I'm a complete novice, but I remember hearing that we actually like to hear music ever so slightly off key. What does this analysis tool say for expert recordings?
I was interested in this so did some empirical work-- yes, people consistently prefer mild dissonance over perfect consonance -- at least with combinations of 3 sawtooth waves. Perfect consonance sounds colder while very slightly off tune sounds richer. It's an obvious effect (try it with a generator) but would be unrelated to violin playing
I think what you are referring to is "temperment", and a TLDR version of that topic would be that for tuning a piano so that it can sound in tune no matter what key, it is tuned to be evenly out of tune everywhere, aka, "equal temperment". This little app follows equal temperment. A string player playing unaccompanied solo might tend to play in a way that sounds better, aka, "just temperment", and so would seem to be out of tune according to this tool.