The enchanting exhibit “Dancing the Dream” at the National Portrait Gallery begins with a magnificent art nouveau poster of Loie Fuller in all her silk-swirling, Folies Bergère radiance. It ends with an image of a leather-clad Lady Gaga in a reptilian crouch. The logic is clear: Fuller, who set Paris aflame (in more ways than one, as we’ll see) and inspired a generation of artists, is Gaga’s great-grandmother, in spirit, at least.

That shared spirit — free-thinking, independent, and inclined to spectacles and intoxicating physicality — runs through this exhibit’s toast to American dance icons. The timing is good: Popular culture is saturated with dancing on various screens and arena stages, and live performances can be found all around town as a busy fall season gets into swing. The show also marks dance’s migration into official Washington’s palaces of the, shall we say, more rigid arts. “Dancing the Dream” opens on Oct. 4, the same weekend that the National Gallery closes its “Diaghilev and the Ballets Russes” exhibit, a dance-related show that was such a hit its run was extended.

All of those happenings outside the National Portrait Gallery enforce the point made inside: that dance is an especially attractive vessel for the American soul.

That native independence, pioneering drive and entrepreneurial bent, not to mention the cultural diversity of recent decades and an ever-present fascination with athletes and athletic bodies, is all here, in some way or another. It’s a representation of American culture, history and identity in motion. The exhibit’s photographs, posters and a few sketches and charcoals — most taken from the gallery’s collection but seen together for the first time — are organized into five categories: “Broadway and the American Dream,” “Lights! Camera! Action!,” “Choreographing Modern America,” “The Rise of American Ballet” and “Choreography Goes POP!” There are also video and film clips on flat-screen televisions.

Thus a top-hatted James Cagney, ringed by the lifted thighs and bare shoulders of pinup-worthy showgirls in a poster for “Yankee Doodle Dandy,” presides over a group of film stills that includes a scene from “Dirty Dancing.”

Cagney’s showgirls — a display of 1940s gigantism, which you still see in the Rockettes (curiously absent from the show) — gave way to the intimacy of Patrick Swayze and Jennifer Grey doing their own moves, but dancing serves the same purpose in both movies: vicarious freedom of the spirit.

She had a blast in Paris

If this is one of dance’s primary powers — at least as a performing art — there are innumerable ways that power has been deployed, starting with Loie Fuller’s conquest of Paris in 1892. This is the strength of “Dancing the Dream”: It offers a big tent, an all-encompassing embrace of the art form in defiance of anyone’s snobometers. TV’s “Soul Train” is enshrined along with cerebral modern-dance eminence Merce Cunningham, and rightly so, for both reflected cultural directions and left their mark on the times.

But it’s worth bearing in mind that the pictures on the walls are not the art. Each image is more like a portal to an era — and to a story. Unfortunately, the stories are only partially told. There is no catalogue to this exhibit; funding didn’t exist to cover the publication rights. The wall text helps, but hopefully visitors will be moved to investigate some of the artists here further, for their stories are remarkable.

Take Fuller, nee Marie Louise Fuller near Chicago in 1862. She toured with the circus, vaudeville and Buffalo Bill, but her big success came when she discovered how stage lighting could transform a silk costume into waves of shimmering mystery. She wound herself in yards upon yards of white fabric, manipulating it with hand-held wands so it billowed around her like wings and clouds; she also invented special lighting devices to shower rainbows and sunsets on the silks, in a kind of dream weather. With her undulating, uncorseted form and transcendent tints, Fuller dazzled New York and Paris. Making her life, aptly enough, in the City of Light, she hung around with Rodin, Toulouse-Lautrec and Marie Curie.

The plump, plucky Fuller was a one-woman phenomenon in her day: a burlesque seductress who held patents in lighting and other technology, a visionary modernist who sponsored Isadora Duncan’s first European tour. She was fearless, too. Fuller asked Curie to let her use radium in her stage act, and when Curie talked her out of what has to be one of history’s worst ideas, Fuller turned to phosphorescent salts. She wanted to invent a glow-in-the-dark costume.

She blew up her lab.

Clearly, the famous riot touched off by the Ballets Russes’ “The Rite of Spring” wasn’t the only explosive moment for modernism, for dance or for Paris.

Shirley MacLaine and earlier lives

Fuller is only the most colorful example of the spirit of innovation that guided “Dancing the Dream” curator Amy Henderson.

“When I talk about dancing the dream, it’s about that search for creative freedom and not going by the tradition,” Henderson said in a recent interview. “In America, nothing was baked in.”

The pioneering spirit is what led Agnes de Mille and Jerome Robbins to shake up the ballet world with works about cowboys (de Mille’s “Rodeo”) and sailors (Robbins’s “Fancy Free”), and then to invigorate Broadway with the same moxie. In Maurice Seymour’s high-kicking photograph of her in this show, de Mille lets us know we’d better get the heck out of her way. Robbins is represented by an Al Hirschfeld drawing, which grants us a view right up the domineering choreographer’s nostrils.

A tremendous amount of zest is on view here, but also introspection.

There is something painterly about the photograph of a young Shirley MacLaine with bobbed hair, legs spread wide, hunched in a chair in a rehearsal studio. She embodies the emotional ambiguity of the bone-weary chorine, in a pose at once suggestive and defensive. She could be modeling for Lautrec or Degas. She could also be the seated hooker in Picasso’s “Les Demoiselles d’Avignon.”

In the modern-dance room you’ll find plenty of bare feet and good-looking bodies. One of the best is captured in Boris Chaliapin’s illustration of a lean, muscular Katherine Dunham, the electrifying dancer, company director, humanitarian and collector of dances throughout the African diaspora. The dance world is relatively cozy, and here is delightful evidence of one of its entwinements: Chaliapin was the son of the Russian opera star Feodor Chaliapin, whose heavily beaded costume from a Diaghilev opera production was featured in the National Gallery’s Ballets Russes exhibit. That Dunham-Diaghilev link would likely please them both.

Yet a dance exhibit composed of works under glass is only a sliver of the experience. What of the living component? That will be represented by Dana Tai Soon Burgess, the gallery’s first choreographer-in-residence. On Nov. 16 in the museum’s courtyard, his dance company will perform a world premiere inspired by the exhibition. (Burgess will unveil another in April.) And every Saturday afternoon from Oct. 5 through Nov. 2, 11:30 a.m. to 3 p.m., he will be rehearsing with his dancers in one of the galleries.

Dancers? In a room with art?

“We’ll be very careful,” Burgess says with a laugh.

The rehearsals will be streamed live, and Burgess says he planned them this way to encourage visitors and online viewers to give him comments and suggestions.

“People don’t generally understand the rehearsal process,” he says. “They think it’s perfect right from the start.

“I think it’s fine to get feedback,” he continues. But after a moment, he adds: “I don’t necessarily need to use the feedback.”

Independence, creative freedom: Still alive and well.

Dancing the Dream

opens Oct. 4 and runs through July 13, 2014. National Portrait Gallery. Eighth and F streets NW. 202-633-1000.

“Dancing the Dream” Family Day features free dance performances and other events from 11:30 a.m. to 4:15 p.m. on Oct. 26. Dance performances are provided by ReVision dance company, Dance Place Step Team, Devi Dance, Joy of Motion Dance Center’s Youth Dance Ensemble and the Dance Institute of Washington’s Washington Reflections Dance Company.