It turns out that there is really no such thing as a "perfectly tuned piano". Something is always a little dissonant. Different tunings can move this dissonance

It turns out that there is really no such thing as a "perfectly tuned piano". Something is always a little dissonant. Different tunings can move this dissonance around, but (on a standard 12-notes-per-octave keyboard) they cannot eliminate it. Here is a nice article from Slate about all this: http://www.slate.com/id/2250793/ http://www.slate.com/id/2250793/ (EDIT: GMTA, it seems.)