Twyla Tharp’s Broadway bust The Times They Are a-Changin’ (2006) proved that however rich and multifaceted Bob Dylan’s work is, it’s not exactly dance music. But Dylan wanted to try again, and so we have Girl From the North Country, which after its West End debut last year has been rapturously received at the Public Theater. By some, I should add; for others, myself included, the third time will have to be the charm.

The show has all the earmarks of High Seriousness, starting with the venue, which tilts toward earnestness outside Shakespeare in the Park. Its writer and director, Conor McPherson, is a two-time Tony nominee. There’s “movement”–God forbid, no choreography, not after the last time. It’s set in the Great Depression–the characters are broke, hungry, and adrift in their own funk, nothing to tap dance or sing a happy tune about in their threadbare outfits. While “Like a Rolling Stone” is performed most of the twenty songs are deeper cuts, for harder-core Dylanologists who may have rolled out to see it after an afternoon perusing used record stores. Design is minimal: chairs, a table, some projections to break the monotony.

But monotonous, and lugubrious, Girl From the North Country is. The problem isn’t Dylan–orchestrator, arranger, and music supervisor Simon Hale has done a fine job recasting some of his outstanding songs for a theatrical ensemble. Show music they’re not, but McPherson is best known as a monologist, and the songs are matched as organically as possible to each vignette. Which is the problem; his play is choppy and uninvolving, with characters who have little momentum other than to get through their numbers and cede the stage to the next cut. It’s also achingly dull, which will dismay anyone looking for the raucous fun of The Seafarer, his Broadway hit, or his prior, nervier work. “There will be none of that foolishness here; it’s Dylan, you see,” you can hear him saying, on his knees, prostrate with admiration. He worships Dylan the Inscrutable, the seer. But witty, incisive Dylan, the only Nobel Prize recipient with a Christmas album, has never been above entertainment.

A peculiar framing device doesn’t help. The show is set in a boarding house in hardscrabble Duluth, MN, in 1934, and the characters seem to be on a radio show. (A nod, perhaps, to the fourth wall-breaking of Dennis Potter’s Pennies from Heaven, but only just.) One criticism of the London production was that the performers weren’t authentically American, which is handily remedied here. House owner Nick (Stephen Bogardus) is depressed that his wife, Elizabeth (Mare Winningham) is drifting into early-onset dementia. Elizabeth is depressed that their writer son (Colton Ryan), an alcoholic, is uncommunicative. (She breaks out of her fog long enough to sing “Like a Rolling Stone,” with, strangely, disco ball accompaniment, but perhaps all of this is taking place in her addled mind.) Mr. Burke (Mark Kudisch) and Mrs. Burke (Luba Mason) are depressed about their man-child son, Elias (Todd Almond). Everyone’s so depressed, in fact, they may as well be British.

The songs do give the show some Prozac, even if the energy is sometimes misplaced. (“Hurricane,” the story of a specific person, doesn’t make much sense out of context, but the spirited rendition should highlight the cast album.) Underutilized by the play, which at the end strains to be Our Town, veterans like Winningham and Kudisch give them their all. But Girl From the North Country isn’t my kind of town, to steal from a singer Dylan lionized in a recent album.