If, however, that "A" is played on a piano, an 880Hz sampling will destroy it. The fundamental tone will be sampled accurately, but the overtones and harmonics (that is, the components that make a piano sound different from a sine wave) will get lost. You'll end up with an "A" that only sounds vaguely piano-like.
While the wave itself will be at 440Hz, the shape of that wave will be fairly complicated. From an engineering standpoint, it can be thought of as a composite of many waves at different frequencies and amplitudes (most of which will be integer multiples of the fundamental 440Hz.) In order to accurately sample the shape of the wave (and not just its fundamental frequency), you'll need a sampling frequency much higher than 880Hz.
So, although 44.1KHz can accurately sample fundamental (that is sine-wave) frequencies as high as 22.05KHz, a complex wave-shape at 22.05KHz will require a much higher sampling rate if you want an accurate representation.
We're going around in circles, here miro, because you keep ignoring some basic facts (and, yes, they are facts, and not just things we think are facts because of the limitations of our current science.) What David says above is all true, until the last paragraph. It would be truer if he added the words, "of any potential harmonics of that 22.05KHz signal". (Technically, less than 22.05 because of the aliasing filters, but we'll put that aside for a moment.)
But it still ignores a couple of basic points:
First; that there's nothing creating *fundamentals* at 20k or above, except for a couple of brands of dog whistles. Anything existing up that high is already going to be a multiple order harmonic of a much lower frequency fundamental. For example, the A440 he uses as an example would be at it's 45th harmonic by the time you got up to 20k, which just plain isn't going to be anywhere near audible - *if* a piano even created harmonics of that order. In fact, the highest fundamental a piano can create is a C8 at about 4.2k. 20k is almost 5 overtones above that, which again, is going to be a negligable amount of energy; even if we *could* hear or "feel" it, there'd be next to nothing to hear or feel.
OK, there are some pipe organs which can go slightly more than a half-octave above that on their fundamental to an A8, which is still only 7.1k. If anybody really wants to listen to a pipe organ at sibilant frequencies (even though we all know how grating sibilance sounds), we'll be limited to reproducing approximately the third overtone of that sibilance. Somehow I doubt anyone is going to miss the 4th overtone and above of a 7k fundamental which is already giving them headaches.
Other than that, even if we ignore the fundamentals, when it comes to harmonics of instruments, about as high as they go is the violin and some cymbals, which tend to end their audibility at around 16-17k (where dog whistles start.)
There is real physics involved here. The higher the order of harmonic, the less energy it carries, and that for anything that sounds even remotely pleasing to the human ear, by the time our harmonic order gets high enough to worry about Nyquist, they simply become virtually irrelevant to the timbre of the instrument or sound.
The second entry to physics is in the design of the human ear, as I said before. Dogs and cats can her much higher frequencies than we can, and the exact,specific reasons are measurable; first, it's because of the size and shape of the cochlea, which, like a french horn or tuba, is designed to channel certain frequencies in certain ways. The dog and cat cochleas are measurably designed to handle higher frequencies, just like the size and shape of the french horn handles higher frequencies than the tuba does.* Second is the characteristics of the cilia, the hairs within the cochlea, whose vibrations turn the sound into the nerve impulses which go to our brains. Their size and position within the cochlea determine which frequencies they can deal with. (It's the degradation of the finest of these cilia which are the main cause if tinnitus, BTW; they "malfunction" and send constant impulses to your brain which we hear as "ringing of the ears".) And the design and build of the human ear dictates that it just cannot send ultrasonic signals to the brain any more than a tuba can generate a 16k overtone
This is all known science which further science can build upon but will never repudiate. To try and sidestep this by going to the unknown future is just taking random pot shots that have a far greater chance of missing the side of a barn than they do of hitting any real factual target, now or in the future (I'm still waiting for my flying car and ESP-in-a-pill, which they told us when I was small we'd all have by now!
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If, however, you do actual audio work (live recording, mixing, editing, etc.), it is necessary.
Every single time you perform an edit (mix, equalization, effects, etc.) you introduce errors into the data. This is because computers don't have infinite precision - every computation prduces a small amount of "round-off" errors in the least-significant bits and in the highest frequencies. The more you edit, the more the errors accumulate.
Incorrect. The kind of quantization errors he's talking about are NOT cumulative in the way he describes them. Refer back to Ethan's discussions re this earlier in this thread. Nor will the errors be concentrated in higher frequencies just because you have higher sample rates; the distribution of the digital noise remains even across frequencies and it's level is a function of bit depth, not sample rate.
There is a reason professionals always use 24-bit interfaces at 96 or 192KHz sampling
There might be a reason if they actually did. But this is a mis-statement; te majority of professionals that I have worked with and talked to on these forums use and recommend 44.1k/24 for pure audio and 48k/24 for audio for video post. Perhaps, as George mentioned, 96k/24 for SACD production, but that's not for the point of capturing phantom overtones, it's for the idea of avoiding extreme sample rate conversion factors.
Again...if we just assume that everything outside of the 20-20kHz range is useless info, then the bar will never be raised higher, and we will just accept not needing recording gear that can capture outside of that range.
Yep. And there's nothing wrong with that. What's the point of dealing with useless information - or more to the point, information that doesn't exist?
It's not a question of us setting the bar too low, it's a question of Mom Nature setting the bar herself, and all we have to do with our technology is clear it. There's absolutely no point in jumping 50 feet over an 18 foot bar.
This is all sidestepping the real question, though, miro; why do you feel the inner need to discuss, accept and defend the fringe topics? No offense intended, here, but I notice that we seem to always wind up getting the biggest head bumps on subjects like MP3 encoding bit rates, sample rate and so forth which frankly mean so very little in the grand scheme of audio engineering.
*BTW, have you ever noticed that even though dogs and cats can hear up to maybe 40k-50k, that they NEVER find the ultrasonic stuff to be pleasing? They are not attracted to dog whistles any more than we are attracted to air raid sirens, and I have never met a dog that actually enjoyed the ultrasonics put out by the suction motor of a vacuum cleaner
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