Great Noise Ensemble. (Courtesy of the National Gallery of Art/Courtesy of the National Gallery of Art)

“La Commedia,” by Louis Andriessen, is one of the most important operas written in the past 20 years. It won a Grawemeyer Award, one of composition’s plum prizes, three years after its 2008 premiere. Although the opera has been seen in Los Angeles and New York, Washington has not had a presenting organization that would bring this kind of eclectic, patchwork piece, conceived as a “video opera” with the director Hal Hartley, to this city.

Enter the composer Armando Bayolo, who has become a significant figure on the D.C. cultural landscape. He has brought major contemporary groups to his series at the Atlas, and he has brought Andriessen’s music here, first with a performance of the seminal “De Materie” in 2010 and now with a city-wide festival celebrating Andriessen’s 75th birthday that kicked off at the National Gallery on Sunday night with the local premiere of “La Commedia.”

Bayolo is not a major conductor; the Great Noise Ensemble (which he founded and which performed on Sunday) is not a nationally known group; and the garden court of the National Gallery’s west building has some of the acoustic properties of an indoor swimming pool. But everyone involved in Sunday’s performance took those lemons and made quite a potable beverage. “La Commedia,” even without the video, is an exciting, powerful and rich piece that shows Andriessen at the top of his game, and to hear it live, with Cristina Zavalloni, the vocal soloist who’s been called Andriessen’s muse, and other committed soloists and musicians, was exhilarating.

“La Commedia” is in five parts, and like most of Andriessen’s work, it draws on a broad palette of references both cultural and musical. Based on Dante’s Divine Comedy, it leads from Hell through Purgatory to Heaven (Purgatory, the fourth section titled “The Garden of Earthly Delights,” is ushered in with a big-band sound that some might find all too appropriate to the location it is describing), weaving in texts from Dante, medieval satires and the Song of Songs along the way. Andriessen’s musical palette includes a range of sounds and textures, both traditional and contemporary, from taped music to bells and gongs to the sighing of strings, from Zavalloni’s expressive, clear, amplified voice to the limpid soprano of Lindsay Kesselman, her angelic, classical, non-amplified counterweight.

The piece is never anything less than involving, even if you had to wade through the foggy haze of sound in the Garden Court to find its musical core. The sinister spasms that opened the third section, “Lucifer,” yielded to what in this space threatened to become a more generic vocabulary of large, melodic, “classical music” gestures, but then the baritone, Andrew Sauvageau, began a sneering sung monologue, Lucifer as conceived by a 17th-century Dutch playwright named Joost van den Vondel, and the general malign sense of the movement gained a point and bite and focus.

A lot of Andriessen’s earlier work has a relentless sense of drive — like the 144 crashing chords that open “De Materie.” “La Commedia” doesn’t have this, because the composer no longer needs it; the piece sustains its energy without having always, literally, to drum its points home. It shares the rich, expansive sense of its literary model, despite its relatively small size (“relative” in operatic, or Divine Comedy terms; the piece is less than two hours long). And it doesn’t shy away from sheer beauty: it’s there in the radiant choral setting of “The Song of Songs” at the end of the Purgatorio section, or the clanking, shining bells that underscore the shimmer of Paradise in the fifth and final movement.

The performers outdid themselves in showing what local forces with heart can offer. The eight members of the chamber chorus Third Practice did evocative heavy lifting. The Great Noise Ensemble, swollen to unrecognizable dimensions through the addition of so many instruments, negotiated a tough room and score with honor. And the Washington Children’s Chorus had the last word. Andriessen uses kids, in the best children’s chorus tradition, as angelic voices in heaven, but then, with a characteristic wry humor, mixes up the trope a bit by having them close the piece with a postlude, scolding audience members that they’d better listen up if they want to make it to the Last Judgment. Bayolo presented this moment as if it were an encore, after the first round of applause, which was slightly confusing — but like the evening’s other foibles, didn’t ultimately detract from the whole.

The Andriessen75 festival continues Tuesday with a recital by Zavalloni and other soloists at Strathmore. See for details.