The quality or state of being discordant, disagreeing, or out of harmony.
From discordant plus the -ness suffix, which converts adjectives into abstract nouns representing the quality or state they describe. This follows standard English word-building patterns.
Adding -ness to adjectives is how English creates the abstract idea of a quality—it's like how we turn 'happy' into 'happiness' to talk about the feeling itself rather than just one happy moment.
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