A few days into the recording of their new album “Silfra” in Reykjavik last year, violinist Hilary Hahn and Hauschka, a German composer and prepared-piano virtuoso, noticed ashes drifting into the recording studio. Grímsvötn, a volcano on the other side of Iceland, had erupted, and a coating of ash had come through the open door of Greenhouse Studio. It was May, a time when the sun set for only a few hours a day and there was little darkness; but, Hahn said in a recent interview, during the eruption, “we actually got nighttime.”

Some of the people who worked at the studio wanted to find a way to get to see the volcano. The two musicians, Hahn said, “hunkered down and worked.” Hahn and Hauschka (whose real name is Volker Bertelmann) created “Ashes,” the ninth track on “Silfra,” which captures the gentle yet foreboding alteration of the sky’s color. Hahn’s violin offers spare fragments of melody over the muted, metallic tone of Hauschka’s prepared piano, punctuated by a few unsettling rumbles at the bottom of its range.

Like the other 11 tracks on “Silfra,” “Ashes” was completely improvised, created in the studio without any preset plan or rehearsal. Hahn and Hauschka – who play a concert at the Institute for Contemporary Art next Thursday – spent two years building a musical relationship that allowed them to create music of hypnotic beauty on the spot.

It is yet another step forward for Hahn, whose career already ranges from her instrument’s repertoire, new and old, to tours with singer-songwriter Josh Ritter to playing on records by the alt-rock band . . . And You Will Know Us By the Trail of Dead. Some of those projects had involved a limited amount of improvisation. But, she said last week from Tokyo, “I wanted to work with someone where I would not just join in and enhance but, rather, see what it’s like to start from scratch.”

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Hahn and Hauschka were brought together by folk musician Tom Brosseau, who had toured with each independently. The two met in 2009 and took to each other, artistically. “It struck me that it would be fun to just play stuff with Hauschka,” Hahn said. “Not even have a project in mind, but just get together and make up some music and see what came out.”

Over the next two years, they created music wherever they could — in the same city when their travels coincided, swapping files when they couldn’t. Originally Hahn thought that they would work out ideas and write them out. “But it wound up being better for us to just improvise. We had more fun and learned more from each other just doing that.”

Going into the studio, Hahn explained, wasn’t initially about making a record; the pair just wanted to strengthen the musical rapport that had blossomed, and needed time and focus to do so. Greenhouse, a live-in facility, allowed them that, as well as the services of producer Valgeir Sigurðsson, who’s worked with Björk and Nico Muhly, among others. “There’s this feeling of creativity in Iceland,” said Hahn. “It just felt like a good, open space to do something creative, something we’d never done before.”

Mostly Hahn and Hauschka listened to one another, trying to get themselves in that mindset that allows one musician to listen to an idea, then extend and reshape it, in real time. It came remarkably quickly.

“After a while, we started doing chord changes in the same place,” said the violinist. “The partnership grew to a point where it felt like the right place to develop something new – just at that moment, the other person would make the exact same change. It’s not exactly instinctive, where you just do whatever occurs to you; you develop a feel for the other person’s direction just by playing together.”

After a mere 10 days of recording, with overdubbing on some tracks, they had a fully produced record, and Hahn still sounds kind of amazed by how quickly it came together. Many of the tracks are ambiguous, open-ended dialogues. Hahn’s tone is silvery and beautiful, while Hauschka’s piano – filled with various objects, including ping-pong balls – sounds alternately fragile and noisy. “Rift” creates a desolate landscape, while the 12½- minute “Godot” demonstrates the prepared piano’s sonic range in all its dark, plunking glory.

Given the spontaneity that went into “Silfra,” the live shows that the duo are playing present a tricky question: How can each concert be newly created when, as Hahn put it, “we have the record in our head now”? They’ve opted for a sort of middle ground, where they quote snippets from the record, so that audiences will have something to grasp, but get at them in a new way. “It’s like remixing,” she explained.

“It’s important to keep moving forward as well – to keep developing the musical language and keep figuring out what we can do that’s new. Every time, I try to do a couple of things I’ve never done before. It’s not exactly touring the record; it’s touring the process we put into making the record. And maybe that will help bring people into that space better than if we were actually doing something else.”