Lin-Manuel Miranda turned 27 on Tuesday. To celebrate, he spent eight hours rehearsing and making last-minute changes on his new musical “In the Heights,” which is in previews at 37 Arts, an arts complex on West 37th Street. In the evening, he performed — in addition to creating the musical, he is also its star — for an audience that included dozens of family and friends, some of whom have been following “In the Heights” from its conception seven years ago.

Mr. Miranda, who grew up in Inwood, wrote the earliest version of the musical for a student production during his sophomore year at Wesleyan. He spent all of winter break working on it, and on his 20th birthday, his parents organized a reading at their home. The show has changed a lot since that first reading, particularly with the addition in 2004 of the playwright Quiara Alegria Hudes, who wrote the book for the production. But “In the Heights” remains at its heart what Mr. Miranda envisioned back then: a traditional musical set in a nontraditional locale — the Latino neighborhood of Washington Heights — and which blends the musical influences of Broadway, hip-hop, salsa, and merengue.

One of the sad facts about the American theater these days is that the audience is overwhelmingly white and wealthy. But with its eclectic musical influences and its story about a New York immigrant community, “In the Heights” has the potential to break through the culture barrier and capture a young, diverse audience. To overcome the obstacle of ticket prices (though some producers claim that non-theatergoers spend just as much money on other entertainment), the producers, Kevin McCollum, Jeffrey Seller, and Jill Furman, decided to offer reduced ticket prices during previews. Through this Sunday, tickets are $25. From Tuesday, Jan. 23, through Wednesday, Feb. 7, they will be $35. After that, tickets will be $55-85, with a small number of $25 tickets available the day of performances by lottery at the box office.

The show is advertising in a manner that both fits the producers’ budget and targets a young, local demographic: with posters in subway stations, which feature Mr. Miranda in front of a bodega storefront that says “In the Heights.”

“Typically, when you launch a new musical, you try to get on radio, you try to do as much as you can,” Mr. McCollum said. “We don’t have the money. So what we felt is, everybody rides the subway. Here’s a way we can communicate to people who live, work, breathe Manhattan that there’s a new musical about this community.” The show has also advertised in the Manhattan Times, a bilingual weekly newspaper distributed in Washington Heights, Inwood, and East Harlem.

“In the Heights,” which follows a handful of characters through a Fourth of July weekend, comes very directly from Mr. Miranda’s and Ms. Hudes’s lives. Both of them grew up in strong Latino communities, he in New York, she in Philadelphia. Both relate to the character Nina, who has returned to the Heights from her freshman year at Stanford and is trying to decide whether to go back. As the first in her family to go to college, “I had no idea what college was going to be, and it was a huge, huge culture shock to me,” said Ms. Hudes, who attended Yale. “Nina feels like a version of me, 10 years ago in my life.” She and Mr. Miranda both see Nina’s father Kevin, a hardworking small-business owner who is proud of the opportunities he has created for his daughter, as similar to their own fathers.

Most important, Mr. Miranda and Ms. Hudes both grew up with music as a major presence in their lives and their communities. Ms. Hudes’s family listened mostly to Afro-Caribbean music, while Mr. Miranda described the musical atmosphere of his childhood as “balls-to-the-walls salsa and merengue.” He listened to Rubén Blades, Gilberto Santa Rosa, El Gran Combo, and Juan Luis Guerra — of whom Ms. Hudes is also a huge fan. “Juan Luis Guerra is a genius,” Mr. Miranda said. “He should transcend nationality.”

The spirit of Mr. Guerra’s music — which tells stories and even makes political statements — infuses “In the Heights.” “Juan Luis Guerra writes songs about the failing health care system in the Dominican Republic,” Mr. Miranda said. “You’re dancing, but at the same time he’s giving you these amazing messages.”

In “In the Heights,” too, the characters sing to an up beat even when they’re singing about unhappiness. In the merengue song, “It Won’t Be Long Now,” a character named Vanessa sings about wanting to get out of the Heights. “It sounds like it’s this happy song, but it’s about how she can’t wait to get out of here. She’s choking, she’s suffocating,” Mr. Miranda said. “But I wanted it to have this Juan Luis Guerra dah-dadada-dahdah” — he sang and clapped out a merengue rhythm. “Because you have to do it: You’ll go nuts if you don’t dance.”

That need to dance and sing — or freestyle rap — drives much of “In the Heights,” making it at once theatrical and lifelike, in a way that young audiences will recognize. In the original version at Wesleyan, Mr. Miranda said, there were two scenes of the characters Usnavi and Benny freestyling outside Usnavi’s bodega. “It was one of those things where you could literally see the audience sit up,” he recalled. “At that point, I didn’t know anything about hip-hop theater as a movement. I just knew that me and my friends used to freestyle outside of bodegas, and I wanted to see that onstage.”

So far, the audiences at the $25 performances have been diverse and enthusiastic. People from Washington Heights have approached Mr. Miranda and Ms. Hudes after the show to say how well they captured the neighborhood, and others have left their testimonials on the show’s MySpace page. One man thanked Ms. Hudes for a brief mention in the show of Lares, Puerto Rico, the small town where he was from. (Ms. Hudes put Lares in the script because her grandmother was from the town, as well.)

Mr. McCollum — who, with Mr. Seller, produced “Rent” and “Avenue Q,” both of which are currently running on Broadway — was cautious about saying what kind of audiences he hopes “In the Heights” will attract. “I can’t control that, nor do I try to control it,” he said. But he did say that one thing that drew him to the show was Mr. Miranda’s unique voice. “It’s a very contemporary musical vernacular that he’s speaking, which could be attractive to people who don’t think the theater is for them.”

Begins February 8 (450 W. 37th St., between Ninth and Tenth avenues, 212-307-4100).