Tuning any musical instrument is an art, not science.  The human
ear does not like mathematical perfection in most cases.  Large pipe
organs sound magnificent because they can never be in perfect tune.
We enjoy a breathy flute much more than a perfect electronic sine wave.

How good a piano sounds depends mostly on the preferences of the
listener, and some can tolerate a lot more off-tuning than others
can.  I think that pianos in perfect tune are quite boring, lacking
in character, but that's just me.  Accordions often have one reed of
a given note tuned sharper than the other to give a fuller sound.

Also keep in mind that pianos are tuned with some "stretch",
meaning that the octaves are a little sharper as you go up the scale.
Determining the proper amount of stretch requires an experienced ear
and may be becoming a lost art.  Randomness and subtle variations are
the secrets to good sound.

Gordon Ramsey - Ramsey Music Service
Wichita, Kansas, USA