Music that consists of a single melody without accompaniment is called?

Monophony. Monophony is the simplest of musical textures, and is one of the earliest historical musical forms. Plainchant, or Gregorian chant, is a commonly cited example of monophony, and was popular in Italy, Ireland, Spain and France. While 9th century plainchant incorporated extra voices in parallel fifths, Byzantine chant, Armenian chant, and Mozarabic chant are all strictly monophonic.