The term you are looking for would be polyphony, or more correctly contrapuntal. This basically means there is more than one melody being played at a time. This is different from just hearing a melody accompanied by chord figures.
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At the related link below is an example of a modern fugue written by Nick Vasallo, a 21st century composer. It is also a tribute to J.S. Bach, the master of fugue.
The Fugue
progression
The cast of Katong Fugue - 2007 includes: Luke Kwek as Son Swee Lin Neo as Mother
The texture most common to fugues is polyphony or counterpoint.A polyphonic or contrapuntal (same thing) means there are two or more melodies of the same importance being played at the same time.Contrapuntal isn't the same as a polyphonic texture.Contrapuntal texture describes the melody moving in an opposite direction:File:ContraryMotion.png