Sometimes you need to isolate the parts to comprehend the whole. The first time I heard Jewellery, the debut of London avant-pop trio Micachu & the Shapes, it sounded so willful that I didn't quite trust it. It's an easy response—too easy—and even then, there was something almost bubblegum beneath the brittle surface, but revisiting it seemed daunting.

Then I started listening to "Golden Phone," the album's single, on its own—as a single. It still sounded willful, but there was intrigue, too: Someone decided this odd thing should be on the radio—clunking guitars, cheerfully cheesy keyboard, lumpy beat, flat take-it-or-leave-it vocal, and all. What's more, it turns out they were right: "Golden Phone" is the kind of song you keep playing simply to figure out what's going on, and then you find yourself hooked and wanting to hear more. Jewellery didn't simply make more sense in the single's light. It, too, grew addictive: What once seemed arch grew to sound... almost natural.

Or if not natural, then at least homemade in a way that suggested that Mica Levi, aka Micachu, the 21-year-old mastermind behind the project, valued happy accidents as much as thought-through composition. Take track "Turn Me Well," which opens with the sound of a vacuum cleaner before sliding into a slithering beat-driven lament: "You squeezed my heart so tight tonight/You must return it before you leave."

"'Turn Me Well' began as a piece for soprano and someone hoovering while breathing continually through a harmonica," Levi explains via e-mail. "But in the end, I made this grime beat and arranged it as a sort of ballad thing. I initially wanted to start the record off with a Hoover switching on. The song is about a long-term relationship like marriage and how lust often evolves into something more codependent but less enjoyable."

The other songs on Jewellery are no less specific. "Calculator" begins with chunky, familiar acoustic-guitar chords—"The beginning riff is [an] homage to the song 'Tequila,'" Levi notes—before turning into a jagged post-punk rocker. "It's about technology taking over the world," she explains. "The keyboard is supposed to sound like random button-pressing." (It does.) "Golden Phone" may have simply been, per Levi, "an effort to write a solid pop song [with] a simple riff and a sickly chorus," but the lyrics are anything but straightforward. "The lyrics are nonsense," Levi avers, but also that "it's about suicide"—the "golden phone" of the title refers to the suicide hotline at San Francisco's Golden Gate Bridge.

The anything-goes bent of Jewellery is hardly surprising, given that its producer is notorious tinkerer Matthew Herbert, whose studio full of "interesting hardware" was, Levi says, crucial to the end product. ("He was quite keen to nurture my megalomania, which was great," she enthuses.) Additionally, Levi's musical background is notably varied even for the iPod age. She builds her own instruments: The name Micachu is a combination of Levi's first name and the "chu," a small guitar modified with a bass string and played with a paddle. Levi has also been involved with the UK garage and grime scenes, as well as studying composition at London's Guildhall School of Music & Drama, where she wrote an orchestral piece for the London Philharmonic Orchestra.

The Shapes have gotten the thumbs-up from Levi's mentors: "Everyone's impressed I have my own CD! The institution I studied at is really supportive of anyone doing anything in music as a job. It's hard to get work, especially as a classical musician. I was expecting to do work in a shop and [do] composition in my spare time, or study for as long as I could for free like most composers. I probably will still end up doing those things."

For now, though, she's happy to be in a band. "[The Shapes] are beginning to write more together, which we all really enjoy. We know each other's taste pretty well now. Playing the same songs all the time is boring, but we try to alter things to freshen it up. The real difference for me being in the band is that it's not just an ensemble playing dots you have written. We have a relationship, and it can give you more confidence to try things out. It's more sincere."