“Fantasy” is a theme of superstar violinist Hilary Hahn’s current recital tour, which is making its way to Meany Hall for the Performing Arts next Tuesday, April 29.

It’s not, however, the kind of musical fantasy Hahn enthusiasts engage in while waiting for her next concert.

In the world of music, fantasy goes back to the 16th century and refers to imaginative, free-form compositions largely devoid of ties to pre-existing genres. The emphasis in fantasy was and is on inventiveness, ideas and virtuosity and has appealed to the expressive side of composers from the Baroque era (J.S. Bach) to recent years (John Corigliano).

Many historic fantasies were written for solo keyboard performances.

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But Hahn, 34, a Grammy-winning artist who’s been playing professionally for 20 years, says some of those fantasies lend themselves quite well to violin and piano duets. That’s good news for Hahn and her current recital accompanist, pianist Cory Smythe.

“The pieces in the program are not typical sonata formats,” Hahn says.

“There are variations on themes that allow us to take advantage of possibilities as a duo.”

Hahn says a Mozart sonata for violin on the bill has a fantasy edge, while some of the other pieces she will play — Telemann’s Fantasia No. VI in E minor for Solo Violin; Schubert’s groundbreaking Fantasie in C major (“Wanderer Fantasy”); and Schoenberg’s Phantasy for Violin and Piano — are illuminated by being linked in one program.

“We started rehearsing the Schoenberg and then said, ‘Hey, what about the Schubert fantasy, too,’ ” says Hahn. “I had also been interested in learning the Telemann piece for a while, so I figured this would be the right time. This program extends over quite a few centuries, ending with new pieces by Anton Garcia Abril and Richard Barrett, which were written for the ‘Encores’ project.”

That project is Hahn’s latest and most significant contribution to violin repertoire. While she is no stranger to commissioning new music — Hahn has premiered concertos written for her by bassist Edgar Meyer and her former music professor, Jennifer Higdon — she embarked on ambitious plans a decade ago to persuade 27 composers to write short works for diverse, exciting encores.

The result — “In 27 Pieces: the Hilary Hahn Encores” — has consumed much of her career the past few years. Hahn has been busy seeking sponsorships for each piece, taking the new works on tour, recording a double album (“In 27 Pieces”), hosting YouTube video interviews with some of the composers (who include Higdon, Japan’s Somei Satoh and Oscar-nominated composer James Newton Howard), and publishing the original scores to ensure those encores are available to others.

On her current tour, Hahn is introducing the last of the encores (Abril’s “Third Sigh” and Barrett’s “Shade”) in concert. While, in some ways, those debuts represent the end of an era in Hahn’s life, she remains enthusiastic about the next phase of “In 27 Pieces.”

“It feels like a beginning in a way, because there are other, different phases to a project,” she says. “When you start out, you don’t know what form it’s going to take. In time a project fulfills itself, and the global audience begins to internalize the results. One of the most rewarding things is that beyond putting individual pieces together, the project put people together in ways that might never have happened.”

Tom Keogh: tomwkeogh@gmail.com