This is my (very) basic understanding of the logic in laymen's terms-

Let's say you play a 'C' on piano an octave below middle C
Now if all the strings are perfectly in tune on that note, it would ring certain harmonics.
One of those harmonics is the C two octaves up. In a perfectly tuned piano (only possible theoretically) that C two octaves up would simpley re-inforce the harmonics of the lower C when you played them both; it wouldn't be a distinctive note but would quickly vanish into the harmonics. Not totally but significantly. Each note has many harmonics so the problem would compound.

Throw it out of tune just a hair and you can easily notice it.
If you throw it out of tune by making it flat it will be annoying. Throw it out of tune a little sharp and it fits much better.
That's the 'stretch' part (as I understand it). The higher you go up on the piano the more it is adjusted (sharp) to be distinguishable from the lower harmonics.
Hopefully someone else has more info.

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