The quality or state of being aberrant; deviation from what is normal, expected, or proper.
From 'aberrant' + '-ance' (a state or quality suffix). 'Aberrant' itself comes from Latin 'aberrans,' the present participle of 'aberrare.' This noun form became standard in English by the 18th century.
The noun 'aberrance' is less common than 'aberration,' which shows how language favors certain related forms—English speakers prefer the slightly shorter word for the same concept, naturally selecting the path of least resistance.
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