'aristocraticalness' is formed from the adjective 'aristocratical' plus the nominalizing suffix '-ness'; 'aristocratical' in turn derives from 'aristocrat', which comes ultimately from Greek 'aristokratēs', where 'aristos' meant 'best' and 'kratos' meant 'power' or 'rule'.

'aristocraticalness' developed by adding the English suffix '-ness' to the adjective (an older form 'aristocratical', related to 'aristocratic'); the root 'aristocrat' entered English via Old French/Latin adaptations of Greek 'aristokratia'/'aristokratēs'.

Originally the Greek root referred to 'rule of the best' (political rule); over time the root's sense shifted toward social class and manners, so the modern formation denotes qualities associated with aristocratic social status.