Max M. answered 06/27/19
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I'm afraid the answer doesn't have much to do with story structure or other artistic considerations. Though if you read this all the way through, there is a very interesting story-based point to consider.
For the most part, as long as theater has been a business--which is to say, any time later than Ancient Greece--pretty much every aspect, including act breaks, has been driven by economic considerations and fashion. Shakespeare wrote 5-act plays because 5-act plays were in fashion then. There are a lot of likely reasons why: About half his audience was standing, so they were probably getting restless. I've been a groundling at the Globe in London a number of times, and while it's fun, standing for a full hour or more when they do the plays with only one break gets a little tough. Multiple act breaks are also a nice opportunity for the theater to sell more refreshments. Plus, since the plays were performed by set companies, the actors could use the breaks to change costumes.
By the time 3-act plays came into fashion, around the 20th century, the theater-going experience had changed a lot. Mostly they were indoors, they turned the lights off, so the audience's attention was occupied fully by the stage, so it was easier to stay focused for longer. Plus, act breaks take longer when you have to lower a curtain, turn the lights on, have everyone get up, go to the restroom, buy a drink, drink it, and then sit back down. Trying to do that four times in an evening would take forever. It's not that the plays got simpler, and certainly not shorter. Tennessee Williams's and Lillian Hellman's 3-act plays, for instance, are comparably long and complex to Shakespeare's and Middleton's. The shift to 2-act plays, around the late 1960s / 1970s is similarly fashion- and economics-driven. Neil Simon's 2-act plays, like Lost in Yonkers, are not significantly shorter or less complex than his 3-act plays like Barefoot in the Park or The Odd Couple.
All that said, yes, the different structures do demand that playwrights pace the action differently, build tension and relieve it at different rates. Neil Simon wrote that he thought of 3-act plays like a pyramid (I'm paraphrasing here): the play starts at point A at the bottom in act one, then builds to a crisis at the top in act two, then lands at a resolution on the other side in act three. (The great American musical-theater director George Abbott was even more succinct: "Act one--get your hero up a tree; act two--throw rocks at him; act three--get him down.")
But here's the thing--that basic pyramid structure applies to 5- and 2-act plays too. It even applies to 1-act plays. And writers and teachers still talk about 5-act structure regardless of how many intermissions they actually take. Different writers and teachers use different vocabularies, but you'll find that they're mostly some version of this:
Act One: Introduction of the play's "problem" and the hero / heroes who are going to try to solve it
Act Two: The problem gets more complicated
Act Three: A major turning point (some call this the climax, others call it the crisis) in which the world changes forever (Shakespeare often kills pivotal characters right in the middle of act three--Caesar, Polonius, Mercutio, Banquo...)
Act Four: The forces gather for the definitive confrontation
Act Five: The problem is resolved once and for all, and a new order is established (in Shakespeare's tragedies, the hero usually dies, usually not alone; in comedies, there's a wedding, usually more than one).
If you try to map that onto 3-act plays, you'll find it still works pretty well. Not to paint with an overly-broad brush, but I think most put one intermission after the complications and the other after the turning point. So there might be some marginal differences in how the stories play out, but nothing you could really point to as definitive.
But here's the really interesting point I promised you at the beginning. There's one number we haven't mentioned yet, and it becomes a big deal in what we now call the dawn of modern drama. Guys like Chekhov, Strindberg, Ibsen, and sometimes Shaw started writing plays in FOUR acts, basically straight-up omitting act five, the part where everything is supposed to be definitively resolved and a new order established. THAT, I think you can argue, marked a big difference in the kinds of stories being told, and it has nothing to do with refreshment sales.
I hope this helped--hit me up to talk more about this or other theater / Shakespeare questions. I promise to (try to) keep it briefer!