general

A Boolean function has parity and depravity.
It is even, iff the first digit of the truth table is false. (Its Zhegalkin index is also even.)
It is evil, iff the last digit of the truth table is false. (Its Zhegalkin index has even binary weight.)

even evil (0)
even odious (2)
odd evil (1)
odd odious (3)





noble

All noble Boolean functions are even.
But they are also partitioned into quadrants. The place of parity is taken by strength.
There are as many n-ary nobles as there are (n−1)-ary Boolean functions. (E.g. the number of 3-ary nobles is 16.)
The nobles sorted by size are the rows of table  A358167.
The indices to this row can be assigned general quadrants (because integers can be interpreted as truth tables).
The general quadrants of the indices are equal to the noble quadrants of the entries.

weak evil (0)
weak odious (2)
strong evil (1)
strong odious (3)
Own work
WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".