🚀 go-pugleaf

In article <1is3e2INNrvq@rave.larc.nasa.gov>, kludge@grissom.larc.nasa.gov 
(Scott Dorsey) writes:

>>Of course, being digital in no way limits the number of available pitches.
>
>Bzzt, try again.  Being digital does indeed limit the number of available
>pitches.  There is quite a variety of them, and certainly more than the ear
>can pick out, but it's not continuous, since time is being quantized when
>the sampling is taking place.

Could you explain that so that a layman can understand it? 
I am willing to accept it, but incapable of arguing in favor of it. Now,
this is how I am thinking:

Imagine, say, a sine wave of 100 Hz exact as the only sound. That gives 441
samples per full wave - the next maximum value comes 441 samples later than
the previous one. Nyquist claims that (in theory) I can have a perfect 
reproduction of it.

Now a 101 Hz sine wave: The next max value comes 445.41 samples later than
the previous one. This sample does not exist, so the 445 one is "almost max",
the 446 one is "almost max", but the 44,541 one *is* max, exactly at the
right time. Nyquist claims that in theory, this is perfect reproducible.

Now for a 100.01 Hz sine wave --- and the same thing again, leading to the
sample 4,410,441 being exactly perfect, max value.

And so on, down to any frequency precision that you want. And since an
arbitrary complex sound pattern can be represented as a sum of sine waves,
this logic holds for any sound, not only 100.0000??? Hz sine waves.

For any given frequency, there will be a lot of samples that are displaced 
from the signal maximum along the time axis. But the sample value will be
correspondingly off the maximum signal value, too. Whenever n*441/f is an
integer value, the sample will be exactly max at exactly the right time,
no matter the frequency. So the information *is* there, isn't it?

I may be missing out something, but I don't know what!