What happens to the Broadway musical when it’s a choreographer, not a composer or librettist, who reigns supreme? What happens when there isn’t much narrative, when there isn’t even one moment of spoken dialogue?

If you’re familiar with Twyla Tharp, you probably have an answer. It might sound unbelievable, but everyone I’ve spoken with who has witnessed her work has come away impressed. When I told people who’d never heard her name, however, that I was going to attend last night’s opening of Come Fly Away, they kind of squinted at me and replied, “Oh, yeah, that’s just dancing, right?”

I’m pleased to report that this evening of “just” dancing might be one of the most thrilling performances you’ll experience, and I’m certain that after, you’ll never hear a Frank Sinatra song in quite the same way. That is, if you’re lucky enough to see this “New Musical” at The Hobby Center for the Performing Arts. More precisely, it seems to be an evening-length dance work for the crowd that craves musical theater, but who’s quibbling about labels?

The lowdown: A genius who has already choreographed most of the American jazz canon (starting with Scott Joplin and moving up into the present) has set choreography to 25 of Frank Sinatra’s greatest hits on a cast of stellar dancers. She has placed them in a sort of situation, namely, an evening at a bar, where they flirt, fight, and fall in and out of love.

A smokin’ 14-member live band plays the original arrangements by such greats as Nelson Riddle, Quincy Jones and many others, along with a recorded voice track by Ol’ Blue Eyes. It’s homage of sorts to the popular singer from Hoboken, but there is an emotional archeology going on in this material that is even more intriguing.

Produced with the utmost sophistication, the show is dazzling in scope and intent. One of the best things I could say is that it is never cute. Tharp’s choreography has a certain depth and density about it. There are numerous events in each minute of her work, and this is what occupied my rapt attention for the 80 intermission-less minutes Tuesday night.

A kick from Tharp, for example, is never a throw-away thing like it is in so many Broadway shows. Tharp’s kick always has a purpose. Things get kicked at, places get kicked in, people get kicked around, and there are always just a few more kicks to be had. This is emphatic dancing, even dangerous at times, and often imbued with a sense of the forbidden.

When we’re no longer pre-occupied with determining a story, with worrying if we missed an important line here and there, or with deciphering a song or waiting for the chorus to chime in, we can look more closely at the movement.

Most American adults know Sinatra’s oeuvre pretty well-it’s inescapable. Such gleaming standards as Luck Be a Lady or Body and Soul, however, are reinvigorated by this choreography. In the hands of a lesser artist, it would seem like little more than just another quick challenge on So You Think You Can Dance.

I noticed, though, that Tharp rarely “interprets” the lyrics with obvious gestures. When she chooses to do so, it’s haunting. Last night, after a truly stormy passage in the classic Pick Yourself Up, the dancers did just that, and somehow it rang completely honest without being coy.

The dancers act, to be sure. They are iconic in a necessary way. We don’t learn their particularities, really, only that one of them has an evident drinking problem, two are younger than the rest; one couple enjoys violence mixed with their intimacy, and so on.

The blocking is filled with details, however. When one couple comes forward to claim the limelight, the bartender is doing something underhanded in back, and a girl goes to flirt with a group of young men at another table. It’s a kind of constantly-controlled chaos. When the lighting shifts suddenly, just as it would in an actual nightclub, one feels complicit in the action.

When Sinatra begins with I’m Gonna Live “Til I Die, the men’s ties start to come undone, T-shirts get tossed aside, and the booze starts to, well, kick in. Like I said, always more kicks, especially in Teach Me Tonight, which is the erotic highpoint of the evening.

Twyla Tharp began using Sinatra’s songs for her choreography as early as 1982, when she created the suite Nine Sinatra Songs. The dance became so popular that in 1984 it was offered at the White House to President Reagan, with Sinatra himself providing the “accompaniment.”

It seems that Tharp has been developing the material for 30 years. Come Fly Away is a culmination of sorts, not to mention an evident masterpiece, so deeply American and so complex in its mixture of the bitter and the sweet.

Come Fly Away is at the Hobby Center through Sunday. Click here for details.