Conquering death with song, the mythological Orpheus has been an inspiration to composers beyond number. This fall, London’s purveyor of opera in the vernacular offers a quartet of distinctive treatments: Gluck’s stately Orpheus and Euridice, laden with court dances (October 1 to November 9); Offenbach’s saucy romp Orpheus in the Underworld, which explodes into a can-can (October 5 to November 8); Harrison Birtwistle’s modernist Mask of Orpheus, hieratic and austere (October 18 to November 13); and Philip Glass’s Orphée, after Jean Cocteau’s film (November 15 to 29). The productions are all new. —M.G.