[Morphious]

While doing research on Lossless,  I downloaded 2 dozen albums and MQS files from LINN and others. I also have a program called Similarity App. In this application you can run an Analysis of a files to see lots of information about the audio track. Most of the files barely had any peaks in the frequency Khz range that reached above 88Khz.  I did a little checking and found that ultrasonically, Not many instruments can go over 100Khz no matter what, Symbols can hit up to 102Khz.   My style of music had a high peaks of 55Khz on a 2014 master hi rez file. Everything above this if encoded into a 192 Khz files is useless and empty space ( I.E. a 0 in digital language) Most space above 100Khz is set to 0. This means it is just wasted space that cannot affect the soundstage, or anything else in the audio spectrum as there is nothing there to play or affect anything as it is a 0 ( or row of zeros )   But zeros do take up physical space in a file, and makes the file larger. This would lead me to believe that 96Khz would be near the best any file can be heard ( if we could hear that high), Maybe with clipping on an a properly recorded symbol, but even the reference material out there are not recorded to this level.   
 
Bit depth is a different story. the more / wider the bit depth the more it affects the whole spectrum of sound. It's more 1's and 0's that be crammed into the full frequency spectrum as the file is being played, and this has to have an effect on the sound in every way.   Similar to color bit depth, the more bit depth you have, the more colors you have. Even if you cannot see all of the colors above 24bit, it does affect the image clarity and depth. 
 
Being Hi-Fi type people, we all want to listen to the best quality audio we can, even if we cannot hear it  
 
Someone please correct me if I have went off on a misinformed tangent... 

 

[Head Injury]

  Someone please correct me if I have went off on a misinformed tangent... 

To keep it simple:
 
Anything above what we can hear (or anything above 20 kHz for virtually all humans) won't be audible and won't affect the audible frequencies except in unwanted ways like IMD, so it's all wasted space. We can't hear what we can't hear, seems pretty straightforward right?
 
Bit depth only determines maximum signal-to-noise ratio (6 dB per bit) of the file, and has no other effect on sound quality. It doesn't improve image clarity or depth or other meaningless terms. Just how loud things can get above the noise floor. Your color depth analogy is flawed because color and sound are both stored in very different ways; color bit depth determines the number of possible colors a pixel can display while audio bit depth determines the number of volume steps (but not the size of the steps). Color depth is actually more analogous to the sampling rate in audio, but still not quite the same so don't go claiming it means higher sampling rate improves the sound.
 
16 bits sampled at 44.1 kHz can perfectly capture all sounds up to 96 dB above the noise floor within the range of human hearing. The only thing increasing the depth to 24 bits does is allow the perfect capture of all sounds up to 144 dB above the noise floor. There's no increase in quality up to 96 dB, just an increase in range above it.

 

[SilverEars]

  Your color depth analogy is flawed because color and sound are both stored in very different ways; color bit depth determines the number of possible colors a pixel can display while audio bit depth determines the number of volume steps (but not the size of the steps). Color depth is actually more analogous to the sampling rate in audio, but still not quite the same so don't go claiming it means higher sampling rate improves the sound.
 

I agree that they totally different.  People that fall for HD audio marketing are likely thinking it's the same as panel resolution and bit depth which are different.

 

[sandab]

  I agree that they totally different.  People that fall for HD audio marketing are likely thinking it's the same as panel resolution and bit depth which are different.

No, 88x16 has exactly the same entropy limit (maximum information content) as 44x32.  There is absolutely no difference.  People who tell you otherwise are clueless.

 

[SilverEars]

  No, 88x16 has exactly the same entropy limit (maximum information content) as 44x32.  There is absolutely no difference.  People who tell you otherwise are clueless.

Can you explain this further?  I'm not familiar with entropy limit, so I don't understand what you are referring to.

 

[castleofargh]

  While doing research on Lossless,  I downloaded 2 dozen albums and MQS files from LINN and others. I also have a program called Similarity App. In this application you can run an Analysis of a files to see lots of information about the audio track. Most of the files barely had any peaks in the frequency Khz range that reached above 88Khz.  I did a little checking and found that ultrasonically, Not many instruments can go over 100Khz no matter what, Symbols can hit up to 102Khz.   My style of music had a high peaks of 55Khz on a 2014 master hi rez file. Everything above this if encoded into a 192 Khz files is useless and empty space ( I.E. a 0 in digital language) Most space above 100Khz is set to 0. This means it is just wasted space that cannot affect the soundstage, or anything else in the audio spectrum as there is nothing there to play or affect anything as it is a 0 ( or row of zeros )   But zeros do take up physical space in a file, and makes the file larger. This would lead me to believe that 96Khz would be near the best any file can be heard ( if we could hear that high), Maybe with clipping on an a properly recorded symbol, but even the reference material out there are not recorded to this level.   
 
Bit depth is a different story. the more / wider the bit depth the more it affects the whole spectrum of sound. It's more 1's and 0's that be crammed into the full frequency spectrum as the file is being played, and this has to have an effect on the sound in every way.   Similar to color bit depth, the more bit depth you have, the more colors you have. Even if you cannot see all of the colors above 24bit, it does affect the image clarity and depth. 
 
Being Hi-Fi type people, we all want to listen to the best quality audio we can, even if we cannot hear it  
 
Someone please correct me if I have went off on a misinformed tangent... 

 ultrasonics... ^_^
they could replay my music with the star spangled banner sung by the chipmunk from 40khz to 60khz it wouldn't change a thing for me. make yourself a favor, go to your audiologist and ask him to test you, to see where you actually hear something. it should clear things up like A LOT.
 
 
now bits wouldn't work with an analogy for colors, but it would for brightness in a way. every time you add a bit you can lower the brightness a little more. the music close to 0DB(loudest) would be a spot in your face changing intensity. and adding bit depth to 16bit would be like adding a little spot next to it that would do brightness dimmer than the minimum the first spot ever does. what are the odds for you to ever see the second spot? not much.
and to that you have to add the fact that the dimmer level for the first spot was already lower than what you can normally see. meaning that the second spot will have variations between "is it off?" and "I think it's off".
that's what we do when we go from 16bit to 24bit. we don't add inter values for the first spot, that's some misunderstood marketing stuff. all the sound between 0db and -96db will stay the same on 16 and 24bit(given we actually have 16bit).
personally I like to output 24bit(but don't use 24bit tracks) so that I can set my volume with the computer. but that's a gadget, it's not really for music and I could move my butt and go change the volume on the amp.

 

[sandab]

  Can you explain this further?  I'm not familiar with entropy limit, so I don't understand what you are referring to.

Entropy is the amount of information.  The limit is the upper bound on the information content.  Shannon's Sampling Theorem underlies much of modern information theory.  When the entropy has reached its limit we call it a random sequence.

 

[sandab]

I took a look at the magnitude of the quantization error over 25 cycles.
 
Here's 44.1/16 with a 0dB 20k sinusoidal:
 

Top is the samples (just over 2.2 per cycle) in blue.  Overlaid in green is the numerical error, scaled so 0 to 1.0 is 0.1%.  The bottom in red is the real part of a cooley-tukey DFFT (approximation of frequency spectrum).  Phase is ignored here.
 
Here's the same in 44.1/24:

For comparison, here's 44.1/16 at -12dB (2^(-12/3) = 1/16), which is equivalent to 44.1/12:

44.1/24 at -12dB:
 

A good spectrum should spike to 1.0, like 44.1/16 at 1kHz 0 dB:
 

By comparison, here is 96/24 at -12dB, 20kHz:
 

Hard to say how precise the frequency spectrum is for 44.1, but needless to say there's quite a bit of distortion going on.  That energy is going to go someplace else on the spectrum, and with 44.1 it's almost guaranteed to be "someplace audible".
 
Even 48/16 looks better:

 

[sandab]

I also added an FFT of the error, which shows an even spread across the spectrum:

The pink line is the error (QE) spectrum... clearly it's across the board.  Its Y axis is 0.1%, so it's about 0.01% evenly distributed across the spectrum.
 
At -12dB:
 

So around 0.1% at -12dB.  By comparison 44.1/24 @ -12dB doesn't rise from the X axis:

 

[castleofargh]

and what about a more usefull frequency? like 14 or 15khz, or just something in the medium, where it matters. because I have no record with loud 20khz signal, and in fact no headphone that doesn't roll off long before that. given the improvement from 44.1 to 48khz, I would suspect the differences become marginal very fast at lower frequencies.
 
but thanks for taking the time to do all this.

 

[esldude]

And of course there is the change adding dither would make.

 

[sandab]

Dither would just randomize the noise - flatten the spectrum.  But it's already pretty flat, so I'd have to question the usefulness of dither except to flatten the error spectrum in conjunction with resampling or applying gain, or some other numeric operation, to reduce rounding error bias.

 

[RRod]

But our ears would have to be able the hear the lower-frequency content, which is several dB below the 20kHz tone, in a time-span of 0.00125 seconds.

 

[sandab]

  and what about a more usefull frequency? like 14 or 15khz, or just something in the medium, where it matters. because I have no record with loud 20khz signal, and in fact no headphone that doesn't roll off long before that. given the improvement from 44.1 to 48khz, I would suspect the differences become marginal very fast at lower frequencies.
 
but thanks for taking the time to do all this.

I think that depends on the recording and exactly how the highs were rolled off during the CD-rate cut of the master.  If you put a mic to an instrument, you'll find it has supersonic content; so at some point that needs to be filtered.  Filters don't have perfect cutoffs but a wide attenuation ramp - and the wider, the better they tend to sound due to reduced ringing and phase distortion.  Except for digital sinc-based pass/stop filters, which have flat phase response, meaning the phase has no complex component - so represents a simple propagation delay.  But they still ring; that's inevitable when parts of the band is removed from transients.  I think you'll find most if not all 44.1 content has some signal at 20k.
 
Since the error spectrum is so flat, it just tells us that treble content reduces the noise floor, potentially beating the noise floor for any repeating waveform.
 
And since you mentioned it ...  15.5kHz @ 44.1/16 and 12 bits (0dB and -12dB)
 

 

Edit: the second error spectrum might benefit from dithering, as it has an odd low-frequency bias.  Not sure if that's simply an artifact of the limited signal window (FFT assumes an infinite signal).  I'll see what adding a dither instead of mathematically correct rounding might do to the error for this.  It could also be a beat in which case nothing can be done about it other than redithering to add enough additional white noise to swamp it.

 

[doraymon]

Interesting article here.