That attention has grown steadily since 2013, when Webster, then 16, self-released her debut album, “Run and Tell,” a folksy whirl of slide guitar and twang. She grew up in Atlanta, where she still lives, listening to her mother play Allison Krauss records and bluegrass fiddle songs, an aesthetic she has incorporated into her own music. But she has also moved, solidly and smoothly, into a middle ground between indie-rock and country — pedal steel mashed with bass, simmering drums beneath tropical synths — as she homes in on the banal brutalities of relationships.

On her new album, “Underdressed at the Symphony,” out Friday, she traces the minutiae of piecing herself together after a breakup: She congratulates herself for eating before noon, scrolls through her eBay search history, reminds herself to call her mom.

Webster is reluctant to call it a breakup record. “I wish there was a better term for it,” she said, after sighing. The first song she wrote for the album, “But Not Kiss,” began with a 10-second voice memo she brought to the studio. She slowly unspools the line, “I want to sleep in your arms,” and then, after a pause, rushes out the words, “But not kiss.” She had been searching for music that could speak to that feeling, what she calls “an anti-romantic love song.” When she couldn’t find it, she wrote it. “I was able to create this really off-balance, contradicting almost, meaningful thing,” she said.

The title comes from a ritual she started in the months after her split. She would decide to see the Atlanta Symphony Orchestra, a 15-minute drive from her house, moments before a performance was set to begin. “It was therapeutic to me,” she said. “I was like, nobody knows me, I don’t know anybody here, they don’t care about me. I’m incognito, and I’m listening to music I don’t know anything about.”