The quality or state of being contemporaneous; simultaneity or the fact of existing at the same time.
From 'contemporaneous' plus '-ness,' a productive suffix for creating abstract nouns from adjectives. This is essentially a synonym for 'contemporaneity,' showing how English often has multiple ways to form the same concept.
English speakers have created at least three different nouns for this same idea—'contemporaneity,' 'contemporaneousness,' and even older 'contemporariness'—which shows how languages love to have redundant options!
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