Many people only know classical music from high school orchestra concerts. For others, public television’s “Live at Lincoln Center” is the closest they’ve been to a concert hall. Having the time and patience to sit through a 15-minute violin solo or a 30-minute symphony is a virtue these days, and it’s also something less and less people are doing on a regular basis.

But, it’s a task that can be well worth the undertaking if a person is in the right mood and has enough background to understand and recognize brilliant music when it’s being performed. Music aficionados, especially those who love indie rock or hip-hop, are often overwhelmed by new music. There isn’t enough time to hear everything, and, occasionally, one feels the need to put down the iPod and just take a break. Classical music, in this case, might serve as an audible breather, a reminder of what pure songs really sound like.

The producers behind the Housing Works Used Bookstore and Café in New York taught a group of bluegrass fans this lesson by pairing popular mandolin player Chris Thile (of bluegrass trio Nickel Creek) with 25-year-old violin prodigy Hilary Hahn—a woman who made her first classical recording at 17. I’ll admit: Thile was the reason I was at the show myself. I’d never heard of Hahn.

The 25-year-old Thile, considered a prodigy himself when he began playing at 12, is known for his impeccable fingering and string work. Perhaps the most popular mainstream bluegrass group behind Alison Krauss and Union Station, Nickel Creek display an impeccable balance of pop intelligence and integrity.

Thile started the show with a solo performance of an unreleased, untitled instrumental song and the single “Stay Away” from How to Grow…. While he joked and made fun of himself between songs, his music showed countless tones of emotion, from longing and yearning to bittersweet happiness and outright comedy.

The show took a serious turn when he began playing Bach’s Gigue in D minor. When I mentioned my amazement at this feat to a friend the day after the show, she replied that trained musicians play most music from memory. Still, it isn’t everyday that a mandolin player busts into Bach. Leaning his head back and making strained John Mayer-esque faces, he played the piece almost flawlessly, muddling some fast trill sections, but recovering at the end with a flourishing cadenza.

Hahn joined him on stage for two classical pieces and a version of an Irish dance song. It was at this point that the show became purely classical, with Hahn eventually taking the stage on her own for two solo pieces, Ysaye’s Sonata for Solo Violin, No. 2, and a Heinrich Wilhelm Ernst arrangement of Schubert’s “Der Erlkonig,” based on a Goethe poem. She explained each piece beforehand, almost apologizing for their length as she recognized that the audience probably wasn’t used to sitting still and paying attention for 15 minutes straight.

A more educated classical-music critic could probably find some fault with her playing, but after she explained the background of “Der Erlkonig”—a story about a father and his sick son being pursued by a demon, complete with different voicing for each character—one couldn’t help but be thrilled. It was such a surprise to hear quality classical music in a quasi-rock setting, and it seemed that only someone like Hahn—a young person in tune with the general musical preference of her generation—could pull it off successfully. And she did so because of her calm attitude and innate skill.

Thile joined her again for the last movement of Niccolo Paganini’s Violin Concerto No. 1. Earlier in the show, Thile had accompanied Hahn quietly, letting her take the spotlight. The rushing, trill-filled Paganini movement allowed Thile to prove his pluck once again, with Hahn and Thile tossing leads to each other effortlessly.

In a way, the show was the definition of excitement: It was exciting to see live classical music in such an in-your-face presentation because it was so unexpected. At that moment, only Thile and Hahn could have pulled off a show like this as successfully as they did. Their wildly different musical backgrounds combined perfectly for a display of music that was as happily educating and entertaining as the best kind of rock concert.