The quality or state of having mixed emotions—both happiness and sadness at the same time, like graduating and leaving friends behind.
From 'bittersweet' (something that's both pleasant and painful) plus the suffix '-ness,' which turns adjectives into abstract nouns describing their quality.
Bittersweetness is actually how humans experience most major life transitions—graduation, moving, first loves, retirement—and artists have been obsessed with capturing this feeling because it feels more real than pure happiness or sadness alone.
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