The quality or state of being frowsy; mustiness, stuffiness, or slovenliness in appearance or condition.
From 'frowsy' (or 'frowzy') plus the abstract noun suffix '-ness' (from Old English), which turns adjectives into nouns describing the quality or state they represent.
The suffix '-ness' is the most productive way in English to turn any adjective into an abstract noun—'frowsiness' captures a whole atmosphere of mustiness and neglect, the feeling of a room that hasn't been aired out in weeks.
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