The oft-discussed repetition in Utena (inb4 “it saves money”) is, I think, related to the revolutionary business:
They have wandered around in circles, confined to the narrow room in which they’ve been given a deadly brainwashing.
Hélène Cixous, “The Laugh of the Medusa”
Cixous was talking about women, and certainly that would apply to Utena Tenjou herself, but you could describe any viewer of Utena that way. Which might just be the point.
If you want a good explanation of the “what” of repetition, cf. Otou-san. He also has this to say about the “why” (in the first arc, anyway), which is my main fixation:
…[T]he end result (for me) was to reinforce the futility of the Student Council’s quest for Revolution. For all of their dedicated faith in dueling, they can’t keep Utena from beating them and walking away with Dios’s power, and the Rose Bride.
Futility indeed. Here’s another take courtesy of ADWM:
…[W]e view [the recycled scenes] so many times, they become devoid of meaning. If we watch them at all, as opposed to fast-forwarding through, we watch it on auto-pilot, since their significance has been stripped away by our multiple viewings of it.
This is exactly how we’re supposed to feel about them, because this is how Anthy essentially views the entire process. …
I had trouble parsing this until I realized you can sum it up as, “it’s Endless Eight.” Substitute Anthy for Nagato. And how long have Akio and Anthy been doing this, anyway?
The aforementioned posts read quite differently, but there’s a common thread. We could call it futility or the banality of seeing a thing dozens of times. I think of it as entrapment. The state of being stuck on a treadmill. Looking back, you’ll find that some transitions between scenes essentially show characters moving but going nowhere, struggling in place against a backdrop of repeating scenery.
The approach to the dueling arena does this. Utena walks (or elevators?) in place for a few seconds, then she’s suddenly where she intended to be. We’re obviously supposed to fill in the blanks ourselves — it isn’t practical to show every step a character takes — but often these scenes correspond to the plot, to characters’ inabilities to move beyond what they believe to be true. You may recall how that’s true of Utena; she has to “break the world’s shell,” the shell of her subjective world, before she can go anywhere. I picked the screencap above for a reason, too — Shiori accomplishes jack shit, plus or minus fuckall, unless you count dragging Juri back (emphasis on back) into the dueling cycle once, arguably twice. (Until the movie, anyway. Don’t make the mistake of thinking she can’t turn into a car.)
So there’s a lot of repetition and it’s thematically appropriate. Also, I’m pretty sure the elevator is a golden spiral at one point, but please don’t ask me to explicate math.
I think that ADWM had it right, that the repetition does something to us directly. Not once did I skip a scene, but sometimes I felt lulled, admittedly. Sometimes we the (first-time) viewers are the Echo in the equation. We talk back to the show, we relate to it and puzzle through it, by latching on to the vocabulary that it gives us. We become comfortable with this vocabulary. On two or three distinct occasions the vocabulary expands beyond our imagining, the setting blows up, the room gets bigger. I don’t think it’s an accident that these blowups signal changes in the way the duels work, establish new standards for repetition. As for the characters, so too for us. Call it pretentious jargon if you like, but there’s only one word for this, and it’s performative.