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Ok, Confusion is abounding..
Higher sampling rates increase frequency response bandwidth (ie the greater the sampling frequency the higher pitched sound that can be captured). That is all.
Number of bits is dynamic range. (ie Amplitude)
In photographic terms they also correlate. Sampling rate is analogous to resolution, bit depth is the same (amount of colours in your palette).
To reccap, for a digital system to be correctly balanced to the analog part you need enough bits to put the noise floor of the digital equipment below that of the analog. Where that floor is depends on your source material.
For all practical purposes 24bits of fixed float precision, and 32 bits of floating point precision have a dynamic range that exceeds even an SSL or Neve analog console. More bits than this will do nothing for your sound, and consume correspondingly increased CPU/DSP resources. So it's unlikely you'll see 64bit recording files unless it's in a marketer's wet dream.
On sampling rate there are 3 key root standards, one of which is falling by the wayside. I say "Root" standards, as the higher rate sampling frequencies are exact multiples of these for reasons that you are aware of.
32Khz (Old Long play digital format) Used in older broadcast systems, but pretty much retired unless it's field recording by journalists doing speech, and even then it's dying.
44.1Kz (Pop quiz, anyone know why this specific Frequency, and not say 44.2KHz?) the CD standard, and one of the most common sampling rates out there. If you ever want your stuff to go to CD then this is the one (or a multiple of it, say 88.2KHz) you want to be at to avoid ikky sample rate conversion.
48KHz TV broadcast standard. I you're doing sound for picture you'll almost certainly be working here or some multiple of it)
As for high sampling rates, this is where things get controversial FAST.
I'll begin by saying that Nyquist Theorem states that to accurately capture any waveform simply requires sampling at 2x the frequency of the waveform.
This theorem has stood up to an awful lot of scrutiny, so with that in mind and all things being equal recording at 44.1KHz should be enough for anyone (or 48KHz if you need the standard), as only a young child's hearing goes up to 20Khz or so. At my age it really stops around 15-16Khz (and less if you have hearing damage.
Not only that but 44.1Kz should sound the same as 48KHz, or 192KHz or even 2Ghz.
The problem is, all things are not equal, and there is a lot more going on than simple sampling rate.
You've disovered this with your "Harsh harmonics".
What's happening is that part of every A/D Converter there is a Lowpass filter. This ensures that nothing out of the Niquist range gets into the signal and cause audiable artifacts (Alaising) to be generated.
With a 44.1KHz or 48KHz sampling rate the filter cutoff has to be pretty sharp, and doing it right is very very expensive, and also requires an awful lot of clever design. This is a major reason why people will spend buckets of cash on Apogee and Prism (to name but 2) converters over your regular joe soundcard converters.
Too sharp a filter, one with a non-optimal response or one that is poorly designed in general will have a significant impact on the sound passing through it. You already know about filters and tonality if you have played with more than a couple fo synths. The effects of this are very real.
Now, if you sample at is higher rate, say 96KHz or 192KHz what the designer can do is to create a filter with a much more gentle cutoff slope, which is much easier to design, and also (and more importantly) has substantially less sonic impact (Ringing) than a steeper filter.
This, and not the extra samples is why your interface sounds better at 88.1KHz instead of 44.1KHz. Remember, your hearing at best only goes up to 20Khz, which means that a 44.1KHz sampling rate is more than 2x so you're clear under Nyquist Theorem even at 44.1Kz.
Anyone who tells you that 881.Khz sounds better than 44.1KHz because there are more datapoints doesn't have a handle on the maths..
As for which sampling rate you should use, that depends on your predicted output format. You've already worked out that 88.2KHz is better than 96KHz if you are going to CD as your ultimate destination. The reverse is true if you are working to picture.
What every you do though you really REALLY want to avoid sample rat conversion. It's ugly at the bes of times, and going from non multiples to another is just plain bad. If you have two decent sets of AD DA converters it is ofeten more desirable to step back through analog than it is to perform even the best SRC.
Finally, there's another factor as yet undiscussed that has an impact too. That's clocking accuracy, also known as Jitter. Think of it as sloppy drummer Vs a drum machine, this can produce awful artefacts that cannot be fully undone. I think I've blabbered anough about this subject so far, so I'll leave jitte for another time (if ever).
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