Barker (26), Dunn (100) and Terry (286) opine that this is merely made-up Greek. Halton (147) calls it a doleful song. Cameron (66), on the other hand, says that the word is consistently misspelled in every known version of the libretto. Gilbert probably intended to say “diegerticon,” which “means a rousing song or anything stimulating or exciting. In some Greek writers it means aphrodisiac. Surely not in Gilbert.” I endorse Cameron.
Sing a Diergeticon