In 1819, Ludwig van Beethoven was middle-aged, almost broke, nearly deaf, and suffering a mid-career cold streak. When music publisher Anton Diabelli asked him to remix a middling beer-hall waltz Diabelli had composed as the basis for an all-star compilation volume, Beethoven first refused, then changed his mind. Over the next three-odd years, the Maestro was intermittently obsessed with Diabelli’s tossed-off little ditty, creating not one, not two, but yes, three-and-thirty variations on a piece he had initially — apparently — thought unworthy of his attention.

Why he did this is the mystery at the center of 33 Variations, a world-premiere from Moises Kaufman, he of the great Gross Indecency: The Three Trials of Oscar Wilde and the ubiquitous The Laramie Project. But whereas those plays were assembled from the testimonies of real people, often quoting their sources verbatim and at length, this is more of a conjectural work derived from Beethoven's musical sketches and a small number of his conversation books that survive from the era.

Not that this is purely a period piece. In fact, it takes Beethoven himself, nicely played by Graeme Malcolm in full Christopher-Lloyd-as-Doc-Brown mode, 25 minutes to show up. While we’re waiting, we get the beginnings of a parallel story, set in the present day, of a musicologist’s (Mary Beth Peil) journey to Beethoven’s archives in Bonn to figure out for herself why he’d been so consumed by such a seemingly minor project. (He was composing his Ninth Symphony — the immortal work of genius without which the Home Alone trailer, and perhaps Macaulay Culkin's entire career, would never have been possible — during roughly the same period.)

Katharine, the musicologist, is dying of course — there needs to be some urgency to the proceedings, right? — and while her daughter (Laura Odeh) wants her to come home and prepare for the inevitable, Mom’s having none of it.

Wait, it’s better than it sounds. The sources of conflict in Kaufman’s script may be familiar — Mom vs. mortality, daughter vs. Mom’s expectations, daughter vs. the Central Casting nice guy (an underused Greg Keller) whose overtures she resists for all the phony rom-com reasons, etc. But as with the titular variations, it’s the inventive recasting of unremarkable material that gives this production, which Kaufman also directed, its considerable charge.

There’s real pleasure to be taken in, for example, the elegant way Kaufmann compresses the two story's dual eras: My favorite is when Beethoven’s faithful secretary, Schindler (an efficient Eric Steele), explains to Diabelli that his master’s hearing has vanished completely and that he now must use conversation books to communicate. In the same scene, Gertie, Katherine’s Teutonic ally in research, lifts the book from Diabelli’s hand, instantly shifting the scene from Beethoven’s flophouse in 19th century Bonn to his archives in the present day.

Another graceful touch is the way pianist Diane Walsh plays each little figure of music as it's discussed, or even when someone just looks at the score. Set designer Derek McLane deserves props here, too, for his striking motif of four wheeled panels each hung with sheets of music, surrounded by dozens of short-stack file boxes.

There are nits to be picked. Odeh and Keller’s slow-blooming romance is pretty lame in the early going, though it eventually proves itself a key movement in Kaufman’s symphony, one he may yet revise. (Meanwhile, a great, brief awkward-date scene nearly justifies this meandering subplot all by itself.) And the heavy-handed scene that closes Act I makes the point of juxtaposing Katharine’s physical decline with the loss of Beethoven’s hearing, oh, about 33 times.

All in all, though, it's pretty damn seductive. And there’s something sweet and egalitarian about the brazenly bad dancing that brings this rather fine evening of theater to an elegiac close.

33 Variations is at Arena Stage through Sept. 30. Tickets are available online. Pictured above: Graeme Malcolm and Mary Beth Peil share a surreal moment in the show.