In the earliest days of jazz, a musical texture emerged that utilized the creative prowess of jazz pioneers to improvise an arrangement of a song. This texture is known as collective improvisation. In this musical setting, the three wind instruments, Cornet (or trumpet), Clarinet, and Trombone improvise their parts together to create an improvised arrangement with nothing written down for the players to read. 
In this texture, there are roles that the horn players fulfill. The cornetist interprets the melody. The clarinetist improvises a melodic counterpoint to the melody utilizing the harmony of the composition. Finally, the trombonist improvises their part based on the roots of the harmony, or if there is a bass player, the lower structures of the harmony. Together, these elements fuse to create a rich full musical texture. The greatest performers in this tradition know how to create their part and leave space for the other musicians so that the texture does not become too crowded or cacophonic.
Here is a short video that explains the essence of collective improvisation. It features a friend of mine who has made his life performing this style of music, Jon Erik Kellso on cornet. When we were in college together in Detroit Michigan, Jon worked so much performing Trad Jazz that we nicknamed him “Johnny Gig.”
Please enjoy!