The mandolin and the double bass are the Laurel and Hardy of musical instruments. One is small and sleek, existing on the high end of the register; the other is a big, booming instrument that definitely makes its presence known. Side by side as a duo, they make an unlikely pair. But in the hands of Chris Thile and Edgar Meyer, they make beautiful music together.

A onetime child prodigy, Thile, now 33, is best known as the mandolinist for the progressive bluegrass group Nickel Creek, as well as for his side project Punch Brothers, a quintet in which he first began to meld bluegrass and country with classical. His solo projects include the highly praised album, “Bach: Sonatas and Partitas, Vol. 1,” which was produced by Meyer.

A classically trained bassist and composer, Meyer, 53, has a remarkable range of genres, including bluegrass, newgrass and jazz. He’s collaborated with classical, country and pop stars such as Joshua Bell, Yo-Yo Ma, Emanuel Ax, Amy Dorfman, Jerry Douglas, Bela Fleck, Zakir Hussain, James Taylor, Alison Krauss and Mary Chapin Carpenter.

Thile and Meyer, who will appear Oct. 17 in an SCP Special Concert, began playing together in 2003. They made their recording debut in 2008 with a self-titled disc, and in September, they followed that with the simply titled “Bass & Mandolin” (Nonesuch), which features 10 original compositions by the two artists. It’s an extraordinary blend of two genres not usually in close company — bluegrass and classical. The disc also highlights just how rare their talents are on their instruments.

Thile was around 11 when he first heard Meyer performing the tune “Limerock” with fiddle player Mark O’Connor. At the time, he had little knowledge of the range of classical music. “It was a good-natured almost classical rendition where Edgar was doing the most delightful kind of bass fireworks,” Thile recalls. “As a kid, my impression of classical music was that it was stuffy and devoid of rhythmic interest. I credit Edgar’s approach to it with showing me the light.”

Until that point, Thile had existed solely in a bluegrass world. As he followed Meyer’s work and their friendship grew, it “blew the door” off his musical world. “Everything started to become curiously blurry,” he says. “And I began to focus on the similarity between great pieces of music rather than the differences.”

“Chris’ interest in music is all consuming,” Meyer says. “He understands a broad swatch of music in much more than a casual way. Instead of being like a generalist and dabbling here and there, he’s more like a specialist in everything.”

While Thile and Meyer have busy careers all over the board, they have continued to play together sporadically over the past 15 years. The second album came about because they felt they had more to say in their ongoing musical conversation. Last summer, they toured with cellist Yo-Yo Ma and fiddler Stuart Duncan as members of The Goat Rodeo Sessions, a project that brought together the four string virtuosos in a cross-genre project.

They credit that experience with adding a new dimension to their duo partnership. “I think with Goat Rodeo, Edgar and I learned a tremendous amount about working together as a collaborative entity,” Thile explains. “As the lead composers with that group, we wanted to create little musical environments for people to poke around in and explore.”

Their relationship has grown from one of mentor and student to one of musical equals. The fun they have performing together is evident in the back-and-forth playfulness of their music. Both agree that on the first recording, they were feeling each other out as collaborators and perhaps that held them back a bit.

Meyer feels the biggest change on the second album is in “the intensity of the writing.” “I think there was a slightly laissez-faire quality to the writing on the first album,” he says. “We wouldn’t question each other about the material we each brought to the project. We just made it happen. With this album, we had enough time and enough rapport established that we could stop and evaluate the music before we committed to it. So this time there was a large pile of scraps left on the floor.”

Over his career, Meyer has turned the double bass into a modern virtuoso instrument. He is the first bassist to win the Avery Fisher Prize. (Both he and Thile were recipients of the MacArthur Foundation “Genius” Fellowship.) Meyer’s father played the bass, and he remembers asking for one “as soon as I could talk.” He started taking lessons when he was 5 years old. “My identification with the instrument was very early and very complete,” Meyer recalls. “It was so early that I was quite old before I realized it might be considered by some an odd choice. But for me, it was the most natural of choices. I’ve never known anything else. It simply is my voice.”

As for Thile, he feels the way a musician comes to his instrument is the same way a vocalist comes to his voice.

“It almost feels that there’s not much choice,” Thile says with a laugh. “The mandolin is my voice. It’s what I understand. But I also love the violin. I love the piano. But it’s the mandolin that makes the most sense to me. And It’s the instrument that’s brought me to an always expanding love of music. All of it.”

Mary Houlihan is a Chicago-based arts writer and reviewer.