... Rob Watts mentions tap length and I can give you my understanding of it. The perfect analogue reproduction from a digital to analogue conversion will be the one with the sinc function as an impulse respons. ...
This of course a ridiculous choice of course for doing reconstruction. One can design either a constant delay, or mixed delay filter of quite finite length for any purpose, while providing reconstruction to any arbitrary level, say, under 1 LSB, without having to resort to sinc functions, etc. Look up "remez exchange" for one well-known way to design a finite length filter that will give, assuming you feed it properly (never assume people know what they are doing) the best filter one can achieve for a given length.
Then you look at the results, and either make the filter longer (if it's not good enough) or shorter (if it's excessively good) or you simply allow yourself to be satisfied with over kill (the usual way to do this).
It's really not hard. If you must do some kind of resampling (say by 14 as you mentioned, although 14 is pretty silly, it would be much more efficient to do 16, Crochiere and Rabiner showed how to do this to any arbitrary cleanliness, efficiently, back in the very early 1980's. I know, I worked for them, some of my work is in the book.
https://www.amazon.com/Multirate-Digital-Signal-Processing-Crochiere/dp/0136051626
If you want to do variable-rate resampling, Proakis shows how to do that to any arbitrary level in one of his early books on digital signal processing.
These are almost hoary-old methods, and they work JUST FINE. There's no need for this "sinc" stuff, you're spouting theory that is both inefficient and unnecessary there. (Yes, the theory is right, but so is the theory of filters and wavelets.)
Why do we need "infinite precision and timing"?
How would the sinc function not being "infinite precise and timed" manifest itself in measurable parameters?
Are there no hearing thersholds that apply to these parameters?
Well, precisely. Given the basic atmospheric noise that nobody seems to want to remember, there's no such thing as "infinite precision". That's really a very basic point here, basic atmospheric noise due to the particulate nature (i.e. molecules, argon atoms) makes any kind of "infinite precision" nonexistent, timewise, levelwise, you name it.
(Not directed at Geert here)
Furthermore, air propagation at high levels (above 120dB or so, detectable, barely, maybe, at 90dB, by an accurate machine) is NOT LINEAR. So enough with these silly "infinite precision" arguments. If you want to argue about multistage interpolation and decimation, your first job is to prove that Gauss was wrong, and the Fourier Series does not converge in L2 with finite power signals. Good luck with that.