Euterpe (1775). Emmanuel Jakob Handmann (Swiss, 1718-1781). Oil on canvas. Jegenstorf Castle. In Greek mythology, Euterpe was one of the Muses, the daughters of Mnemosyne, fathered by Zeus. When later poets assigned roles to each of the Muses, she was the muse of music. In late Classical times she was named muse of lyric poetry and was depicted holding a flute.