NEW YORK — This era of round-the-clock agita in America might call for a couple of hours of escapism every now and then, don’t you think? That, anyway, seems to be the sentiment on Broadway, as evidenced by some of its latest high-profile offerings.

Earlier this month, a British mentalist of mind-boggling agility, Derren Brown, arrived in the Cort Theatre with “Secret,” his latest dive into astonishing an audience with the power of suggestion. And now, three blocks away, comes another show meant to lull you out of your state of anxious world-weariness: the Broadway transfer of “Freestyle Love Supreme,” the hip-hop improv show dreamed up by Anthony Veneziale, Thomas Kail and nonstop entertainment machine Lin-Manuel Miranda. After striking a giddy chord in downtown audiences, with a sold-out run in Greenwich Village, this rapping romp is angling for larger crowds through its irreverent displays of rhyming wit.

It may be coincidental that these novelties end up in Broadway houses at the same moment, but they appear well-timed for the art of taking people out of themselves. Along with ventures like the long-running, two-part “Harry Potter and the Cursed Child,” these productions seem poised to sate our desire for someone to snap their fingers and replace anxiety with wonder. As the appeal of “Freestyle Love Supreme” is explained by Kail, Tony-winning director of “Hamilton,” who has known Miranda and Veneziale since they were all undergraduates at Wesleyan University: “It’s about a freedom of expression, about a joy and a possibility of making the mundane magical.”

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The process has begun at the 800-seat Booth Theatre on Shubert Alley — one of Times Square’s crown jewels — where “Freestyle Love Supreme” is in preview performances before an official opening Oct. 2. That its route to Broadway has been so serendipitous seems to add some magical gloss to the enterprise, one that started long ago as tension-relieving gamesmanship among friends. Fueled in part by the power and success of Miranda and Kail, the show found an audience and a cachet. (Over the summer, it tested the elasticity of its appeal with a short stint at the Kennedy Center, featuring some of the performers who would be part of the Broadway cast.)

And it has propelled these old friends and collaborators into new roles, as theatrical producers. Miranda also appears on some unannounced nights in the production, which Kail directs; Kail happens also to be a producer of Brown’s “Secret.”

“I never in a million years thought it would be a Broadway show,” Veneziale, an actor who teaches and performs musical improv, says of “Freestyle.”

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He serves as a kind of emcee for the evening, during which the cast solicits ideas for comic raps from the audience, based on randomly suggested words or ordinary events in their lives.

A rotating cast of inspired rap and music improvisers assembles on the stage each night, among them several well-known actors in the orbit of “Hamilton,” such as Daveed Diggs, Christopher Jackson and James Monroe Iglehart. Others, like Maryland native Utkarsh Ambudkar (known as “UTK”) and Chris Sullivan (whose specialty is sound effects), have been absorbed into the “Freestyle” family, with yet others newly signed up for the Broadway run scheduled to end Jan. 5.

“Freestyle Love Supreme” is modulated for that extremely modern wavelength, the one that seeks to evaporate the barriers between performers and spectators. The inclusiveness that these 75 minutes of laughter and boisterous entertainment engender begins with the guys (and occasionally, a female rapper) onstage. The camaraderie, Veneziale says, is a result of an openness to each performer’s distinct hip-hop style. “We often look for people who are able to express their version of what’s happening in the world,” he says. “It’s about tapping into your authentic voice.”

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Unlike, say, a night out in Vegas, or at a comedy club where the pattern tends to be one act at the mic at a time, “Freestyle” is communal, with the cast members sharing the stage and handing off the spotlight as if it were a baton in an Olympic relay. It’s democratic comedy, with a lowercase “d.” Sort of.

“We create these things where people feel like their voices matter,” Veneziale adds. “Everyone up there has a moment to express their point of view, and add to the totality.”

Ambudkar, who grew up in Columbia and Gaithersburg, became disillusioned with training as an actor at New York University’s Tisch School of the Arts and gravitated toward spoken-word performance and honed rap-battle skills. More than a decade ago, a producer, Orin Wolf — later to bring “The Band’s Visit” to Broadway — attended one of the rap battles, Ambudkar says, and introduced him to the guys who would develop “Freestyle Love Supreme” into a full production.

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“I came from a hip-hop rap-battle background, a very competitive environment, in which emcees are in­cred­ibly self-aggrandizing,” Ambudkar says. That boastful style was seriously one-dimensional. “Tommy Kail sat with me and said, ‘Listen, man, there’s a lot of ego in your performance. You can’t go onstage and talk about how great you are.’ ”

He credits Kail with making his performance less solipsistic, more observationally about the world around him — what Ambudkar calls “a focus on listening and enhancement of the group experience.”

Comedy is not renowned for its generosity of spirit, but maybe the escape we’re craving is an entertaining environment that’s both funnier and more familial than the brittle reality we endure day-to-day. “Freestyle Love Supreme” could be a good test of this thesis.

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Ambudkar says that when he’s on the stage with his cast members, “I want to show love in the same capacity that they show me.

“We are in the same exact boat,” Ambudkar adds, “as the audience.”

Freestyle Love Supreme, created by Thomas Kail, Lin-Manuel Miranda and Anthony Veneziale. Directed by Kail. $59-$199. Through Jan. 5 at Booth Theatre, 222 W. 45th St., New York. 212-239-6200. telecharge.com.

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