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One of various musical textures, heterophony is a kind of complex monophony - there is only one melody, but multiple voices each of which play the melody differently, either in a different rhythm or tempo, with different embellishments and figures, or idiomatically different. The term was invented to differentiate between European polyphonic music of separate melodies; however, it can also be seen as a type of polyphony. The term, heterophony, was coined by Plato and is used in many areas of the world.
An example of heterophony is the Gaelic band: The Chieftans' tune: The Wind That Shakes The Barley. Each instrument plays the same melody, but embellishes it slightly with grace notes, vibrato, etc. See Texture (music)