Take five: Aaron Dessner, Scott Devendorf, Matt Berninger, Bryce Dessner, and Bryan Devendorf (from left) Graham MacIndoe

The National are easily damned with faint praise, the kind of modest approval that is better suited to a tailor (elegant, precise) or a handyman (steady, reliable) than a rock group. Among the crop of bands who emerged from Brooklyn in the first decade of the new millennium — Grizzly Bear, Dirty Projectors, TV on the Radio — the National (who were based in Brooklyn but all hail from Ohio) were the only ones without an obviously catchy selling point. They built their career the old-fashioned way, with regular releases and ceaseless touring. (They’re back on the road this fall.) While they’ve never disappointed their fans, their painstaking craftsmanship tends to satisfy rather than surprise. It can feel a little uptight and precious. In short, they sorely needed to break their own rules — and on Sleep Well Beast, their seventh album, they do. Up to a point.

Like many Brooklyn bands, the National no longer call Kings County home. Scattered across five different cities since 2013’s Trouble Will Find Me, members have been separately busy forming new bands, scoring movies, curating festivals, and orchestrating a tribute to the Grateful Dead. They reconvened in earnest in spring 2016 at guitarist and producer Aaron Dessner’s Long Pond Studio in Hudson Valley, New York, where they did what bands do when they’re not on the clock: try anything. The National’s sound is always a treaty between the desire of Aaron and his brother, Bryce (the band’s keyboardist and arranger), to complicate the music, and frontman Matt Berninger’s inclination to pare it back. This time the Dessners seem to have won the upper hand. During an experimental residency at Funkhaus in Berlin last year, they invited musicians including Justin Vernon and German duo Mouse on Mars to tinker with the almost-completed tracks. “We allowed ourselves to have more sounds that are just hanging out there in the mist,” Aaron has said. Nobody is likely to mistake Sleep Well Beast for Kid A, but it’s full of twists that enrich and intrigue, from the flickering electronic pulse of “Empire Line” to the glitching orchestra that closes “Dark Side of the Gym.”

Berninger lets go a little, too. With his grainy, conspiratorial baritone and his eye for details that illuminate everyday unease, he sings like a man discussing his divorce in a dark bar after a long night of steady drinking. (In real life he is happily married to Carin Besser, a former New Yorker fiction editor who sometimes co-writes his lyrics.) Sleep Well Beast opens with Berninger arranging a rendezvous in a deserted stairwell during a New York winter, which is pretty much his ideal milieu. “I have helpless friendships and bad taste in liquids,” from “I’ll Still Destroy You,” might be his quintessential lyric. Averse to high drama, he paces the side streets of frustration, uncertainty, and regret. Only Berninger would place “Carin at the Liquor Store,” a meltingly tender love song, next to “Guilty Party,” in which he imagines a marriage in ruins and, of course, blames himself.

So it’s all the more arresting when he lets himself soar on “Day I Die” or rant on “Turtleneck,” channeling Nick Cave while the Dessners conduct a writhing guitar duel. Guitar solos are usually on the long list of things the National don’t do, but there’s an extraordinary example on “The System Only Dreams in Total Darkness” (perhaps a side effect of honoring the Dead), along with a gnarly, blurting riff, a bustling groove from sibling rhythm section Scott and Bryan Devendorf, and a chorus weirdly reminiscent of the Bee Gees. It’s the album’s pinnacle and lodestar.

Berninger has described the song as “an abstract portrait of a weird time we’re in,” but to be honest it could be an abstract portrait of literally anything. While the National have never shied away from politics, playing campaign events for both Obama and Clinton, Berninger is too opaque a lyricist for protest songs. “Turtleneck” contains a glancing reference to “just another man in shitty suits that everybody’s cheering for/This must be the genius we’ve been waiting years for, oh no,” but the clearest political statement comes, on the sequencer-led “Walk It Back,” from a quote attributed to Karl Rove that infamously dismissed the “reality-based community.” Unnerving at the time it was first reported, the phrase’s blithe contempt for facts is terrifyingly pertinent now. Amid the clicks and drones of the title track’s bad dream, Berninger’s helpless everyman point of view is a good fit for the psychological trauma of the Trump era. “I’m at a loss. I’m at a loss,” he murmurs with fathomless exhaustion. “I’m losing grip. The fabric’s ripped.” He scales down a national crisis to the size of a bar or a bedroom.

Sleep Well Beast is comfortably the National’s best album since 2005’s Alligator, and the first to really screw with the idea of what a National album should sound like. Every rupture is a thrill, every reversion to type a missed opportunity. Their songwriting is sturdy enough to withstand rough handling, so why not go even further next time? Let that fabric rip.