– The times, they are a-changin’ on Broadway and not just because of the new Bob Dylan musical, “Girl From the North Country.”

The Dylan show, which finds fresh ways to incorporate an existing song catalog into theater, is part of a wave of rock or pop-based musicals that have supplanted the dominance of Disney adaptations, which once clogged five Broadway houses at the same time. Of the 23 musicals running before the coronavirus shutdown, six were either the stories or songs of rockers (or both). Before year’s end, more than a third of the musicals will likely be based on rock catalogs.

Disney is still a player, with “Frozen,” “The Lion King” and “Aladdin” all doing good business, but that’s nothing compared with the onslaught of Dylan, Alanis Morissette (“Jagged Little Pill”), the Temptations (“Ain’t Too Proud to Beg”), Tina Turner (“Tina”) and the greatest hits parade of “Moulin Rouge!,” which draws on songs from the Rolling Stones, Whitney Houston and others.

And those don’t include Bruce Springsteen, who ended a Broadway residency last year, or David Byrne, who soon will restart his concert/theater piece, “American Utopia,” or the yes-it’s-really-still-happening Michael Jackson musical, “MJ,” which is slated to open in July.

All are Broadway hits, with national tours in the planning stages. “Tina,” “Too Proud” and “Moulin Rouge!” all regularly join the exclusive club of shows that gross at least $1 million weekly.

Not all are trailblazers, creatively. “Tina” and “Too Proud” follow the typical jukebox musical path, sprinkling hits onto a biography of the icon being impersonated at the center of the show. Based on the reviews, “Moulin Rouge!” is its own crazy thing, faithful to its Baz Luhrmann movie inspiration and packing in parts of a jaw-dropping 70 recognizable songs along the way.

The Disney and rock models are not dissimilar, since both bring together phenomena that drive everything now: boomers and money.

As others have pointed out, Broadway musicals are expensive, so creating one from a pile of songs that audiences hum even before they enter the theater is not a bad way for investors to hedge their bets. Sure, jukebox shows do fail; who thought it was a good idea to carve “Escape to Margaritaville” out of the catalog of Jimmy Buffett, who has precisely one song audiences can be expected to know? But their record is better than original musicals, whose writers now find themselves aced out of Broadway’s limited real estate by the likes of Elton John (who composed the long-running “Lion King,” although it’s not built on his persona) and Morissette.

The trend is not going away, which is bad news for anyone who had to sit through the worst jukebox musicals, such as “Motown: the Musical,” whose exhausting series of medleys made you long for Motown: the Originals — that is, Stevie Wonder and Diana Ross singing those songs on your listening device of choice. But this season’s catalog-based shows bring good news for folks who love musical theater. “Girl From the North Country” and “Jagged Little Pill” take compelling new approaches to Broadway’s renew/re-use/recycle trend.

“Jagged Little Pill” is built on the 13 songs from Morissette’s 1995 album of the same name, plus a few more because they couldn’t resist “Hands Clean,” “So Pure” and “Thank U,” from subsequent albums. It’s a jukebox musical in that its seams strain to contain songs that don’t feel written for Broadway voices or even for storytelling purposes, but it bucks the trend in that it’s not the story of Morissette’s life (like “Beautiful” was for Carole King) or even based on details from the album.

Instead, book writer and former City Pages journalist Diablo Cody created a story that will feel familiar to fans of “Next to Normal,” which has toured here and been produced at Mixed Blood: A middle-aged woman, unsatisfied with her life, ignored by her family, and struggling to maintain her balance while sampling a mix of prescription and nonprescription drugs, tries to make sense of her marriage, her children and her own dreams.

There are times you can feel Cody’s hand as she bulldozes the narrative to fit Morissette’s well-known songs but their drama and power work surprisingly well in a theatrical setting, especially when delivered by Elizabeth Stanley as the central character, MJ (not to be confused with the title character of “MJ,” also known to have had pill problems). But, in general, “Jagged Little Pill” is so much more creative than other jukebox musicals that it doesn’t even belong in the same category as, say, “Jersey Boys.”

Rockers including Morrissey have played short runs in Broadway theaters, similar to Springsteen’s longer stand at the Walter Kerr Theatre, but Byrne’s “American Utopia,” a version of which played in Minneapolis two years ago, is a category-defier from an artist whose band, Talking Heads, was at the forefront of the punk/New Wave movement. It is scheduled to return in September.

In the meantime, “Girl From the North Country” is one of the most adventurous shows on the Great White Way. For one thing, it’s not a greatest-hits collection. Many Dylan biggies are missing, including “The Times They Are A-Changin,’ ” “Blowin’ in the Wind” and “Knockin’ on Heaven’s Door.” (Maybe the show has something against g-dropping?)

Instead, “Girl” veers toward less familiar songs. Only three of the two dozen “North Country” tunes are from Dylan’s 1960s heyday and many date to the early ’80s, when he wasn’t exactly a hit machine. As playwright/director Conor McPherson was putting together the show, he may have benefited from the lessons of an earlier, more traditional attempt to put Dylan on Broadway. That 2006 effort, “The Times They Are A-Changin,’ ” was a dance-based piece that tried to cram the hits into a work modeled on the Billy Joel show “Movin’ Out,” which was also created by director/choreographer Twyla Tharp. “Times” closed after less than a month.

With full access to Dylan’s enormous catalog, the effort seems to have been to choose songs that would shine in a new setting, whether by illuminating the thoughts and desires of the characters, drifters in a Duluth boardinghouse in 1934, or by taking on a new life that seems to have nothing to do with Dylan at all. If you didn’t know he had written the rave-up “Duquesne Whistle,” you’d never guess he did, based on the massive power of its “Girl From the North Country” performance. And “Is Your Love in Vain” would feel at home alongside “Rose’s Turn” and “Sit Down, You’re Rockin’ the Boat” as a legit 11 o’clock number.

Since the show divorces Dylan’s songs from his performances, it puts the emphasis on his songwriting versatility. That’s not a message you take away from most jukebox musicals’ attempts to contort existing songs into a story with a happy beginning, middle and ending. Instead, “Girl From the North Country” is full of memorable melodies and piercing lyrics that attest to Dylan’s ability to get to the heart of matters of the heart.

On an early March trip to New York, the show seemed poised to conquer New York. I saw three ads for “Girl” on the monitor in the back seat of my cab during a 45-minute drive from the airport and it also felt like a good sign that mere steps from my hotel was The Dylan, a swank apartment building. But whether or not “Girl From the North Country” is a smash — and its originality and bleak subject matter may make it a difficult sell for the group sales that help create long Broadway runs — it’s clear that it will burnish the already stellar reputation of the pop star whose work inspired it.