Dysfunctional families abound in today’s independent movies, and we’re introduced to yet another in Gillian Robespierre’s period comedy. In “Landline,” set in the New York City of 1995, the Jacobs family—father Alan (John Turturro), mother Pat (Edie Falco) and daughters Dana (Jenny Slate) and Ali (Abby Quinn)—are a loving but troubled lot. Alan, a frustrated playwright stuck in a dull job composing ad copy, tries to keep up a happy face, but he’s constantly put down by his sharp-tongued wife, a hard-driving businesswoman who views him as a failure. Dana is bored by her live-in relationship with pleasant but humdrum Ben (Jay Duplass), while Ali is a typically rebellious high schooler, who particularly resents her mother’s surveillance as she deepens her friendship with classmate Jed (Marquis Rodriguez).

The plot revolves around infidelity. Dana slips into an affair with a pal from college, handsome Nate (Finn Wittrock). Meanwhile Ali discovers, while examining her father’s clunky computer, that he is apparently cheating on Pat with a lover simply called “C.” Dana moves out of the place she shares with Ben and returns home—supposedly temporarily—when Ali tells her about their dad’s indiscretion, and they team up to try to find out who the other woman is.

Part of what might draw you into this farrago of domestic shenanigans is the mid-nineties setting, which allows Robespierre to play around with technology that seems, from the present perspective, almost absurdly primitive. Not only are there no cell phones, but there are even stores stocking real CDs you can sample in listening booths! The time warp aspect of “Landline” would seem irresistible.

And so it might be, if the characters were even remotely likable. It’s not simply that all of them seem to be deceiving one another somehow, but that while the men are basically low-key sleazy (Wiitrock’s Nate) or doormats (Turturro’s Alan, Duplass’ Ben), the women are screeching banshees. Slate, who has been amusing before (she also starred in Robespierre’s “Obvious Child,” and was recently in “Gifted”), is intensely irritating here. The character, who’s duping her boyfriend, might come across like a self-centered jerk anyway, but Slate doesn’t ameliorate Dana’s flaws at all, endowing her—among other things—with an eardrum-piercing laugh that would presumably send any potential suitor fleeing into the night. Yet we’re supposed to believe that both Nate and Ben are smitten with her imperceptible charms—which would win back even a man she’d treated like dirt.

Falco is almost as shrill, berating her husband consistently as a nothing until she finds out about his infidelity, at which point she’s desolate. (“You broke the rules,” she tells him.) To be sure, Alan is a nebbish, and from what we hear of his latest play (publicly read at a friend’s house), he’s also an untalented hack. But to be referred to repeatedly as a nothing while trying to keep a game face even when humiliated makes you want to sympathize with him. Duplass gets less opportunity to tug at our heartstrings, but he comes across as a nice enough schlub.

That leaves Quinn, who makes Ali basically a younger version of Dana, in terms of loudness and volubility She’s not as insufferable as Slate, though, simply because her character doesn’t have anybody to betray, although she’s adept at lashing out against her sister and parents with the best of them. Quinn is at her worst when Ali teams up with Dana in their quest to track down Alan’s paramour. Doubled up, the two seem to feed off one another’s worst qualities, and the result is exponential aggravation. A scene where the sisters literally drive everybody else from a swimming pool with their raucousness sums things up perfectly.

The technical side of the movie is okay—Kelly McGehee’s production design has some nice touches, though Chris Teague’s cinematography is nothing special. Neither, unfortunately, is the movie—a slender indie sitcom, peopled by characters who are simply annoying rather than quirkily charming.