Los Angeles is a city of background noise. No matter where you are, listen close and you'll probably hear the distant thrum of freeway traffic or the buzz of a passing helicopter. We're so used to it, we barely notice it.

Maybe that explains why The Milk Carton Kids, the most successful folk duo to emerge from L.A. in recent years, are so obsessed with silence. They do notice the noise. They once asked a bar in Cleveland to unplug its beer refrigerator because the hum was too loud. As they became more established, they would play only at venues with no bar or food service inside the theater, so that their spare sound — two harmonizing voices and two acoustic guitars, amplified by only a single microphone — wouldn't have to compete with clinking silverware and rattling cocktail shakers.

“We're potentially too precious about our show,” Joey Ryan admits, between bites of a Reuben at Greenblatt's Deli, down the hill from his Laurel Canyon home. He's the taller Milk Carton Kid, a 33-year-old with a deadpan demeanor and a mop of tousled brown hair. “But it's also a response to the fact that for four years we ran around North America with no options. We just had to play whatever room would have us.”

Those four years culminated in The Milk Carton Kids' big break: an appearance in the Showtime documentary Another Day/Another Time: Celebrating the Music of Inside Llewyn Davis, which chronicled a one-off concert featuring music from and inspired by the 2013 Coen brothers film. Even alongside such luminaries as the Avett Brothers, Gillian Welch, Jack White and Joan Baez, Ryan and partner Kenneth Pattengale's breathtaking harmonies stood out. During a rehearsal performance of their song “Snake Eyes,” the camera panned through the studio to reveal a quietly awestruck Marcus Mumford wiping a tear from his eye.

“That was the most nerve-racking three minutes of my life,” says Ryan, who still believes that, as the new guys on the bill, they weren't so much rehearsing as auditioning. But he and Pattengale were thrilled when they saw that the cameras had captured both Mumford and Ethan Coen getting weepy. “We got lucky with that scene.”

Ryan and Pattengale met at Hotel Cafe in late 2009. Both had worked for years as solo artists, but without much success. “Our albums as solo artists were defined by a lack of any discernible identity,” says Ryan, who grew up in West L.A. “It was sort of disparate and floundering.”

Pattengale, also 33, an Eagle Rock native who now splits his time between New York and Nashville, echoes this sentiment. “I spent eight years prior to Milk Carton Kids doing music that some people were interested in — not very many,” he says with a self-deprecating laugh. He's baby-faced and quicker to scowl or smile than his more inscrutable partner. “When Joey and I started, it was very clear that we struck upon something that immediately resounded with people.”

That something is a pared-down approach to folk music that borders on the ethereal. On Milk Carton Kids' four albums — including their latest, Monterey, out last week on Anti- Records — Ryan's and Pattengale's voices weave together in hauntingly close harmonies over Ryan's gently strummed 1951 Gibson J45 and Pattengale's rich but muted leads, played on a battered 1954 Martin 0-15 with a handkerchief tied over the neck to keep the strings from buzzing. Their sound evokes other folk duos past and present — The Everly Brothers, Simon and Garfunkel, Welch and Rawlings — but has a fragile magic all its own.

The duo recorded about half of Monterey while on a 55-city tour last year, setting up microphones on the stages of the old churches and theaters that are their preferred performance spaces and trying, as much as possible, to capture songs in a single take, with no overdubs and a minimum of edits. They completed the album in a Nashville church that “felt like the 56th venue,” in Ryan's words. “We wanted to do the opposite of renting a cabin in the woods; we wanted making the album to be just another thing that we were doing that day.”

Those who love The Milk Carton Kids' music are nearly as enamored of Ryan and Pattengale's between-song banter, which breaks the spell of their gorgeous songs with dry, occasionally caustic humor. Ryan does most of the talking while Pattengale tunes — but when Pattengale does speak, he often undercuts his partner to hilarious effect. “I can be a bit of a dick from time to time,” Pattengale admits.

“It was something we came by honestly,” Pattengale says of their droll chemistry. Ryan naturally takes the lead, partly because he needs to tune less frequently and partly because, as Ryan notes, “It's the only time I get to be improvisational.” During the duo's songs, only Pattengale's lead-guitar filigrees vary from night to night.

Banter was also, in the duo's early days, a necessary survival skill, honed to hold the audience's attention between songs in noisy bars and nightclubs. “It's not an easy thing to stand on a stage and have anything come out of your mouth that doesn't seem entirely ingratiating,” Pattengale says. Asking for silence proved easier when it was done between jokes.

The Milk Carton Kids' mix of reverent songcraft and irreverent humor made them an immediate hit at Largo, the venue that has served as an unofficial hub for L.A.'s singer-songwriter community for two decades. And since moving from its old supper-club location on Fairfax into the Coronet Theatre on La Cienega in 2008, Largo is now the embodiment of Ryan and Pattengale's ideal space: a midsize room with no bar, good acoustics and an audience accustomed to giving quiet performers their rapt attention.

“Largo does everything exactly right,” Ryan says. “I've yet to find fault with any of their practices.” Pattengale calls it “the ideal 280-person listening room, certainly in the United States; I'd say that it probably gives anywhere in the world a run for its money.”

Booking similar venues elsewhere around the country isn't easy. Pattengale and Ryan often find themselves at loggerheads with their own agents and management over decisions about where to play.

“It frustrates our agents,” Ryan admits. But the frustration can be mutual. “You're telling me in Houston, Texas, there's not a fucking theater?” he says, recalling one particular dispute. “There is a theater in Houston, somewhere. It's just that everybody only thinks about the rock clubs. So we go on Google … and we'll send the agents a list of seven places that would be perfect.” (For their next tour, they'll play their Los Angeles stop at the Theatre at Ace Hotel, where the bar is in the lobby, on Oct. 1.)

Call them precious or high-maintenance, but as far as The Milk Carton Kids are concerned, it's worth sweating the small stuff in order to preserve the integrity of their melancholy, contemplative sound.

“From an artistic perspective, to me that's sacred,” Pattengale says. “From a business perspective, I think it's crucial. The stupidest thing The Milk Carton Kids could ever do is go into a room where, five times during every song, somebody's shaking a mixed drink at a bar. What we do, that stuff gets in the way.”

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