“I know the feeling of being made of glass myself,” says Danish singer/keyboardist Agnes Obel, reflecting on Citizen of Glass, her third album. She doesn’t just mean being a European star in today’s world of social media oversharing, even though the title came from the German term “gläserner bürger” (meaning “glass citizen”), which Obel saw in a magazine article about privacy and surveillance. “It wasn’t just the political idea, but it was also the feeling of being sort of fragile.”

The Berlin-based musician realized her own fragility a decade ago when she went from playing in bands to pursuing a solo career. “I was quite overwhelmed by the whole thing, especially performing—I felt very exposed and vulnerable,” says Obel, 36. “I don’t show any of my music to anyone until it’s almost completely done. It’s a secret that I have with my piano and my mind and the melody.”

Now the secret’s out—to some degree, given the abstract, ethereal nature of her austere chamber pop. After two albums that topped the charts in Denmark and Belgium, she’s expanded her reach with Citizen of Glass, released in October.

“I liked the idea that we were all these glass citizens walking around, potentially just about to break,” Obel says from her mother’s home in Copenhagen. “I also felt like glass had a sound. When I heard [the term], it sounded like something that could be turned into music.”

To paint the self-produced album’s icy textures, Obel employed keyboards from piano to mellotron to trautonium, an early-20th-century synthesizer with metal keys and wires to press for vibrato. “I wanted to have some metallic and high sounds, a sharper kind of sound,” she says. “The trautonium is perfect for that.”

Obel says she particularly liked the edgy sound of trautonium when mixed with strings. And she used a violinist and two cellists to outsized effect on Citizen of Glass, compiling 250 layers in conjunction with vocals, keyboards and percussion.

“I’ve always been into minimal instrumentation, and I think I still am,” she says. “I really wanted to have a ceiling of tension built into the songs. And I was trying out different ways to do that, and I found that if I made these crescendos or swells of strings, it could sound like that. Obviously I didn’t have a whole orchestra at my disposal, [and] I was sort of arranging it while I was recording.”

For a tour that includes a March 8 date at the Sinclair, Obel is joined by three women who double on cellos, loops and percussion in addition to lending mellotron, bass clarinet and ukulele. “We had a lot of rehearsals before we were able to play any of the songs,” Obel says, “just figuring out how we could do this.”

They all sing as well, helping to reproduce the album’s vocals, which were partly inspired by Obel’s listening to choral music and a Bulgarian women’s choir. She also experimented with manipulating her voice, to especially spectral effect in “Familiar” when she sings, “Our love is a ghost that the others can’t see.”

“It’s a secret love thing. And the secret becomes a ghost in the life of the person in the song, and I wanted the ghost to sing the chorus,” says Obel, who altered her voice with a pitch-shifter, evoking a man. “It sounded a little like a nightmare.”

That low-pitched alternate voice reminded her of the singer Scott Walker, whom she credits for making “songs that are like a state of mind.” She cites him among her key influences, along with Portishead and the Swedish jazz pianist Jan Johansson.

Obel grew up in a musical household, though her parents pursued other careers. Her mother played classical piano, while her father listened to jazz and collected old instruments. “Before I was born, he’d been a musician, a jazz guitarist,” Obel says. “And there definitely was an element of sadness that he wasn’t anymore.”

Her father died shortly before Obel tackled her most ambitious album. She’s hesitant to describe how he specifically inspired Citizen of Glass—and not just to keep that secret, noting, “Being aware that we don’t know everything is very important.”

Agnes Obel plays the Sinclair on March 8.