Grab a cup of coffee, put on your thinking cap, and start working through this newly-released video from Minute Physics, which explains why guitars, violins and other instruments can be tuned  to a tee. But when it comes to pianos, it's an entirely differently  story, a mathematical impossibility. Pianos are slightly but necessarily  out of tune.

https://www.openculture.com/2015/09/why-you-can-never-tune-a-piano.html