According to Wikipedia and Eric W. Weisstein's wonderful Wolfram Mathworld, a synonym for "harmonic mean" (n.) is "subcontrary mean" (n.). This is an interesting terminology because it evokes the image of the square of opposition:
$\require{AMScd}$ \begin{CD} \textrm{All S are P} @>{\textrm{contrary}}>> \textrm{No S is P}\\ @V{\textrm{subalterm}}VV @V{\textrm{subalterm}}VV\\ \textrm{Some S are P} @>{\textrm{subcontrary}}>> \textrm{Some S are not P} \end{CD}
(note: due to the limitations of the AMScd package the case of contradiction could not be represented.)
What is the reason behind naming the harmonic mean the subcontrary mean?