I was told that a perfectly tuned piano (according to math) would make the octaves blend in as harmonics and make the distinct note 'disappear' a bit, so the stretch tuning is done to keep the notes distinct and clear. (as Mac said - 'not to be in tune with itself')
Not sure how true this is in apllication, but this was from a guy that tuned pianos for a living. Back when you could make a living doing that!

Sounds reasonable enough to me.. close enough explanation?

Here's a chart to answer the original post question -
http://www.phy.mtu.edu/~suits/notefreqs.html

I do not work here, but the benefits are still awesome
Make your sound your own!