Nothing to do with the attics of houses -- "Attic salt" is a term for a type of wit, "peculiar to the {ancient} Athenians," in Webster 1913's words under "attic." The phrase comes from "Attica," the region of Greece which contains the city of Athens, and the idea that humor adds to a conversation as salt does to food; both Greek and Latin used "salt" as an expression for "wit," and the Athenians were renowned for elegant thoughts expressed skillfully. Webster 1913 says Attic salt is "poignant, delicate" and A.Word.A.Day calls it "refined," but the definition used by the Attic Salt Theatre Company of New Jersey also notes that it should be "Particularly acute, graceful, biting" and adds that the satirical comedies of Aristophanes are considered samples of this particular type of wit.

Attic Salt is also the name of a theatre company in New Jersey as mentioned above, a greeting card company in Kansas, a now-defunct band from San Francisco, and several blogs and newspaper/magazine columns.

Sources:
http://wordsmith.org/awad/archives/0602
http://www.atticsalt.org/name.htm
http://www.bootlegbooks.com/Reference/PhraseAndFable/data/73.html
Googling to see who's used the name.

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