I noticed the following use of aesthetical in a comment on an English site:
Thus I use the incorrect case [object form instead of subject form] as my domain name for aesthetical reasons.
The correct word here is aesthetic. The writer is not concerned with the science of aesthetics, but with his personal aesthetic feelings about the beauty of words.
aesthetic adj. Of or pertaining to the appreciation or criticism of the beautiful.
One has aesthetic feelings, aesthetic reasons, aesthetic sensibilities.
Aesthetical, on the other hand, is used to modify things relating to the science of aesthetics. For example, Frederich Schiller wrote aesthetical essays. The professor enumerated the aesthetical values of photography.
aesthetic n. (commonly pl. aesthetics, as collect. sing.) The science which treats of the conditions of sensuous perception.
aesthetical adj. Of or relating to aesthetics; relating to the philosophy or theory of beauty. _ Often interchanged in use with aesthetic, but properly distinct; thus my aesthetical notions are the notions I have on the subject of aesthetics; my aesthetic faculties are those which exercise aesthetics. –OED