It's just a name: it used to be based on four bars, which probably would comprise one set of chord changes (eg doowop, I vi IV V), but could just as easily be two or eight bars.
It's like calling a song's bridge a 'middle eight', even though the number of bars may be different.
The Beatles always called their bridges 'middle eights'.
music.stackexchange.com/users/8587/No'am Newman
In swing setups such (e.g. tenor sax battles), it is not uncommon so see "trades" of varying (typically decreasing)
length : trade 16, then trade 8, trade 4 and sometimes even trade 2 then
trade 1, each time building up the tension.
Things could also end in both musicians improvising simultaneously.
Nice example from Robert Altman's Kansas City: As for the reason behind 4 bars, I think it comes from the structure of the typical 32 bar form AABA, in which the 8 bars of A are often divided in 4 bars (tension / question) often ending in half cadence (V7) + four bars (relief / answer) ending in IMaj7.
This means having 4 bar solo by one musician followed by for bars by another is quite natural.
music.stackexchange.com/users/1079/gurney alex
"Trading twos" is definitely a phrase people use. "Trading eights" might be.
More generally, you can call it "trading licks".
8 bars is long enough to be thought of as a whole solo.
Get any longer than this and you're not really "trading" any more; you're just taking it in turns to solo.
When I say "trading", I mean that you base your lick on whatever the player before you played.
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Generally it'll be even numbers, 2, 4 , 8 as a 'line' of a song tends to be that long, so phrasing sounds more balanced.
It follows from songs usually being 8, 12, 16 or occasionally 24 bars long.
Never heard in a band "Let's trade 7s."
Although that could be interesting.
Both to play and listen to...
music.stackexchange.com/users/2808/Tim
There are great answers already here, but perhaps the most important consideration is making sure no one gets cut short when the trading is over.
Consider a 12-bar blues.
It wouldn't really work for the soloists to trade off every 8 bars, because whoever goes second in soloing would only be halfway through his/her turn when the 12-bar form ended.
(In particular, the first soloist would take bars 1-8, and the second soloist would take bars 9-12 followed by bars 1-4.)
Spilling over like
that can undermine the listener's sense of the form itself.
Our ears generally expect to hear the soloist change at the very top/beginning of the form.
If that doesn't happen, it feels uneasy, and we might get the feeling that we don't actually know where the top of the form is.
Jazz songs very frequently use 12-bar forms, 16-bar forms, or 32-bar forms.
Letting the soloists trade off every 4 bars is great because all of those forms are evenly divisible by 4.
Thus no soloist's turn will be interrupted by the end of the form.
Trading 2 bars at a time is also common, and this frequently comes near the end of the trading, after having spent some time trading 4 bars.
Trading 8 bars is also pretty common, although only if the entire song has an integer multiple of 8 bars.
music.stackexchange.com/users/40842/jdjazz
In most tunes, four bars is the smallest unit you will find a complete phrase, musical idea, or melody.
Although you will often see a complete chorus or bridge or A section of the tune in eight as well, but youll never see it in two because two bars is too short to express a complete musical idea.
music.stackexchange.com/users/5919/Michael Martinez
I've run across the idea of "trading fours" when playing in (and listening to) jazz groups; i.e. where two or more musicians take it in turns to play four bar licks or solos. I understand that it can encourage creative interaction between musicians.  However, I was wondering why it seems to be specifically  four  bars? Would trading twos or eights (for example) be less effective?
Why do jamming musicians "trade fours" (rather than any other number)?
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<jazz><improvisation><band><jamming>
music.stackexchange.com/questions/14208
music.stackexchange.com/users/7328/Peter Bloomfield
Trading Fours is just a name: it used to be based on four bars, which probably would comprise one set of chord changes (eg doowop, I vi IV V), but could just as easily be two or eight bars. It follows from songs usually being 8, 12, 16 or occasionally 24  bars long. Trading 2 bars at a time is also common, and this frequently comes near the end of the trading, after having spent some time trading 4 bars. Trading 8 bars is also pretty common, although only if the entire song has an integer multiple of 8 bars. In reality, this could be just a musical term and the actual trade may not be strictly four bars. However, the term "trading fours" originates from the fact that four bars or a multple of four is normally the length of a complete phrase or melody. "Trading eights or "trading twos" is certainly possible, but "trading twos" is less likely since it's quite a short length of time to express a complete musical idea.
It might be that this is just a term, but the reality is that there is no need for the trade to literally be four bars. This relates to songs usually being 8, 12, 16 or 24 bars long. In most tunes, four bars is the shortest section that contains a complete phrase or melody. Trading 2s or trading 8s can indeed happen. Trading 2s might be less common because it is too short ot express a complete musical idea.