Grit and grace with the band Sleepy Kitty

“There’s something fascinating about a two-piece, because there really just aren’t enough people to do all the parts,” says drummer Evan Sult (right, with guitarist and vocalist Paige Brubeck).Shervin Lainez

Grimy meets shiny in Sleepy Kitty’s music. The duo’s chugging drums and crunchy guitars are sweetened by catchy melodies and vocal harmonies that summon memories of 1960s-era girl groups.

Take “Seventeen,” which transmogrifies the Beatles’ “I Saw Her Standing There” into a clanging drone that directly channels the Velvet Underground.

“Everything that I love about music, especially rock band music, is something about the texture of the noise and those textures relative to each other — something really smooth against something really grating or rough,” says drummer Evan Sult, 40, who forged the group with guitarist and vocalist Paige Brubeck in late 2008.

The aesthetic extends even to the band’s posters, which the pair create themselves along with all their album art. “All the crap and noise and staple holes and torn edges and all of those things, those are at least as important as whatever the pictorial image is in a rock poster, as far as getting across that this is what you’re going to see,” Sult says. “When somebody walks by on the street and sees it . . . I want them to have an impression that they know something about what we sound like, because they saw a poster we made that looks like a sound.”

Sleepy Kitty grew out of experimental jams the two held while Brubeck was still a student at the School of the Art Institute of Chicago. (An earlier band of Sult’s, Harvey Danger, emerged from the Seattle alt-rock scene in the late-1990s.) Their sound solidified into a style that bears the three-dimensional heft of some of their favorite ’90s-era bands, but is lightened by Brubeck’s vocal harmonies and conversational lyrics.

Their two LP records feature plenty of overdubs, creating an effect that Brubeck replicates in concert, to an extent, by busily working guitar and vocal loops. (Sleepy Kitty plays the Red Room at Café 939 on Saturday.) She’ll lay a rhythm track underneath a lead guitar line, or harmonize off her own vocals. But they aim to speak in their own musical vocabulary, not compensate for a missing bassist.

“I guess it started with the convenience of both being there and playing music together. But after a while we really got into the challenge of it and what it feels like to play as a two-piece,” says Brubeck, 28, who, like Sult, speaks on the phone from Chicago between tour dates. “I’m very aware that if I stop playing guitar all of the melody instruments in the entire band stop playing. There’s a pressure to that, but it’s kind of exciting too. It gives you a lot of space and freedom but also a lot of restrictions.”

Sult sees this as the reflection of an essential interplay that’s always going on between band and listener. “There’s something fascinating about a two-piece, because there really just aren’t enough people to do all the parts,” he says. “One of the things that happens in indie rock is that what you’re listening to is partly what you hear on the album and it’s also partly the potential that you hear. You hear more than the sum of what’s there, and that’s part of what’s so exciting about it.”

In keeping with their multimedia interests (Brubeck and Sult, who are also a couple, run a screen-printing studio), the newly released sophomore album, “Projection Room,” is dense with influences from film and other art forms.

For the peeling guitar solo at the center of the ambitious new tune “Godard Protagonist Inflection,” Brubeck attempted to mimic the odd cadence with which a certain character in a Jean-Luc Godard film speaks. “The Agony and Ecstasy of Mike Daisey” references the actor/monologist. “Speaking Politely,” from Sleepy Kitty’s 2011 debut, “Infinity City,” makes musical reference to George Gershwin’s “Rhapsody in Blue.” Another song recounts the long wait for an amusement park ride based on the Batman character.

Many of the references in Sleepy Kitty’s songs, musical and otherwise, spring from its members’ shared interests and experiences. But Brubeck says she’s not looking to keep listeners at arm’s length. “It’s meant to be welcoming. Even if you don't know what these references are, you can find out. I don’t want it to be an exclusive thing, even though it’s a very specific thing,” she says.

“Projection Room” initially took shape as an opportunity to “get the most from our vinyl,” Sult says. The record label run by Euclid Records, in the band’s adopted home of St. Louis, was committed to putting their work out on vinyl. Though Sleepy Kitty only had an EP in mind, it seemed a shame not to go all the way and take advantage of the length of an LP.

“We’re not used to format really affecting length anymore, because the mp3 is such a common thing,” he says, “but it was the physical format of the vinyl that led us onwards towards making an album. Which is exactly what I want. I want the physical object to affect the band that we are.”