Has anyone been able to define well or measure differences between vinyl and digital?

@fair ,

One last point,

For higher frequencies, at 44.1 KHz sampling rate, this may correspond to only a few samples. The shape of a quickly changing signal can’t be faithfully captured by such small number of samples.

This demonstrates, succinctly, a lack of understanding of the topic we are discussing. Perhaps the problem is you only see a few samples. What you should see is a few samples, taken at very precise time intervals. The information is not only the sample value, but the exact relative time of each sample. Both are critical.

There are so many errors in @fair's word salad that it makes my head spin. Kudos to @thespeakerdude for having the patience to sort them out.

One thing to consider about digital audio is that the math that makes it work is the same math that explains the squiggles on an LP: the Fourier Transform. That's not just a theory, but a theorem; it can be proven with math. In that sense, it's perfect, and I'm saying that as an analog guy.

If there is any interest, this is probably the best single article I have discovered that explains digital audio. It is not light reading nor heavy reading. Dan, who put it together obviously put a lot of time into it. It is almost 20 years old so comments about processing power are no longer relevant, but everything else is. I have come across many articles on digital audio written by less technical people. They get the basics right, but they often make mistakes and they never go into the depth that this article provides. You may need to read it 2 or 3 times to understand well enough, but if you do, it will dispel a lot of misconceptions about digital audio.

https://lavryengineering.com/pdfs/lavry-sampling-theory.pdf

If you have any questions about the article I will try to answer them.

This video provides an excellent explanation and actual demonstration of how digital audio works, and how it doesn't.

Thanks for the extensive explanations of digital audio and references @thespeakerdude

Can we now summarize (are we there yet?) and identify general principles that help shape the differences between these two formats. I’m not interested in which one is better, as judgments are too system and context as well as music and preferences dependent.

Rather, can we draw conclusions about their differences that are more or less general or specific conclusions (about dynamics, freq range, noise and noise floor, PRAT, mid or high freq airiness and so on or our hearing preferences, sensitivities and limits) that shed light on common experiences?

I just watched Paul at PS Audio say how what MOFI was doing recording using DSD was in his view the right way to record and preserve masters in digital and then transfer onto vinyl for playback. Is vinyl playback giving anything different to digital playback from the same master copy?

[MOFI Marketing representations aside. I don’t want to touch the Marcoms involved here in this discussion.]