The tuning of a piano is never perfect. It can't be. It would
sound wrong when you switched keys.
That's the only trouble I have with ideas of mathematical
perfection and music. it isn't perfect.
Having perfect pitch, I can hear the slightest out-of-tune
'beats'. I actually like that noise, because I listen for it. I
love hearing an instrument that's a little out of tune, or a
piano that hadn't been tuned, or if an electronic keyboard is a
little brighter or sweeter or more sour in different keys or at
different portions of the keyboard.
Interesting how we have to analogize music to light (brighter)
or to taste (sweeter / sour).
We all have synesthesia, hiding right within the very language
we use to describe Reality.