In order to have done that, each member has to be grounded in both jazz improvisation and classical technique, said founder and violinist David Balakrishnan.
"You have to have that bipolar quality," Balakrishnan said during a phone call with The Park Record from his home in Albany, Calif., just north of Berkeley. "That gives a lot more range to the group stylistically, because most string quartet players don't have that equality.
"Also, to be in Turtle Island, you have to be a serious be-bop head," he said. "You have to know (John) Coltrane or (Charlie) Parker and be good at playing their tunes on string instruments."
It was Turtle Island's agent who suggested they team with singer and songwriter Nellie McKay, who will play with the Turtle Island Quartet at the Eccles Center on Jan. 4.
"He was working with some theater clients and came across Nellie and some of the things she was doing in New York," he said. "He knew Nellie's manager and they waned to put us together."
After listening to her music, Balakrishnan found a quality to McKay's music that intrigued him.
"She's has a unique and personal way of making music," he said. "Her music is deceptively simple, but well-placed in a kooky way."
That's common in jazz music, Balakrishnan said.
"Someone will come out and have this certain style that is unique to whom he or she are," he said.
Balakrishnan thought it might be a fun collaboration, so he flew to New York a year and a half ago to talk with McKay — pronounced MaKAI. (See accompanying story titled "McKay has a long list of accomplishments").
"We sat in her living room and I played some stuff for her and she played some stuff for me and talked about what we wanted to do," he said. "It was delightful."
One of the things Balakrishnan found was McKay is a renaissance woman.
"She's more on the indie-pop side of things and uses retro jazz and (standard) pop as angles for her music," he said. "She does it with such an indefinable quality that touches your heart."
The two decided to add bits and pieces of their musical influences in the show.
"We do versions of Billie Holladay and Billy Strayhorn and some original music," Balakrishnan said.
They also threw in some Doris Day songs that McKay covered in her latest album, "Normal as Blueberry Pie: A Tribute to Doris Day," and some pieces taken from the Weimar period, which took place between the German's defeat in World War I in 1918 to the rise of Adolf Hitler in 1933.
"Nellie was going through this whole thing with the Weimar Era and still is way into composer Kurt Weil and actress Marlene Dietrich," Balakrishnan said. "She likes to channel that type of style and has that actress quality in her music that makes her who she is."
Over the past year, the concert has become very popular pairing.
"I still have a hard time putting my finger on what it is," Balakrishnan said, laughing. "It has sort of a dreamy, acid-trip quality to it, and, yet, it's grounded in solid musical fundamentals. But it's not pop, and not pure jazz."
The program is challenging for the Turtle Island Quartet — Balakrishnan, cellist Mark Summer, violinist Mateusz Smoczynki and violist Benjamin von Gutzeit — because of that intangible aspect.
"As a quartet, we have to rely on our hot chops in these songs," Balakrishnan said. "This is not a performance to show how hot we play, which is the usual Turtle Island style. No. Nuh uh. This performance is all about finding a way to make her music work with us, and showing the audience who we are.
"Since she is the singer, I felt it was important for her to take the lead, but at the same time, the quartet had to figure out what we could add to give the music its own personal quality."
This is a common idea for jazz musicians who play with pop musicians, Balakrishnan said.
"I remember Branford Marsalis talking about playing with Sting," he said. "He said you have to know how to suit the genre you're playing in."
Still, collaborations aren't alien to the Turtle Island Quartet.
It has worked with the Manhattan Transfer, pianists Billy Taylor, Kenny Barron and Ramsey Lewis, the Ying Quartet, Paquito D'Rivera, vibraphonist Stefon Harris, guitarist Leo Kottke, the Assad brothers and the Parsons Dance Company.
"We had to find a way to play with Nellie and one way to do that was that we couldn't over-arrange," Balakrishnan explained. "We had to grope around for ideas and make the music sound more American, if you will.
"When a quartet plays more vocally-styled lines, they tend to play in more the European style with a lot of vibrato, which we couldn't do with Nellie," he said. "Nellie can function well within a band, and at the same time she brings in colors from the orchestral side of her music. She's an intelligent and approachable artist who is totally zany and ironically her own."
Nellie McKay and the Turtle Island Quartet will perform at the Eccles Center for the Performing Arts, 1750 Kearns Blvd., on Saturday, Jan. 4, at 7:30 p.m. The concert is presented by the Park City Institute. Tickets range from $20 to $69 and are available by visiting www.ecclescenter.org.