Medora is a town in Carr Township, Jackson County, Indiana, United States. The population was 693 at the 2010 census. Medora was laid out in 1853 by West Lee Wright in the southeast corner of a square mile of land which he owned. Wright named the town Medora for the musical notes & dubbed it "The Town of Harmony", though it is commonly mi…Medora is a town in Carr Township, Jackson County, Indiana, United States. The population was 693 at the 2010 census. Medora was laid out in 1853 by West Lee Wright in the southeast corner of a square mile of land which he owned. Wright named the town Medora for the musical notes & dubbed it "The Town of Harmony", though it is commonly mispronounced in the most unharmonious way today. It consisted of 10 blocks and 209 lots.