'nonperiodicity' originates from Modern English, formed by prefixing the negative prefix 'non-' to 'periodicity'; 'non-' (from Old English/Latin 'non' meaning 'not') negates 'periodicity', which ultimately traces to Greek 'periodos' where the root meant 'a going around'.

'periodos' (Greek) gave rise to Latin/Medieval Latin forms such as 'periodicus'/'periodicitas', which entered Middle English as 'periodicity'; in Modern English the noun 'periodicity' existed and the productive prefix 'non-' was attached to produce 'nonperiodicity'.

Originally the root 'periodos' meant 'a going around' (i.e., a cycle or circuit); over time the sense shifted to 'recurrence at regular intervals' and 'nonperiodicity' came to mean the absence of such regular recurrence.