No, it’s not based on the 1960s TV sitcom. No, it’s not based on the 1991 movie comedy. Talking to Rivertown Theaters’ Gary Rucker, you start to wonder just what the musical version of “The Addams Family” really is based on.

It’s safe to say the initial Broadway version didn’t exactly dazzle audiences, even after the decision to go straight to the original source of the macabre Charles Addams cartoons that began appearing in The New Yorker back in the 1930s.

“I don’t think it’s a successful adaptation at all,” Rucker said before a run-through of the musical, which stars Johnny Lee Missakian as Gomez and Trina Beck as Morticia and opens Friday . The 2010 Broadway version, starring Nathan Lane and Bebe Neuwirth, opened to negative reviews but did great at the box office — eventually necessitating a massive rewrite. Not exactly an ideal beginning for Marshall Brickman and Rick Elice, the creative team behind “Jersey Boys.”

“Now, it actually has a plot, which is nice,” Rucker said of the rewrite. “I kept joking with the cast, ‘This is “The Addams Family” for people who don’t know who The Addams Family is. … We’ve had to justify why Morticia does a vaudeville number. To me, they kind of took the plot of (‘La Cage aux Folles’), threw the Addams characters in it and kind of went for it.”

The New York Times’ Ben Brantley was not amused, writing, “A tepid goulash of vaudeville song-and-dance routines, Borscht Belt jokes, stingless sitcom zingers and homey romantic plotlines that were mossy in the age of ‘Father Knows Best,’ ‘The Addams Family’ is most distinctive for its wholesale inability to hold on to a consistent tone or an internal logic.”

Which is to say Rucker loves a challenge. “It’s been my kind of joy to make it very ‘Addams Family.’ I think it was kind of a cash grab that didn’t work out. But now, it’s actually kind of a nice story and is more appropriate to what ‘The Addams Family’ is.”

The Addams family is, of course, the more nightmarish version of the American Dream nuclear family in which everything dark is light and good is bad.

Son Pugsley, for example, is at his happiest when being tortured on a rotating rack by sister Wednesday. But in what illustrates the “La Cage” comparison, this plot revolves around a romance between Wednesday (now 18) and a comparatively “normal” young man named Lucas.

It’s the meeting of the two families — with the Addamses expected to be on their best behavior, and Lucas’ parents hoping to conceal their troubled marriage — that drives the show.

Actually, most of “The Addams Family” is driven by couples conflict, to the point you wonder if everyone should just get therapy. Morticia’s sense of her own mortality drives a wedge between her and Gomez’s desire for another tango dance. Pugsley worries that no one will be around to torture him if Wednesday flees the family nest to marry Lucas. Even Uncle Fester has romantic issues.

Derivative though it may be, “The Addams Family” still taps into the occasional darker impulses. That’s fine with Rucker, who used to pore over the Addams cartoons at a bookstore while working in the French Quarter. He still remembers those ashen, Edward Gorey-like illustrations.

“I told our production designer, ‘That’s our bible,’ ” he noted.

While Rucker found Missakian for Gomez through an audition — a process that last year produced the critically praised Kevin Murphy for “Shrek: The Musical” — casting Morticia was a no-brainer. Beck, familiar to theatergoers for her musical and Shakespeare Festival work, gets to tap into her inner Goth chick in this role. A fan of Kander-Ebb musicals, Beck has played Sally Bowles and loves looking at the dark side.

“I’ve always been sort of into the macabre,” she said. “I don’t like horror movies; I don’t like gore and that stuff. I like super-spooky stuff — Tim Burton and Edgar Allan Poe and Edward Gorey. I’ve always kind of gravitated to all of that stuff. I think really ’cause I fear death a lot. I love things that sort of turn that around and celebrate it, and it’s just, ‘Let’s face our fears and get close to it.’

“Morticia is obviously an iconic character within that genre.”

So it’ll be a treat to see how Beck can bring an edge to a vaudeville-inspired number such as “Death Is Just Around the Corner.” Or the entire production, for that matter.

Rucker warms to these kind of situations. He recalls he and co-artistic director Kelly Fouchi taking on the problematic Elvis Presley jukebox musical “All Shook Up” at Le Petit a few years ago, taking the “clunky” story and somehow making it work. “The Addams Family,” creepy and spooky as it is, will be interesting to stage.

“It’s been a real challenge making it recognizable,” Rucker said.