"Sequel" (from Latin "sequela") originally seems to have meant "what happens next"; later it took on the additional meaning of "a story whose events take place later in the same imagined history as a certain other story" — usually with reference to novels, but also short stories, epic poems, and films. In recent years, as far as I can tell, the latter sense of the word has come into almost exclusive use — I don't recall seeing "sequel" used in the more general sense of "events that take place after previously mentioned events" very often in recent texts.
Someone (I don't know who; will update this page later if I find out) later coined the word "prequel" to describe "a story written or published after a certain other story, but whose events take place earlier in the same imagined history". Wikipedia dates the term to the early 1970s, and credits the Star Wars prequel trilogy with popularizing the term since 1999. The Online Etymology dictionary dates it to 1973, but does not give a citation from that year (or any other). Since "prequel" has come into widespread use, it appears to me that "sequel" has taken on the more restricted sense of "a story written or published after a certain other story, and whose events take place later in the same imaginative history".
As "-quel" was extracted by back-formation from "sequel" to signify "a story having some specified chronological relationship to another", why not use other prefixes with it if it seems convenient to do so?
I've seen "interquel" mentioned in a number of places in doing a Google search on "prequel". Wikipedia defines "interquel" as a story taking place between two previously published ones. Jeffrey Henning has a different definition of "interquel," basically the same as my coinage "paraquel" (see below). It appears to me that the sense cited at Wikipedia is more common, though any use of the word is pretty rare (and maybe restricted to computer games; I could not find any instance of its being used for novels or film).
"midquel" is occasionally used in the same sense I've used "inquel", and "threequel" is sometimes used (mostly in the movie industry, it seems) to refer to the third story in a trilogy.
A reader who preferred not to be named suggests "nuncquel" as an alternate coinage for the sense of "paraquel", particularly a retelling of the same events from a different character's point of view. It's not bad, though I prefer to stick to Latin or Greek roots which have become moderately productive English prefixes, by analogy with "pre-", rather than words which haven't really been naturalized in English as much like "nunc" ("now").
Peter Coogan asked what would be the term for the original story after one or more sequels, prequels, etc. have appeared; he suggested "oriquel", from "original"/originem, or possibly a bare "quel". I thought about it and suggested several alternatives, including "urquel" and "protoquel." He made a persuasive case for "oriquel," and though I like the euphony of it and am partly persuaded by his semantic argument, I feel like "protoquel" would require less explanation for the average educated reader -- you might be able to drop it into a text and have readers figure out its meaning from its roots and context without needing a digression to explain it, whereas "ori-" doesn't really have an established track record as a productive prefix.
The Iliad was followed by a sequel, the Odyssey, to which Virgil wrote a paraquel, the Aeneid.
C.S. Lewis's The Lion, the Witch and the Wardrobe was followed by four sequels beginning with Prince Caspian, but also an inquel (The Horse and His Boy) and a prequel (The Magician's Nephew).
If relationships are transitive, then The Lion, the Witch and the Wardrobe is also a "circumquel" of The Horse and His Boy. But I'm not sure that fits the usage pattern, because one would not describe either as a sequel to The Magician's Nephew (which was written, or at least published, later than either).
In the course of searching for usage examples of "prequel", I found a couple of pages where The Hobbit was referred to as a prequel to The Lord of the Rings, which suggests that the word may be gradually taking on a broader meaning (a story taking place earlier than some specified other story, without reference to relative composition or publication dates). Or it may be a couple of ignorant people misusing a word with well-established meaning — depending on whether you take a prescriptivist or descriptivist view. But a prescriptivist is maybe liable to frown on any use of a neologism like "prequel". It's also common (and makes more sense) to refer to The Silmarillion as a prequel to The Lord of the Rings, because it was published many years later. But it's well known that Tolkien began work on what became the Silmarillion during World War I, long before The Hobbit or The Lord of the Rings; then left off work on it for some years while writing The Lord of the Rings, and resumed it after finishing that epic. So maybe it could be described as a circumquel, in a different sense than that I proposed in the list above.
Steven Brust has been writing his Vlad Taltos series out of internal chronological order, with the initial Jhereg being followed by several prequels as well as sequels, and at least one of those prequels being followed by a circumquel: Dragon takes place partly before and partly after Yendi. (Like Jo Walton, I would recommend reading the series in order of original publication, at least the first time you read them; and I would strongly recommend reading them, period.
Another reader helpfully wrote in with a large number of examples from the Ender's Game series, but I prefer not to go into detail about them for reasons. Those familiar with the series will quickly see which ones are prequels, paraquels, etc.
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Last revised September 2023.