Jazz is a conversation, and a friendly debate is a perfectly viable way to communicate; here it is Joshua Redman and James Carter backed by a big-band arrangement of Monk’s “Straight No Chaser” in a great display of the quaint old custom known as “Trading Fours”.
The rules are simple: folk-song structures tend to have phrasings given in groups of four bars of four beats, so the soloists take turns, most often at a break-neck rate, each taking what the other has put forth, and taking it up a notch. It’s a time-honoured mainstay of the jazz culture, maybe not so noticable in the harmolodic free-er jazz styles (tho still appears now and then) and often used in performances for the finale showpiece. The practice probably has its roots in early jam-session playing in the New Orleans bands or maybe before. The earliest I can dimly recall are in Louis Armstrong days, probably because the music was far more arranged for King Oliver’s day; trading fours was honed to a fine art by Bird and Diz, and while it started to fade with the Miles Davis Quintet’s ensemble-improv style and on through the Free Jazz bands, it still lives on strong in the Sun Ra Arkestra shows where it can sometimes be staged like a kaiju battle!
There’s been cross-overs too, with bluegrass bands trading fours and I suppose the custom also persists into the modern day rap poets trading fours in rhyme or in beat-control switching back and forth between DJs.