perception level of human hearing it becomes irrelevant.

JC

Hi,

No, it is not an exact recontruction of the original waveform - quantisation error ensures that it is not a perfect reconstruction.

Quantisation noise is the output of quantisation error.

Shannon's theory assumes that the sampling instant is an exact value of the sampled waveform.

Regards,

Shadders.

 

[shadders]

It is an opinion - you have stated :

It's a fact that 16/44.1 can sound identical to 24/96. This has been proven many times (including in this thread by fr0g).

This thread has not proved it, and you used the word can - which is not absolute.

16.44.1 can sound different to 24/96. But if a 24/96 file is converted into 16/44.1 using any compentent software that does the job properly then it will sound identical.

As I said to lemon: "The differences between 16/44.1 and 24/96 are less than -80dB down in volume or occur at ultrasonic frequencies over 20kHz." Unless you can hear noise that is less than -80dB below the music volume or can hear ultrasonic frequencies they do sound the same.

I asked fr0g whether he believed that cables sound different or not.

Cables can sound different.

But all cables that meet the necessary specification do sound identical.

p.s. If anyone wants to discuss whether cables sound the same or not I respectfully ask that you start a new thread rather than take this one of topic.

Hi,

The point is that if a person states that difference sounds below -65dB cannot be heard, and cables difference are below this threshold, the cables do not sound different. My analysis shows this based on fr0g statement that differences below -65dB cannot be heard.

As such, you cannot state that differences below -65dB cannot be heard, i provide analysis that two cables have a difference below this threshold, and then state that cables do indeed sound different.

fr0g has not detailed his process - hence the process, analysis and results cannot be investigated.

Performing a test and only sharing some of the process and results is insufficient to believe the results and conclusions.

The fact that fr0g cannot hear the difference means just that - fr0g cannot hear the difference - there are many other people who may be able to hear the difference.

Regads,

Shadders

I don't think I said that about -65 dB. (I do think it is still the case, but I didn't say it).

I mentioned 65 dB in a purely hyperthetical example as to the difference between the volume of a "silent" room at 25 dB and a "loud" listening volume at 90 dB

As for the cable question, very off-topic, but I don't mind answering.

I am not sure.

There is definitely a difference if you swap a cable that is too thin or resistive, for one that isn't.

I "think" I have heard differences, albeit subtle, between analogue cables...but I doubt I could ABX them. Moving your head 1cm makes more of a difference to the sound. My opinion is that any reasonably built multistrand copper cable will sound identical to most people. I have a selection of interconnects from before I actually tested myself, nothing too expensive, but between £5 and £100 per metre. They sound the same. So much so I will happily use the freebie black cables that come with some kit. It is the equal of the £100 a metre stuff. And I would literally bet my house that nobody could prove me wrong in a blind test.

Digital cables, within spec, sound identical, or rather, they don't have a sound, they transfer digital data. Audiophile USB, HDMI,optical, CAT5+ etc are without doubt a complete con.

Hi,

OK- to quote :

Your listening room if it is very quiet might be at 25 dB.

Your music if you play it loud may be up to around 90 dB, a whole 65 dB above the "silence" of the room. You will not hear the difference

I am trying to establish the criteria as to what is discernable for a difference - whether -70dB, -90dB etc.

I chose your statement of -65dB as the reference for the threshold since you stated you will not hear the difference.

As i have stated before - the -90dB example is a difference, not an absolute. A better way of explaining is that there is a -90dB modulation waveform on the main waveform.

Without your full process description - we can only guess - the 96kHz sampling frequency is relatively prime to the 44.1kHz sampling frequency - so only once per second do the sampling instance align.

How does audacity proces this when you added the waveforms together ?

There are many questions to your process and results required to be answered before the final statement that the difference cannot be heard.

Regards,

Shadders.

 

[jcbrum]

We know that the analogue signal up to 20 KHz can be reformed perfectly. We know we can't hear sounds above that frequency. I now know that a null plot between HD and downsampled produces a flat signal only differing by less than is humanly audible.

Hi,

This is incorrect - it is an approximation. The use of higher bit rates and higher sampling rates reduces the error introduced by the analogue filter stage used to interpolate the signal - or by the digital filter in the DAC.

Regards,

Shadders.

Er, no, it's not an approximation, it's an exact reconstruction but with added noise.

Go and re-examine your Shannon-Nyquist theory. There is only one curve which resolves.

Don't forget that noise and distortion are the same thing.

As long as noise is kept below the perception level of human hearing it becomes irrelevant.

JC

Hi,

No, it is not an exact recontruction of the original waveform - quantisation error ensures that it is not a perfect reconstruction.

Quantisation noise is the output of quantisation error.

Shannon's theory assumes that the sampling instant is an exact value of the sampled waveform.

Regards,

Shadders.

You're not seeing this correctly

I agree that quantisation error is present, that is the introduced noise by the quantisation process, which dither gets rid of ! . . .

. . . or at least, to a degree which is inaudible, because all quantisation does is vary the noise floor (SNR, Dynamic range) according to the bit depth (wordlength).

The signal is as perfect as the original, plus some noise, which some people call distortion.

You simply correct the quantisation error with dither (preferably noise-shaped) until the error is inaudible, and so is the noise floor. You need sixteen bits to do that, with a bit of room to spare.

Wordlength simply determines dynamic range (SNR), and sampling rate simply determines frequency response (range). That's it. The maths says so.

Claude Shannon's maths is perfect. He designed digital audio in accordance with it. It's not some natural phenonemon like analogue sound.

JC

 

[jcbrum]

It is important to realise, and to remember, that digital audio was designed according to the Nyquist-Shannon Theorem . . .

The Nyquist-Shannon Theorem states that . . .

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

Please note that this is a Theorem, not a theory, . . . i.e. It is a mathematical proof.

JC

 

[Jota180]

Lordy is this thread still going?!

Starting to remind me of a man I once met who never watched (or read) anything anything fictional, as he couldn't accept it was 'made up'.

He was particularly scathing about sci-fi, arguing that the 'sci' bit was invalid as there were so many breaches of scientific fact involved.

How sad.

That needs unpacking by a superior mind to mine, because I tried, and it felt like I'd just read manic's posts all over agian.

Didn't think it was that obtuse (but then I am feverish with lurgy at moment!)

Just saying it seems some people seem determined to make science - rather than enjoyment - the focus of their thinking at all times. Which is odd as we're inherently talking about entertainment and emotional connection.

The guy I met couldn't understand how I could lose myself in the narrative of, say, Star Wars, or even a James Bond movie, while knowing it wasn't real. I equally couldn't fathom how you could go through life analysing everything for its 'reality' before allowing yourself to enjoy it...

I think my main concern, coming back to the topic at hand, in the audiophile sphere is snake oil. It relies on the fact that the emotional amongst us can be carried away without realising it or even admitting to the fact they are succeptable to the oil sales pitch, to the placebo effect and to confidence tricks. Proper double blind testing can remove the chance that the reviewers will subconsciously influence their own conclusions.

I know people think, don't insult my intelligence, I'm too smart to get caught out like this but for your average, emotionally 'standard' person it's in your make up. It's why you're the way you are with emotional links to other people, links based on trust, and it's this ability to trust others that is also your weakness for confidence tricksters, for snake oil salesmen and the like.

The guy you met lacked your ability when it came to losing yourself in fiction but he also probably would not lose himself in anything including any claims made by the hifi manufacturing industry for example. Not even subconsciously.

Speaking as someone with aspergers I accept nothing at face value, from no one, without evidence, question everything and if some company is going market product A as some big improvement I want to see the empirical evidence.

I don't understand why publications like this don't conduct double blind tests in a number of areas as to my mind there's no other satisfactory way.

 

[chebby]

Lordy is this thread still going?!

Starting to remind me of a man I once met who never watched (or read) anything anything fictional, as he couldn't accept it was 'made up'.

He was particularly scathing about sci-fi, arguing that the 'sci' bit was invalid as there were so many breaches of scientific fact involved.

How sad.

That needs unpacking by a superior mind to mine, because I tried, and it felt like I'd just read manic's posts all over agian.

Didn't think it was that obtuse (but then I am feverish with lurgy at moment!)

Just saying it seems some people seem determined to make science - rather than enjoyment - the focus of their thinking at all times. Which is odd as we're inherently talking about entertainment and emotional connection.

The guy I met couldn't understand how I could lose myself in the narrative of, say, Star Wars, or even a James Bond movie, while knowing it wasn't real. I equally couldn't fathom how you could go through life analysing everything for its 'reality' before allowing yourself to enjoy it...

I think my main concern, coming back to the topic at hand, in the audiophile sphere is snake oil. It relies on the fact that the emotional amongst us can be carried away without realising it or even admitting to the fact they are succeptable to the oil sales pitch, to the placebo effect and to confidence tricks. Proper double blind testing can remove the chance that the reviewers will subconsciously influence their own conclusions.

I know people think, don't insult my intelligence, I'm too smart to get caught out like this but for your average, emotionally 'standard' person it's in your make up. It's why you're the way you are with emotional links to other people, links based on trust, and it's this ability to trust others that is also your weakness for confidence tricksters, for snake oil salesmen and the like.

The guy you met lacked your ability when it came to losing yourself in fiction but he also probably would not lose himself in anything including any claims made by the hifi manufacturing industry for example. Not even subconsciously.

Speaking as someone with aspergers I accept nothing at face value, from no one, without evidence, question everything and if some company is going market product A as some big improvement I want to see the empirical evidence.

I don't understand why publications like this don't conduct double blind tests in a number of areas as to my mind there's no other satisfactory way.

The inference above - it seems to me - is that because I can exercise a 'willing suspension of dsbelief' when enjoying drama and fiction (and have relationships with family and friends based on trust and other emotions) that I am somehow more susceptible to believing claims made by unscrupulous hi-fi manufacturers.

I don't think this necessarily true. For instance, my ability to enjoy fiction, movies and dramas doesn't make my understanding of alternating current (and thus my fundamental scepticism of 'directional' cables) go away.

It doesn't make me any more likely to believe that fancy rubber feet, costing hundreds of pounds, will transform a system's performance or that there are differences between any two high-speed HDMI cables that are both made to meet the same industry standard.

It doesn't make me inherently more trusting of salespeople and marketeers or adverts.

Educationally, I have a primarily scientific and technical background. My career so far has all been in IT. But none of this has ever got in the way of my love for history and literature and art. (History especially calls for an imagination as well as a rigorous approach to assessing the veracity of different sources.)

 

[shadders]

We know that the analogue signal up to 20 KHz can be reformed perfectly. We know we can't hear sounds above that frequency. I now know that a null plot between HD and downsampled produces a flat signal only differing by less than is humanly audible.

Hi,

This is incorrect - it is an approximation. The use of higher bit rates and higher sampling rates reduces the error introduced by the analogue filter stage used to interpolate the signal - or by the digital filter in the DAC.

Regards,

Shadders.

Er, no, it's not an approximation, it's an exact reconstruction but with added noise.

Go and re-examine your Shannon-Nyquist theory. There is only one curve which resolves.

Don't forget that noise and distortion are the same thing.

As long as noise is kept below the perception level of human hearing it becomes irrelevant.

JC

Hi,

No, it is not an exact recontruction of the original waveform - quantisation error ensures that it is not a perfect reconstruction.

Quantisation noise is the output of quantisation error.

Shannon's theory assumes that the sampling instant is an exact value of the sampled waveform.

Regards,

Shadders.

You're not seeing this correctly

I agree that quantisation error is present, that is the introduced noise by the quantisation process, which dither gets rid of ! . . .

. . . or at least, to a degree which is inaudible, because all quantisation does is vary the noise floor (SNR, Dynamic range) according to the bit depth (wordlength).

The signal is as perfect as the original, plus some noise, which some people call distortion.

You simply correct the quantisation error with dither (preferably noise-shaped) until the error is inaudible, and so is the noise floor. You need sixteen bits to do that, with a bit of room to spare.

Wordlength simply determines dynamic range (SNR), and sampling rate simply determines frequency response (range). That's it. The maths says so.

Claude Shannon's maths is perfect. He designed digital audio in accordance with it. It's not some natural phenonemon like analogue sound.

JC

Hi,

I am seeing this correctly.

What i stated is correct. Shannon-Nyquist requires that the samples are EXACT measurement of the original.

You have used the word perfectly for existing systems. This is not correct. Perfect means that no quantisation error.

Increasing the word depth increases quantisation accuracy such that dither is not required, and the sample rate increase assists in the relaxation of filter used for initial sampling, and hence reconstruction.

Regards,

Shadders.

 

[jcbrum]

Shadders, the quantisation value is exact within the constraint of the wordlength employed, This is what also determines the noise level.

If you can't hear the noise, then the result is audibly the same as an infinite wordlength.

Analogue sound and analogue systems do not have infinite resolution and infinite SNR either.

Digital systems can easily have better resolution and better SNR, in mathematical terms, than practical real world analogue systems, but you can't hear digits, so you have to listen to analogue. The test is whether you can actually hear the 'noise' in the result.

That is what fr0g's test is about.

JC

 

[shadders]

Shadders, the quantisation value is exact within the constraint of the wordlength employed, This is what also determines the noise level.

If you can't hear the noise, then the result is audibly the same as an infinite wordlength.

Analogue sound and analogue systems do not have infinite resolution and infinite SNR either.

Digital systems can easily have better resolution and better SNR, in mathematical terms, than practical real world analogue systems, but you can't hear digits, so you have to listen to analogue. The test is whether you can actually hear the 'noise' in the result.

That is what fr0g's test is about.

JC

Hi,

I never disputed that quantisation creates the noise in a reconstructed waveform

My statement is that Shannon-Nyquist is based on EXACT sample values.

If you can't hear the noise,...

Agreed - if you can't hear the noise. There may be others who can.

Analogue sound and analogue systems do not have infinite resolution and infinite SNR either.,

I have never stated that analogue systems have infinite S/N. Analogue systems do have near infinite resolution, but this is masked by the noise.

Digital systems can easily have better resolution and better SNR, in mathematical terms, than practical real world analogue systems

Agreed, theory does seem to always be better than any practical analogue system. This is not in dispute.

The test is whether you can actually hear the 'noise' in the result

The test needs to be documented such that its validity can be ascertained and repeated. Partial process statements and partial results are not conclusive evidence.

One question - if you cannot hear an absoute -90dB signal - then why is dither implemented for 16bit words ?

Regards,

Shadders.

 

[jcbrum]

One question - if you cannot hear an absoute -90dB signal - then why is dither implemented for 16bit words ?

Regards,

Shadders.

It doesn't have to be. It depends on how the 16bit words are created.

For example if you make a direct recording to 16bit digital, of a real event, and you do not wish to modify it (such as is commonly done in the production process) then it will be perfectly satisfactory on playback.

However the real world situation is that record producers wish to apply many manipulations and processes during the mastering and production process.

For this reason, 24bit sound is much easier to use, since it provides great room for manoeuvre . During those process quantisation error can build up, and so dither is applied to resolve it.

Additionally, modern dithering processes also incorporate noise shaping, which is beneficial too.

JC

 

[jcbrum]

Agreed - if you can't hear the noise. There may be others who can.

HaHa, are you thinking of Superman, or normal human beings ?

JC

 

[jcbrum]

Actually Shadders, thinking for a moment, If your definiton of exact quantisation applied, then dithering wouldn't work.

And it does, Superbly.

Because it complies with the Nyquist Shannon Theorem.

JC

 

[jcbrum]

I have never stated that analogue systems have infinite S/N. Analogue systems do have near infinite resolution, but this is masked by the noise.

Quite so,

Digital systems have near infinite resolution too, masked only by the noise, that noise is the quantisation error.

As with analogue, if the noise is sufficiently quiet (inaudible), then the result may be considered perfect.

It is impossible, in practical terms to build any real sound system that can utilise more than about 20bits because of residual noise in real world components.

However, in the digital domain (a mathematical environment), much longer wordlengths may be employed for mathematical reasons.

Human hearing cannot resolve anything better than that provided by 16bits, based on studies of the ability of human ears which have been accepted for many, many, years by experienced scientific practioners.

Bats, Whales, Superman, and golden-eared audiophiles, may respond differently.

JC