I’m not talking about tragedy vs comedy (answer: two, obv) here, or even genres like sci-fi vs crime vs romance, etc (answer: maybe half-a-dozen, everything else being the non-genre genre called “mainstream”). No, I really mean how many species of stories are there? – not particular instances of stories, but stories in their abstract essence. Arcs, patterns, templates, stamps, classes, moulds, whatever – dammit, how many?
There is, in fact, a thriving subschool of literary criticism that is obsessed with this platonic question, and the answers it gives varies from one to infinity. For example, Joseph Campbell says there is fundamentally only one story – but with infinite variations! (It’s a good answer, and it’s a real pity that that one story is Star Wars.)
One, said also Robert Graves:
There is one story and one story only
That will prove worth your telling,
Whether as learned bard or gifted child;
To it all lines or lesser gauds belong
That startle with their shining
Such common stories as they stray into.
Water to water, ark again to ark,
From woman back to woman:
So each new victim treads unfalteringly
The never altered circuit of his fate,
Bringing twelve peers as witness
Both to his starry rise and starry fall.
(Not Graves’s best, in my opinion, although he liked it and that should be good enough for anyone.)
Now, the trouble with just having “fundamentally one story” is that your pattern has to be so unifying, so vague, that just about the only template that applies to all stories would be “something happens” – and even that misses much of Beckett. So “one” is out.
Another popular solution is “seven”. In Christopher Booker’s magisterial (yet jejune) the Seven Basic Plots, we read:
However many characters may appear in a story, its real concern is with just one: its hero or heroine. It is he with whose fate we identify, as we see him gradually developing towards that state of self-realization which marks the end of the story. Ultimately it is in relation to this central figure that all other characters in a story take on their significance. What each of the other characters represents is really only some aspect of the inner state of the hero or heroine themselves.
Having more rather than fewer basic types of story arc reduces the risk of tenuous shoehorning, but on the other hand you don’t want to have too many either. At the extreme, if there were “infinity” types, each one would be so specific it would only include each individual retelling, and there isn’t much point in asking the question.
There are many other systems, but it is noticeable that the answer always ends up vaguely kabbalistic, numbers like 3 or 7 or 36 (no one has ever written a book called “the 29 fundamental types of story”). I think there must be something in the psychology of enumerators that makes them number-mystics as well. Since it’s always possible that some hyper-original writer will invent an (n+1)th story type within a “n types of story” model, any scheme based on such magical numbers is doomed. By comparison, it used to be thought there were only four types of taste, and people would draw them in a square of opposites; until monosodium glutamate was discovered.
Be all this as it may, computer scientists at the university of Vermont have recently settled the matter once and for all: there are exactly six story arcs. The preprint at https://arxiv.org/pdf/1606.07772v2.pdf lists them all, and shame on you if you find yourself thinking that their six are simply all the permutations of alternating rises and falls, as given on page 6:
“Rags to riches” (rise).
“Tragedy”, or “Riches to rags” (fall).
“Man in a hole” (fall–rise).
“Icarus” (rise–fall).
“Cinderella” (rise–fall–rise).
“Oedipus” (fall–rise–fall).
Yes, it’s all bunk, all of it. At least the Booker, Campbell and Graves has the advantage of being well-written and interesting bunk, but it is still bunk.