Violinist Leila Josefowicz walks an interesting line between unconventionality and orthodoxy. (Chris Lee)

When the violinist Leila Josefowicz walks on stage, you know she’s a different kind of performer just by looking at her. Her concert attire is angular, sculptural, distinctive. It’s created for her by the designer Jenny Lai, who specializes in inventive approaches to performance attire, and it meets her specifications — not least in that it’s supremely comfortable. “First and foremost,” the violinist says, “I actually want to forget what I’m wearing on stage.”

Josefowicz, 40, is a former child prodigy. After years of wearing “white lacy dresses with bows in my hair,” she says, and abiding by dictates about what she could and couldn’t wear on stage, “I have an absolutely allergic reaction to all of these things.” After trying on one of Lai’s prototype blouses, Josefowicz says, she “gave her all these gowns I had in my closet, and she cut them up and made them into shirts.”

“I’m sure some very conservative people look at me and think I’m off my rocker,” she says, “but that’s fine. I’m proud of myself.”

Josefowicz’s stage appearance matches what she’s done with her career. A big-name soloist, she plays almost exclusively new music — such as the violin concerto by the 65-year-old Scottish-born Oliver Knussen, which she is playing this week with the National Symphony Orchestra as the second installment of a three-part Kennedy Center residency. “It’s more rare for me to play a nonliving composer than a living composer,” she says. When she does play a piece by a dead white male, it’s generally a 20th-century master such as Stravinsky (whose violin concerto she’ll play with the NSO in April) or the German composer Bernd Alois Zimmermann — “To me, he’s one of the greats,” she says — whose concerto she will record in May. To many audiences, even Stravinsky still seems newfangled. To Josefowicz, he’s an anchor of convention in an expanding personal canon.

“When you have so much distance from the original source, it puts everything into a museum,” she says, of the standard classical repertory. “I prefer a living museum.”

And that’s exactly how she presents the work.

“This is something that hasn’t happened often in my life,” said the composer-conductor Esa-Pekka Salonen of the first time he worked with Josefowicz, in Knussen’s concerto. “It’s a very good piece, of course, but she played it with the same kind of commitment and panache as if she were playing Brahms or Sibelius. She approached it like a masterpiece. And then it comes across as a masterpiece. It’s contagious, and that sort of approach transmits energy to the audience.”

Salonen promptly asked her whether he could write a violin concerto of his own for her — and was impressed anew by her authority.

“When we started this process, she said, ‘Remember not to put too much s--- in it,’ ” he said. He asked her to clarify. “She said, ‘I can do a very expressive thing on one note if you let me,’ ” he explains. “She was referring to a sort of over-busy-ness, an over-manipulation in contemporary music, which often happens. . . . Music happens often with less notes, less events per second.”

And then, when he was finishing the work, the violinist, who can rise to any technical challenge, pointed to one passage at the end of the third movement and said, “I’m not going to play that; I’m not going to go anywhere near this; rewrite it,” he says. “I was taken aback, of course, but she said it with such firmness and confidence that I thought, ‘Okay, yeah, listen to this person.’ And I did rewrite the last two minutes of the movement, and it came off better.”

A number of classical soloists are creating maverick careers within the standard concert establishment. The pianists Simone Dinnerstein and Jeremy Denk, the violinist Jennifer Koh; and the soprano Barbara Hannigan are just a few of the artists known for exploring less-trodden pathways while remaining largely within the framework of a conventional classical concert career, seeking out a creativity that an exclusive diet of the standard repertoire of masterworks, great though it is, doesn’t necessarily provide.

Josefowicz’s particular terrain is new music by blue-chip composers, a particular slice of contemporary classical orthodoxy. She has given dozens of performances of concertos by Knussen and Salonen, Thomas Adès, and especially John Adams, who wrote his most recent violin concerto, “Scheherazade. 2” (described as a “dramatic symphony for solo violin and orchestra”) for her, and whose first violin concerto she recently recorded with David Robertson and the St. Louis Symphony Orchestra, to be released later this year.

“I feel like I sort of came into this at a very crucial [time],” she says. “When I started work with John Adams, he was really just starting to skyrocket into being the composer that he is. His first violin concerto had already been written and performed a few times. I thought, ‘This is something really different that I can get excited about.’ Oliver Knussen’s piece had been written too . . . and Tom Adès’s as well. These pieces were ready to be taken around by an obsessive like me ready to devote all their energies to communicating these pieces. . . . I just couldn’t go along the conservative path.” She continues to focus on new commissions. “Once a year is not realistic,” she says, “but at least every other year.” The next two are by younger composers, Andrew Norman and Daniel Bjarnason, “a very exciting composer from Iceland.”

She walks an interesting line between unconventionality and orthodoxy. Apart from Kaija Saariaho, whose music she played at her Kennedy Center recital in November, most of her favorite composers are white and male; she reacts vehemently to the idea of selecting a composer by any criteria other than her own visceral response (like, for instance, gender). “When I hear something in conjunction with looking at the score,” she says, “I literally have sort of a physical reaction to it — not if I dislike it, but if I really like it I get sort of a fire inside. It happens every single time I’ve made a decision to go with something. I know that if I don’t get that feeling, I don’t love it enough. . . . It’s not a decision; it’s like I have to do it.”

And when she does do it, it goes deep into her memory bank.

“When we were recording the Adams violin concerto,” says Robertson, the conductor, “it was almost spooky, like random access memory we know from computers. I would say, ‘We’re going from here,’ and she would be there. . . . It’s like you can drop the needle anywhere on the LP.”

“A lot of times,” he continues, “when people have that incredible mnemonic dexterity, they need to do something quite similar every time or it goes out of the groove. However, somehow she’s absorbed the material. It’s organic within her. When you do three or four performances with her of something, [it’s remarkable] to hear it continue to expand and never be the same thing. . . . She can play Tchaikovsky, or Paganini, but what really gets her excited is this engaged musical discourse that her contemporaries have. She is able to invest it with this mother-tongue quality. She speaks the language of the composer without waiting 50 years for everybody to catch up.”

Josefowicz doesn’t memorize everything. “There are certain languages that lend themselves more easily, at least in my weird brain, to memorization than others,” she says. She also doesn’t absorb everything at first playing. “These scores, some of them, are so difficult and require time,” she says. “It’s one thing to understand the language that they’re writing, and another thing to make that language a natural part of your playing and sort of mental state.”

It’s becoming a cliche to portray performing artists as just folks who happen to have this remarkable gift on the side. This is disingenuous. It takes fiendish focus to create this kind of artistry, from childhood on. Although Josefowicz’s parents wanted her to have as normal a school experience as possible, enrolling her in public schools even after the family, originally from Canada, moved from California to Philadelphia so Josefowicz could attend Curtis, one of the preeminent conservatories in the United States. “Nothing about it was normal,” she says now.

But there is plenty of life outside music, which is more “normal” than many major soloists can manage. A self-described “SoulCycle fanatic” and yoga practitioner, she has wide-ranging pop-music tastes (Amy Winehouse and David Bowie are among her heroes). She is also raising three children ages 3, 5, and 17, from two marriages, “solo with my mom,” she says. Her mother comes down from Canada to help out when she goes on the road. “It’s very busy around here,” she says, “but it gives me a lot, and I don’t think I would be as good a player if I didn’t have these people in my life.”

Breaking free of the prescriptions and finding her own way has yielded abundant rewards, internal and external — like the MacArthur “genius” grant she was awarded in 2008, when she was 30.

“Part of my goal was for people to trust me,” she says. “Administrations, orchestras, audiences. If I choose a new work, I hope they would think there’s something interesting about this that I would like them to hear. It doesn’t mean everybody’s going to love it, but that they find it interesting in some way or get something different out of it. Even if it’s something as simple as, I heard a new sound tonight. Or I got a new almost tactile feeling from this certain chord. You can even dislike it, and dislike it a lot, and that’s a reaction. I’m hoping to rouse people in some way. I guess what I would like the least is if they didn’t feel anything.”

Leila Josefowicz performs Oliver Knussen’s violin concerto with Christoph Eschenbach and the NSO on Thursday at 7 p.m. and Saturday at 8 p.m. at the Kennedy Center.