> You can't tune an instrument to 1/4 of a hz

I mean you can, but for stringed instruments keeping it to an absolute is hard. its the relative that you care about, at least for an instrument with a static fret. pretty much everything other non-keyboard instrument is down to you to adjust on the fly.

when you are within 1hz you get a beat at roughly 1hz, which is normally fairly easy to pickup.

Its part of the reason why brass instruments are never "wide" in stereo on recordings, because they tend to phase like a mother fucker. (there are ways around it)