In 19th-century France, the Paris Opéra was a machine. It was there that narrative and music, art and design, science and technology were transformed into cultural spectacle. Those spectacles had enormous influence on public and private life, as much, perhaps, as Hollywood does today.

So, on one level, it’s no surprise that an artist such as Edgar Degas would turn his attention to the ballet and opera, painting musicians and dancers, in rehearsal and performance, and sometimes offering glimpses of people like him, passionate audience members watching from gilded boxes. But an exhibition first seen in Paris last fall, “Degas at the Opéra,” and now restaged at the National Gallery of Art, raises a deeper question: Why are these works so strange?

Why, for example, does Degas’ 1867-1868 portrait of Eugénie Fiocre, a principal dancer with the ballet, show the young woman caught between a landscape and a stage set, with what seems a real horse drinking from a real pool beside her, and her ballet slippers cast off? Has she danced off the stage into reality? Or has the painter’s imagination done what so many minds do in the theater — fleshed out the illusion into something that seems as or more real than anything outside?

And why, in one of the painter’s most acclaimed paintings, “The Ballet From ‘Robert le Diable,’ ” is the orchestra arranged so oddly, with an audience member prominent in the front, looking not at the ghostly nuns dancing onstage, but sharply off to the left? And why are so many of these paintings, especially of the young women of the corps de ballet, arranged like elongated landscapes, often with a sharp diagonal running through them, as if the painter sees the world aslant through thin, rectangular glasses?

“Degas and the Opéra” includes about 100 works, including many of the artist’s most essential images inspired by the Paris Opéra, which included both opera and ballet among its offerings. This iteration of the exhibition, which opened at the Musee D’Orsay, is smaller but more easily navigated: In Paris, huge crowds and a complicated gallery arrangement made it seem episodic. Curated in Washington by the National Gallery’s Kimberly A. Jones, the show follows both the rough chronology of Degas’ decades-long fascination with the Opéra, from his early portrait of Fiocre to works he called “orgies of color,” made late in life. These orgies — vibrant pastels, some quite large — included the stunning “Dancer With Bouquets,” in which two bouquets cast at her feet look like red eyes, staring up the underside of her tutu.

The exhibition also covers the basic typology of Degas’ theatrical paintings, from those inspired by particular works, including Giacomo Meyerbeer’s early grand opera “Robert le Diable,” to paintings of imagined dance rehearsals, the rectangular “elongated paintings” and images he painted on fans. A final gallery devotes necessary space to the life of the dancers, many of whom were impoverished young women exploited by wealthy older men given predatory access behind the scenes. The National Gallery’s beloved “Little Dancer Aged Fourteen,” a wax sculpture of a performer named Marie van Goethem (whose life was memorialized in a 2014 musical), stands near the end of the show, her defiant three-dimensionality giving voice to the anonymous two-dimensional dancers seen in paintings earlier in the exhibition.

Some of these works have become so familiar that they have been reclassified in the public imagination, now seen as pretty rather than strange. But if you look at them long enough, their strangeness begins to overwhelm their prettiness, as in that late pastel of a dancer with those two red bouquets, which seem less like tributes thrown by passionate fans and more like menacing eyes. In other images, bodies are truncated, just legs showing beneath the partially raised theater curtain, or fused together, as in drawings in which dancers seem to be sharing or missing legs.

Degas’ fascination with ballet was in part a fascination with the contorted body, with legs akimbo, feet going in opposite directions and knees splayed wide. Poses that are dynamically beautiful in ballet often seem bizarre when frozen in a photograph or painting, and Degas was clearly drawn to the visual possibilities of taking them out of context. The familiar and the defamiliarized is a recurring theme, and one essentially derived from theater, a safe space where we expect to see strange and alien things.

Degas may also have turned to the theater to refresh other genera, including history painting and landscape. The theater, especially the technologically sophisticated Paris Opéra, offered aspects of both — heightened moments of great dramatic conflict and sumptuous visions of landscape in its backdrops and stage effects. By painting the theater, Degas could rejuvenate both history painting, which he had aspired to master as a young painter, and landscape, which he was fashionable enough to hold in slight disdain.

These are mostly formal questions, about visual choices and Degas’ relationship to painting. A group of works, disparate in form and materials, suggests a deeper psychological drama. In several images, including paintings, etchings and pastels, we see the distinctively curved scroll top of the string bass protruding disruptively into the image. This was a common sight for those sitting in the orchestra level of the Salle Le Peletier, the opera house that preceded the Palais Garnier and the site of many of Degas’ theater paintings, even though it had burned years earlier.

But the string bass is also the lowest of the orchestra’s stringed instruments, and bears aural associations of masculinity. So its intrusion into the world of women dancing or singing is an imposition of men into a female spectacle. These wooden scroll tops are seen at an angle, which is how they would be seen in real life, but that angle exactly mimics the odd angle at which Degas sometimes painted male patrons of the Opéra, ominous figures in black that lean unnaturally to one side.

During the nascent years of grand opera in Paris, the German philosopher Arthur Schopenhauer published and expanded a book called “The World as Will and Representation,” which may help explain Degas’ ambition in these strange works. Schopenhauer used the tonal range of music as a metaphor for the entirety of existence. The lowest notes represent the “crudest mass” of inorganic nature, while melodies above spoke of the “intellectually enlightened will.” Thus, the scrolls of the lowest instruments intrude into the realm of ideas, articulated nature and women, too.

If there’s some confusion in these overlapping ideas and metaphors (high and low, inorganic and organic, male and female), it’s a confusion that may have been deeply felt by Degas. In 1856, when he was about 22, Degas recorded in a notebook a troubling and enigmatic episode in which he loved a woman, she rebuffed him and he responded in a way that suggests he did something “shameful” to a “defenseless girl.” In images he made later in life, the string bass is on the ground, with a ballerina stepping on it, which would never happen, but is a striking intimation of either Degas’ guilt or a woman’s revenge.

So all of these must be true: that Degas was, like the men of his circle, a voyeur who made women into objects; that he may have felt shame, too, about his relationship to women; that he found in the theater a metaphor for the whole realm of existence, including the relation between the sexes; that he knew this metaphor was deeply problematic even though he found it beautiful; and that painting the opera and ballet enabled him to represent this foment and confusion without resolving it.

Yes, the Paris Opéra was a machine, but for Degas it was also a mirror — on nature and himself.

Degas at the Opéra Through July 5 at the National Gallery of Art.