I have been wondering about this for sometime now.
I often hear people say two-parter. Is it correct/formal?
I want to describe a documentary movies consisting of three parts. Three-parter movie? How about a trilogy?
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Definitely informal. More formal would be, "This is a three-part documentary," or "This week, we'll be airing a documentary, in three parts."
This follows general hyphenation rule #1, as shown at this website.
"My documentary is a three-parter" might be deemed acceptable as informal speech. ("Parter" is defined in a few dictionaries as "one who parts" - and it's even being flagged by my spell checker as I type this - so using it to describe a trilogy would be inappropriate, except in the case of informal slang).
Trilogy is defined as "a series of three dramatic or literary works." I suppose you could use it to describe a documentary, although the word usually connotes a fictional work, such as Lord of the Rings, at least in my mind.
If you often hear people say it, then it must be part of the language. If we can call a bus a double-decker, then there seems to be no reason why we can't call a film a two-parter. Most discussions of films are likely to be in an informal context anyway.
1) may denote something "having two parts"
2) may imply "a situation that is uncharacteristically complicated, that takes a long time or a large amount of effort to resolve" Urbandictionary.
In both case, usage is informal.