Formula and Function: A Critical Lens for Formula in Serial Works

It is often observed that works of an episodic nature tend to fall into predictable patterns over time. Plot structures, character personalities and so forth tend to develop comfortable, consistent shapes, often called “formulas”. Many works, of course, use formula and repetition to a specific end—e.g. in service of a specific thematic goal. Yuasa leverages formula in The Tatami Galaxy to viscerally drive home the work’s thesis; untold volumes have been filled dissecting its use in Revolutionary Girl Utena. But what I mean to discuss here is the function that repetition serves more generally as a narrative, not thematic, device—we arrive at formulas because if something worked once, it’s likely to work again. Repetition, used carefully, can enhance a work as much as effective photography or musical score.

Perhaps the most pervasive example of this in episodic mediums is the opening and ending title sequence. The title sequence is nigh-universal in film and animation, and tends to take a very particular form in animated television series. On a basic, functional level, an average competent opening sequence communicates the content and tone of a work (and the most basic, functional opening sequences do little else). But if information were the only intent, opening sequences wouldn’t need to be nearly so intricate; and, in fact, many excellent title sequences fail to meaningfully communicate much of the “content” of a work. This is because the key function of the title sequence is not to communicate information, but instinct.

As Jim Emerson puts it, “Any good movie teaches you how to watch it.” The serial work takes this a step further: rather than teaching the viewer, it trains them. This is ideal, given that serial works are (a.) generally shorter than films and so don’t have the time to instruct the viewer from scratch for each installment, and (b.) made up of many separate, similarly-shaped installments, so any critical tools the work presents once are quite likely to be employed again. Thus, repetition serves a Pavlovian function: the serial work encodes its key ideas into formulaic elements, and so trains the viewer to understand them, in a sort of emotional shorthand. The recurring title sequence often serves as a “lexicon”, re-indexing all of the key elements in the viewer’s mind. Many of these associations are personal or nostalgic, as explored in A&V’s earlier That Lingering Feeling series.

This is demonstrated excellently in the opening sequence to the animated series Gravity Falls. It contains purely functional elements such as introduction of the setting, characters and so forth, but Gravity Falls‘ opening sequence also primes the viewer’s expectations in remarkably subtle ways. It begins with three ominous establishing shots, with minimal musical accompaniment, before two more lighthearted shots which establish the characters and “main” setting. As it continues, the sequence progressively mixes humorous and ominous elements, setting the stage for the series’ precise blend of overt cartoon humor and quietly disconcerting horror. The opening is also riddled with occult and conspiracy theory imagery, contributing to an underlying, perhaps subliminal sense of alienation—a central recurring theme in the work proper.

Moreover, for serial animation in particular, the title sequence has become so fundamental that its formula can be observed not just at the level of a given work but of the medium as a whole. In the same way that a given title sequence trains its viewers to watch a particular show, title sequences in aggregate train us to experience entire cultural bodies of work in a specific way. Anime openings often reuse established clichés because, as clichés do, they make up the most primitive and fundamental media culture training the viewer has.

One can apply this same analytic principle to other common formulaic concepts; take, for example, the transformation sequence common to the magical girl genre. The transformation is often as semiotically-dense as a title sequence; its intricacy and length re-focus the viewer’s attention. This is vital given its location in the script, i.e. the division between girl and magical girl. It acts as a transition both textually in the logic of the work, and subtextually as a means of softening the effect of the quick change in tone. It also develops its own shorthand with the viewer, creating the same sort of Pavlovian response. This is why magical girl anime tend to shorten the transformation sequence in later episodes—the greater pomp and circumstance early on is needed in order to condition the viewer, but once that conditioning has taken hold it can be recalled with less effort.

To abstract a step further, many works are of course formulaic at the story level. Mystery and detective stories, for example, are often formulaic, and also provide a good example of the pragmatic efficiency of formula. The classic cartoon Scooby Doo, Where Are You? is well known for its very formulaic format—to the point of frequent parody.  But the series earned its status as a classic because of—not in spite of—its well-designed and extremely satisfying formula. Scooby Doo‘s obvious is its talent. Training the viewer to expect given story elements to work in predictable ways—settings, mysteries, villains—allows Hanna-Barbera to focus on executing those elements cleverly and enjoyably.

In fact, this correlation of formula and satisfaction is taken to its logical extreme in Knox’s Ten Commandments, as discussed here previously in relation to Hyouka. Golden-age detective fiction comprised an entire genre of literature explicitly defined by a rigid set of formulas. They are often framed as rules to a game, rather than formulas for writing. In golden age detective fiction, enjoyment is placed explicitly before originality as an artistic priority—and it achieves this through formula.

Formula is of course only a tool, and it can of course be used incorrectly. If a formulaic element fails to be sufficiently elegant or superliminally satisfying , it can distract the viewer from appreciating the formula’s deeper narrative functions. “Formula” in fiction is often maligned, but imprecisely so: the problem is not recurring elements per se—a location is a recurring element, a character is a recurring element—but careless or unengaging use thereof.


Filed under Editorials, Modern Visual Culture

35 responses to “Formula and Function: A Critical Lens for Formula in Serial Works

  1. Someguy

    I find one of the best examples of training the viewer through the use of clichés to be Madoka Magica. I won’t really say why because if someone hasn’t watched it I’d probably be spoiling the show for them, but it makes wonderful use of this.
    Great read, keep it up!

    • 8C


      Madoka does play with the audience’s existing training to some extent, but at the same time it also builds up its own non-ironic formulaic lexicon in lots of ways that are equally worthy of attention. It’s a bit more like a film, structurally speaking, in that the focus of the narrative is on the progress from beginning to end, and there isn’t really a meaningful weekly cycle. Well, other than the opening theme, which I would say is integral to tricking the viewer into continuing to read the show as a work in the magical girl genre proper, rather than a tragedy which makes use of the trappings of magical girls.

      That said, much like in a film there’s a great deal of semiotics packed into Madoka’s recurring imagery: flat medium shots and close-up shots of Kyuubey build up an emotional calculus as the show goes on, for example, and both Sayaka’s and Homura’s combat styles include visual homage to Mami’s at times. There are also at least two lesser cyclic formulas I can think of: the witch battles, and Homura’s time-travel subplot. The former, again, is modeled aesthetically after the parallel cliché in magical girl works, but is again more like a recurring motif and a chance to highlight the emotional state of the characters.

      The latter is a perfect example of non-ironic use of training for narrative efficiency: the account of the first timeline is the most detailed, and the level of detail falls quickly as the viewer comes to grasp the workings of the universally-recurring elements. In the later timelines, as little content as a shot repeated from earlier in the episode serves as a condensed shot of exposition. I think the obvious reading here is more thematic, since all of the episode’s cycles comprise one cohesive story: drawing attention to the similarity between the timelines reveals the futility of Homura’s struggle, and can maybe even be read as Gen summarizing the show’s existing arguments on fate and inevitability one last time before he turns them on their head in the finale.

  2. dm00

    Mushishi had an interesting twist on formula in the way it approached the end of each episode. The background music was unique to each episode (though the instrumentation was the same, and the differences were often subtle). Like the mushi, it would be there in the background. It would then swell to prominence as the credits rolled. I found the effect to be magical, like awakening from a dream.

    Another use of formula is to use a formula’s conventions to establish expectations, then surprise the viewer by deliberately violating the formula. If nothing else, it has the effect of getting the viewer’s attention. I’m chary of providing examples because I think most would count as spoilers.

    Then there’s the “meta-formula” of Chekhov’s pistol.

    • 8C

      I love musical formulas. They’re some of the most viscerally powerful, since there’s essentially no textual element to distract from the core impact. Aria was one of a handful I can think of that integrated its opening music for the same purpose. It’s such a perfect way to begin each episode. Maybe even necessary to have that transition into Aria’s emotional world-logic, since there are some significant differences from our own.

      • dm00

        A friend once observed that some shows have the end-theme music rise during the last part of the last scene in the show. Something about this increased his enjoyment of the show, but he was never sure why. I think part of it amounted to frustration: you’re immersed in the scene, and you want more, but the rising music is telling you that there won’t be any more for another week.

        • 8C

          That’s a good way to put it. I always have thought those scenes had a certain je ne sais quoi in the right kind of show. Maybe it also builds up a kind of parallel momentum – in at least AnoHana, that I can think of, there’s always some sort of emotional revelation or moment in those last few musical seconds. So when you hear that music again, it’s like a cue that something is about to go down. It puts you in “get ready for feelings” mode, so you’re fully prepared to savor them when the feelings hit.

          Another part of it, I figure, is just a formal appreciation of the clever editing it takes to do a satisfying cut to credits. Much less how much more complex it is to bleed from text to credits smoothly.

  3. Sticking with such a definitive formula is a dangerous line to walk for any director or writer. If they do use it, they can’t afford any mistakes, and they must also add their own subtle twist whether through the characters, setting or plot. It’s when everybody offers the same thing that they really have to shine to be noticed.

    • 8C

      Oh, of course. Formula is no substitute for good writing, I only mean to say it’s an integral part of good serial writing.

      I’m more interested in the small, unique formulas that develop inside specific works, it just seemed irresponsible not to connect that to the ways that formulas operate on a larger generic or meta-genre scale.

  4. Series of episodic nature, I like how you dive right into a specific archetype of anime to discuss the significance of the title sequences. If one instead looks at anime with an overarching and comprehensive plot, it would make more sense that the opening sequence, not the title sequence, should play a much more crucial role in gearing the audience for the series’ plot points and the mood of the upcoming episode because of the very information-centric nature of the series. Because of the cliche of the title sequence that permeates all of anime, more frequently, subtle changes (or complete changes) in the title sequence plot the progression of the series rather than opening sequences.

    Now, what I think you want to talk about are static title sequences over the course of a series, which as far as my anime database allows are mostly episodic in nature. Of course, if the anime is over 100 episodes long, like Bleach, Gintama and Naruto, then we can consider the title sequences of the particular arcs i.e. we can subdivide the big series into little ones. Here is where your analysis of the opening titles’ effect on audience shines. Because one need not follow complex plot threads, one relies on ‘instinct’ to introduce the audience back into the mix. I will not repeat your post any further, but your focus on episodic series captures an excellent contrast that many of us miss because of our assumptions that all title sequences only convey information to the audience.

    • 8C

      Thanks for the comment!

      I’m not quite sure how you’re clarifying “opening sequence” from “title sequence”. Is this in the sense of “cold open” versus “theme song animation”?

      And yes, I would argue that formula is still very vital to “linear” series, even if it is less apparent. That was my intent in pointing to recurring musical numbers, since they’re universal to the entire episodic medium, not just the episodic narrative style.

      • I’ll be sure to use the precise vocabulary. In certain plot heavy series, like Eureka Seven Ao, I often find myself lost even after the theme song animation. Because of the complex plot threads, a cold open might actually do better justice. This is especially apparent in American TV shows, which tend to start off with dumping the audience right into the plot, and only later, do they have a short theme song sequence.

        I agree with the Jim Emerson’s quote, which claims that the opening of movie or a show teaches the audience how to watch it. The singular formulaic theme song animation does not do justice for all anime, especially for linear series. I don’t claim that the theme song animation is wrong, but that it is usually misplaced. A great example of strategic placement of theme song animation is in Magica Madoka, which orients the audience in many subtle ways before airing the theme song animation.

  5. Tzu

    In regards to the openings and endings in anime series, I have a somewhat poetic point of view that I think really matches what you were saying here. We live in our world, and series are set in their own worlds. The opening is that special part of the series with the job to take us from our world to the world in the series. The ending is what gently takes us back to our own. This is most notable when you watch an episode of an anime followed by an episode of a different one. Because of this I don’t think the opening needs to be informative of show characters or anything, as long as it “gets you in the mood” then it’s fine.

    Now in regards to a formula, have you heard of the hero with a 1000 faces? It is a book that states that any story, of any medium (episodic or not) follows the same formula (the hero’s path). Since the book shows this formula, there are some authors who explicitly follow it in their stories, while there are many others who reach the same formula by experience. It’s worth checking it out.

    • 8C

      I agree: the subconscious reinforcement of tone is the more important part, the introduction of setting and characters is secondary except where it helps to establish tone. What’s maybe interesting about this is what it says about cold opens—it doesn’t seem too unlikely that they’re often designed to take advantage of the viewer’s disorientation, taking place in the story’s universe before the viewer has readjusted to it.

      I have heard of the monomyth, yes. It’s a fascinating idea, though a bit fanciful. It’s easy to demonstrate that there are a lot of stories that follow Campbell’s monomyth; it’s an altogether different task to demonstrate that the monomyth accounts for all narratives, much less even most—does Lucky Star conform to the hero’s journey? Campbell certainly outlines a very common (in European-derived writing cultures) and very well-designed formula, but it remains only one among many.

  6. I’ve always held that plot originality is not what makes a brilliant literature/show/art, but had a hard time theorizing it, so thanks! But still, a formula doesn’t work on all genres. For detective fiction, yes, but not slice-of-life and romance, since they touch on more than plot-driven elements. And usually it’s the Midas’ touch on conventions that make us love them.

    • 8C

      Thanks for the comment! My hope with this post was to help articulate a new way of looking at things, so I’m glad if it helped you.

      I can’t say I agree on slice-of-life works, though—the genre is rife with interesting formulas. Consider how many of them have main casts of four characters with oddly-similar personalities (e.g. lines 1-3 here), or were originally written in the yonkoma format—in itself a formula with a long and storied history. Just like the conventions of golden age detective fiction, these elements have been arrived at through trial and error as nicely-balanced and effective baselines from which to begin developing a given work or premise or scene.

      Though it does of course, in the end, fall to strong writing and clever use of formula in any genre.

  7. I remember growing up and watching Sailor Moon and Ronin Warriors. In my mind, if you didn’t have an extended transformation sequence, you just weren’t a good superhero anime. Speaking of transformation sequences, what do you think of some of the new magical girl animes and the like? My-Hime and My-Otome; Pretty Sammy; Puella Magi Madoka Magica (which I still have to see). They’ve all become much darker in tone. Think it’s an effort to make magical girl appeal to a more mature audience?

    • 8C

      Thanks for stopping by!

      What’s interesting about the shows you bring up is that there is, in fact, a very concrete answer to your question: yes, those shows are an effort to cater to a more mature audience. Literally, the demographics for My-HIME and Madoka are adult men, and they tend to air in the middle of the night so kids don’t see them.

      To back up, briefly, this isn’t anime creators trying to catch new eyes; it’s them reacting to long-effective trends of adult fans enjoying magical girl cartoons. This goes back almost as far as “magical girl” as a genre: very shortly after the magical girl archetype became popular, adult fans were latching on to the shows as well. The studios have long been aware of this secondary audience, and will occasionally tacitly acknowledge them with more mature storylines, in-jokes, costly merchandise and the like.

      More recently, shows like Madoka (and before it, by the same director, Nanoha in 2004) have abandoned the younger audience altogether and focus solely on the adult audience. They do tend to have darker storylines, and often appeal to their adult fanbase in… more unsavory ways.

      The “maturity” isn’t an industry-wide trend, though: the markets for “adult” magical girl anime and “children’s” magical girl anime are very segregated, and the latter is still very much more popular. For example, the hot new franchise in Japan right now, Pretty Cure, is very much in the “less mature” style (though, I’m sure you remember from Sailor Moon, immature kids’ cartoons have their dark moments as well). It airs in the morning, and makes billions a year for Bandai—far more than late-night anime, which tend to run extremely low margins and cater to a small and self-contained demographic of passionate and affluent fans. Even then, though, Precure’s stated demographics include both young girls and adult men.

      Yeah, it’s a strange industry sometimes.

  8. I love well-done opening and closing sequences, whether they’re in films or series. I haven’t seen too many anime series, but the ones I have seen that I really enjoyed like Akagi, Kaiji, SZS, Mushishi and Cowboy Bebop have fantastic openings and closings with great themes. They really get you excited for what’s coming up next.

    Right now I’m in the middle of watching the giant, 110-episode Legend of the Galactic Heroes. I like how it sometimes cuts out the opening or closing animation and runs an extra story scene while playing an instrumental version of the theme. Something about it just works.

    • 8C

      Ahh, those all have really excellent theme music! Akagi especially, that was one of the first series where I really noticed the role the music played in setting the tone. It has a very unique score in addition to its opening song, so I got very attuned to each piece and the way it shaped the emotions of the show.

      I haven’t seen Legend of the Galactic Heroes, but that sounds like an interesting effect. I wonder if that flexibility happens more often in long-running direct-to-video series.

      Anyway, thanks for stopping by!

  9. chunter

    Be careful, if you read too much into this stuff it will all get old quick.

    The formula for pre-school and young school-age television of any kind is to show a child that day-to-day life can be interesting, because despite all the repeating there are occasional surprises, and those surprises are why you watch. This carries into slice-of-life as well as situational comedy.

    Joseph Campbell over-generalized his super-myth for the sake of making his point, but his theory only works with heroic, epic stories and myths. You correctly observe that slice-of-life does not have that intention, neither does romance. Most of his modern comparisons are to Star Wars, which itself ripped off all kinds of older hero stories in obvious and not-so-obvious ways.

    There is such an onslaught of material in Japan that it’s no surprise that they have to meld age groups and demographics in strange ways to get things to come out, and when an idea works well it is ripped off often, and perhaps to a fault. Familiar quick-change sequences excite the audience for an oncoming conflict and take up space that doesn’t need to be filled with storytelling. If you get used to it, you can find the exact spot to shuttle forward past the fight and into the denouement dialogue, which might have three meaningful statements to set up the next episode and then end with a joke.

    It isn’t wrong to be pleased by this sort of thing, but once you recognize it, it becomes difficult to un-see.

    Also, this classic

    Congrats on FP

  10. Thanks. This was interesting and I enjoyed reading it. Two only at best somewhat related thoughts. Opening sequences of serials often provide “previously on” information so that brand-new viewers aren’t so confused they leave. This info is particularly important if a tv shows goes into syndication, where viewers aren’t waiting for each new episode in sequence. All this comes down to money, the more viewers the better. Openings also have a ritual function. My kids can recite the opening narration of “Last Airbender” the way I can recite the Lord’s Prayer. Whether that is progress or not is another question.

    • 8C

      Thanks for stopping by!

      One certainly could recast my points into a consideration of capitalism: what I’ve demonstrated is only that formula is satisfying, and modern capitalism has a storied history of leveraging things which are satisfying in order to profit. I also wonder, now you mention it, how much meta-textual content there is in those “previously on” segments themselves. They aren’t arranged completely at random, and they tend to look the same from show to show. How much have we needed to be trained to be able to process such densely-packed units of information on the fly?

  11. Pingback: 12 Days of Smile PreCure #2: Rainbow Burst | Cure Blogger

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