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evenness has 1 distinct synonym spread across 1 of its 3 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is unevenness.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the parity of even numbers (divisible by two)
a quality of uniformity and lack of variation
the quality of being balanced
Synonyms, antonyms and the broader and narrower relations for evenness come from Princeton University’s WordNet. Full sources and licences.