Titian’s “Danaë,” an Italian Renaissance painting noted for its sensuality, is on display at the National Gallery of Art through Nov. 2. (Courtesy of Capodimonte Museum, Naples via National Gallery of Art)

Is Titian’s “Danaë” a dirty picture or an example of great, elevated art? The truth is it’s a little of both.

The painting, which went on view at the National Gallery of Art on Tuesday, is on a four-month loan from Naples’s Capodimonte Museum in celebration of the commencement of Italy’s presidency of the Council of the European Union. Painted between 1544 and 1545, it depicts a naked woman lying on an unmade bed, a piece of fabric draped lightly over her thigh in a faint attempt at modesty.

What’s so sexy about the nearly 500-year-old canvas? It isn’t just the subject matter. The mythological Danaë, as detailed in Ovid’s “Metamorphoses,” was impregnated by the god Jupiter after being imprisoned by her father, who feared a prophecy that his grandson would grow up to kill him. (Spoiler alert: He does.) In Titian’s rendering of the myth, one of several versions he made over his long career, Jupiter appears in the guise of a shower of gold coins dropping from above into Danaë’s open lap and between her parted legs.

As David A. Brown, the museum’s curator of Italian paintings, writes in a brochure accompanying the special installation, Danaë’s “languorous pose and rapturous gaze” suggest that she is, somewhat euphemistically, “about to receive” her divine visitor. In other versions of the story, the god manifests himself not as coins, but as golden droplets of a rainlike liquid.

No, what’s most erotic about the painting is, I think, the woman’s right hand, the fingers of which are shown raking sensuously through a clutch of rumpled bed linen. The effect isn’t quite porn, but it’s erotic as heck, the frankly carnal specificity of the gesture barely veiled by what Brown calls the painting’s “mythological gloss.” The woman in “Danaë” has the weight of flesh.

She certainly raised eyebrows back when she was being painted. In a September 1544 letter to the man who had commissioned the work, Cardinal Alessandro Farnese, the papal legate Giovanni della Casa wisecracked that the work he saw underway in Titian’s studio would make an earlier nude that the cardinal had seen “look like a nun by comparison.”

Della Casa also suggested that Titian would be happy to add to the painting the face of Farnese’s mistress, a courtesan named Angela, if asked. Though some scholars believe that the woman depicted in “Danaë” is, in fact, Angela — the cardinal was a well-known ladies’ man — Brown argues that della Casa’s comment was also likely to have been a joke. As Brown notes, subsequent versions of “Danaë” painted by Titian for different patrons show exactly the same face and blissed-out expression. (The head, thrown slightly back, evokes a modern centerfold. Let’s not forget “Danaë” was painted by a man.)

It may be tame by today’s standards, but “Danaë” still holds a potent erotic charge. Its subject is more libidinous, I think, and less romantic than two other “erotic mythologies” painted by Titian and on view at the museum in a nearby gallery.

The painter’s “Venus With a Mirror” (1555) and “Venus and Adonis” (1560) are definitely worth a side visit, along with five portraits by this master of the Italian Renaissance.

The special display of “Danaë” is not the only Italian art we’re going to be treated to in coming months in celebration of Italy’s E.U. presidency, a six-month term that begins this month. Keep an eye out for “Salvatore Scarpitta: Traveler” (opening July 17 at the Hirshhorn Museum and Sculpture Garden); “From Neoclassicism to Futurism: Italian Prints and Drawings, 1800–1925” (opening Sept. 1 at the National Gallery of Art); and “Picturing Mary: Woman, Mother, Idea” (opening Dec. 5 at the National Museum of Women in the Arts).