> I can reliably tune an A440 to within 2 cents, but I doubt I could get some other arbitrary note to within 20.
But you can work your way up and down the keyboard from that initial A440 to check how the other As are and then expand from there until you have them all in tune. So you can't just pick a random note and tune it but you can for instance use your one reference to tune a whole keyboard eventually hitting on that one random note and getting it to within some tolerance.
> I've seen demonstrations of true, "one-in-a-billion" savants doing mind-boggling things like immediately naming every note in bizarre 15-note chords
That's the kind of skill to be very jealous of, at the same time these savants often seem to have to have given up something else.