Nonlinearity, what's the SHAPE of it?

GedLee comments a lot on the shape of the nonlinearity correlating to it's audibility. So my question would be "what is the shape of the nonlinearity?" The next logical question would be "How is it measured?" then "what would be the worst possible shape?"

Thanks! Danke! Dalu! Merci! Grazie! Arigato! Mahalo!