In “Fun Home,” Alessandra Baldacchino, left, Pierson Salvador and Lennon Nate Hammond play children who sing an endearing commercial jingle they’ve made up for the not-so-funny business run by their father. (Joan Marcus/©2016 Joan Marcus)

The musical “Fun Home” poignantly explores the corrosive secrets that send ripples of pain through a Pennsylvania family. The show, though, is mindful that few households — even the most troubled — represent only one thread of experience, and it strives to document the incidental pleasures of its heroine, Alison, and her offbeat family.

One of the most memorable songs in “Fun Home” — winner of the 2015 Tony Award for best musical and beginning a month-long run at the National Theatre on Tuesday — is the opposite of mournful. “Come to the Fun Home” is sung by “small” Alison (three actresses portray her, at various ages) along with her two brothers. It’s the endearing commercial jingle they’ve made up for the not-so-funny business run by their father, Bruce. Who happens to be the town mortician.

But the song is far from trivial. It establishes the buoyant imagination of artistic Alison, who is coming to terms with her sexuality as well as her family’s psychic fissures. The song also submits that bliss and dysfunction needn’t be incompatible, that resourceful people tend to seek out happiness even under inhospitable circumstances.

“The point in Alison [Bechdel’s] book is that a lot of life was lived in that house,” the musical’s composer, Jeanine Tesori, says over a recent dinner in Manhattan, referring to Bechdel’s 2006 graphic memoir, on which the show is based. To Tesori, that notion was essential for the musical. She recalls telling Lisa Kron, the musical’s book writer and lyricist, “This has to have such joy and rhythm or it won’t be something an audience can enter.”

Audiences embraced “Fun Home” to a degree no one had anticipated when it began life at off-Broadway’s Public Theater in the fall of 2013. “A beautiful heartbreaker of a musical,” Ben Brantley wrote in the New York Times. Directed by Sam Gold, with a cast headed by Michael Cerveris as Bruce, Judy Kuhn as Alison’s mother, Helen, and Beth Malone as adult Alison, the production moved to Broadway’s Circle in the Square in March 2015. It garnered 12 Tony nominations, winning five: best musical, score, book and direction and best actor for Cerveris. Perhaps because of the adventurousness of the material and the nagging questions regarding some of Bruce’s behavior, it was never destined to be a hit with tourists, Broadway’s lifeblood. So its run ended after 18 months, a financially healthy engagement but, for an ­award-winning Broadway musical, not an especially long one.

The national tour company of “Fun Home” includes Kate Shindle, a former Miss America, center, who says positive receptions to the show have bolstered her belief in the decency of ordinary Americans. (Joan Marcus/©2016 Joan Marcus)

Nevertheless, “Fun Home” hit the road last fall, with a touring version also directed by Gold and featuring Robert Petkoff, Susan Moniz and Kate Shindle in the lead roles. That its D.C. venue is the National attests to the enduring value of this sometimes underused theater as a destination for major events. This fall, the National will showcase its usefulness again as the pre-Broadway tryout house for “Mean Girls,” a musical by Tina Fey, Jeff Richmond and Nell Benjamin adapted from Fey’s 2004 movie comedy.

The coming-of-age story of “Fun Home” is deeply entwined with Alison’s realization, as a student at Oberlin, that she is gay — an epiphany reflected wittily in the exuberant song “Changing My Major,” sung by “medium” Alison. That her father’s closeted sexuality is a lingering shadow over the Bechdels further complicates Alison’s emotional development. Shindle, who plays adult Alison, says the positive reception on the road has bolstered her belief in the decency of ordinary Americans, even in places such as North Carolina, where a bitter fight has been playing out over the rights of transgender people to use the bathroom of their choice.

“The thing we were most excited about, even before starting the tour in Cleveland, was taking ‘Fun Home’ to Durham [N.C.], and before we even opened in Cleveland, we were almost sold out in Durham,” says Shindle, a former Miss America who also is president of Actors’ Equity, the national union for stage actors. “I think there’s always an audience for good theater, and there are progressive thinkers everywhere.”

Tesori, a composer who has worked over the years with varied writers — Tony Kushner, on “Caroline, or Change”; David Lindsay-Abaire, on “Shrek, the Musical”; and Brian Crawley, on “Violet” — says collaborating with playwright Kron was another growth experience. But immersing themselves in a tale built around a funeral home (thus, the show’s title) was a singular challenge.

“There was a day Lisa was Googling ‘embalming equipment,’ ” Tesori says with a laugh. Now there’s an apparatus you don’t think of every day as the building block of a Broadway show.

If you go
Fun Home

National Theatre, 1321 Pennsylvania Ave. 202-628-6161.

Dates: Tuesday through May 13.

Prices: $48-$98.