Polyphony in Jazz largely originates from the improvisational nature of Jazz. A good example of polyphony in Jazz is the New Orleans style Jazz. New Orleans Jazz is known for its polyphonic texture of many different melodies being played together by different instruments in a Jazz band. 

A New Orleans Jazz musician said, "We didn't know what a sheet of music was. Just six or seven pieces, half a dozen men pounding it out all together, each in his own way and yet somehow fitting in all right with the others." (Kamien, Music An Appreciation)

This is a fitting description of New Orleans Jazz. 

New Orleans Jazz was played by a small group of performers. For example, King Oliver's Jazz Band had seven performers. Out of the performers, the "front - line players", which were the trumpet, trombone and clarinet players, all improvised melodies at once. This created the polyphonic texture that New Orleans Jazz is famous for. The trumpet was considered the leader, playing the main melody. The clarinet would usually play a faster melody against the trumpets melody. The trombone would play a simpler melody against the other two. The front - line instruments are supported by a background of percussion and chords played a drummer and pianist usually.

New Orleans Jazz pieces were sometimes based on popular songs like "When the Saints Go Marching In".

Click Here to listen to Louie Armstrong's "When the Saints Go Marching In"

In this recording, we can here the main theme being played by the trumpet. Also, the trumpet improvises variations of the theme. We can also here the clarinet playing a faster melody on top of the clarinet, and the trombone's simpler line.