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It is not necessary to run different character arcs chronologically synchronized. However, it is important not to create a false impression that these arcs are synchronized. For example in "A Song...
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Source: https://writers.stackexchange.com/a/46435 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
It is not necessary to run different character arcs chronologically synchronized. However, it is important not to create a false impression that these arcs are synchronized. For example in "A Song of Ice and Fire" (which I refer to quite often) first 3 books George Martin tried to run all chapters chronologically. Next book was split into two ("A Feast for Crows" and "A Dance with Dragons") which runs concurrently (but chronologically within individual books). For every character arc, you either make it clear from the very beginning that they do not run at the same time, or at some point, the readers should discover it to their surprise. If you choose the latter, treat this discovery it as a plot twist. Maybe a small one, but it should be pleasant ("Aha, I know what's coming next!") rather than unpleasant ("What?! When this all happened? I'm confused.").