Since trumpeter Wynton Marsalis became artistic director of New York's Jazz at Lincoln Center nearly 15 years ago, the organization has developed a compelling balance between honoring the music's past innovators while replenishing that legacy with ambitious new material.

When Marsalis and his Jazz at Lincoln Center Orchestra (JLCO) plays next Sunday at Orchestra Hall, the second half of its program will be devoted to "Portrait in Seven Shades," by orchestra saxophonist Ted Nash. Each of its seven movements is inspired by iconic paintings from the 19th and 20th centuries.

The artists Nash chose -- Monet, Van Gogh, Picasso, Matisse, Dali, Chagall and Pollock -- are household names, and his distinctive interpretations may be at odds with the preconceptions of the listener, a challenge he welcomes. After a successful premiere and a smattering of performances in 2007, the work is back in the limelight with an album release backed by this national tour.

We caught up with Nash by phone to talk about "Portraits." His father and uncle were musicians involved in TV and film, and he is excited about this new chapter after a precocious career leading small jazz ensembles. "Portraits," his first major long-form piece, has since been followed by his recent recording "The Mancini Project" and an upcoming film score.

Q Obvious first question: How did this project come together?

A Over the years I have been writing a lot for the band, contributing to the repertoire. We do a lot of theme concerts -- the music of Coltrane, or Brazil or something -- and Wynton has had me do a lot of arranging. So [in 2006] he came up to me and said he wanted to commission a long-form piece, create a theme piece on whatever I wanted. I thought about what kind of thing would inspire different movements and came up with modern painters and paintings that fit in with the period of the first hundred years of jazz.

I formed a relationship with the Modern Museum of Art in New York, who were really great. They allowed me to come in whenever I wanted -- before it opened and after it closed -- and I was able to see the paintings that inspired me without a lot of distractions, in the quiet. I even brought my saxophone down and played a little bit to get a vibration off what I was doing.

Q So all of the paintings are there?

A The majority of them are part of the museum's permanent collection. They don't all quite fit with the time of the first hundred years. I had decided to start with Van Gogh and Monet -- who aren't really considered modern artists -- and worked through to abstract expressionism [with Jackson Pollock].

Q Did you do more than the seven compositions that are on the record?

A No. I originally had a master list of painters that also included de Kooning and Cezanne, but I didn't compose more than the seven.

Q You've been with the Lincoln Center Jazz Orchestra for more than a decade now and really know the band. Did you do what Ellington so famously did and write specifically for different members on this project?

A Yes. It is a real luxury because you can pick lead lines according to their strengths and what they love to do. People have written for us who didn't know the band and you can really tell the difference.

Q Can you give us an example?

A On the Matisse piece I knew I wanted to swing with a certain rhythmic characteristic that could be whimsical and traditional at the same time. And I thought of [baritone saxophonist] Joe Temperley playing the blues coupled with the bass, and wrote the melody based on that and a little of the quirkiness I hear in [Thelonious] Monk's music. Joe has such a beautiful tone and I knew I wanted to use that in that context.

Q And of course there are a couple of things that feature Wynton.

A Wynton doesn't have a big ego that way; he's always thinking about how to feature other people and he loves the community effort. But Wynton also loves to play, and when he doesn't he gets itchy -- plus he knows that some people come just to hear him. But none of that is why I featured him. I just heard him being the right person in some particular movements and I especially think he is a great ballad player, so he is [featured] on both the Van Gogh and Picasso [pieces].

Q Did you come into this project thinking you needed more of an overarching concept? Did you know what you wanted to do?

A The through-line was the connection with the painters -- that was the concept. And the other through-line was the band -- we have one band playing the music. After that I wasn't worried because I wanted more leeway with the stylistic approach, to have the individual movements be as different as they could be as long as it was organically in line with [how he felt about] the paintings. I was hoping they would naturally sound different, because otherwise they wouldn't have really been inspired by the paintings.

Q On the JLCO website you provide some wonderful liner notes on how and why you came up with many of the music associations you use for each painter [see tinyurl.com/yk2ecue]. But can you provide an example of that "Eureka!" moment where everything just sort of came together on one of the pieces that will be played by the orchestra when you come to town?

A I had no preconceived ideas about how to approach each movement. The reactions were mostly organic; some more intellectual, some more purely visceral in reaction to the colors and textures.

But I'd say the best example of what you are asking came with the Van Gogh. I'd seen "Starry Night" many times before in books -- it's a famous iconic image. But I remember standing there thinking, trying to intellectualize how to approach the music with all the thick brush strokes and deep colors, and it wasn't doing it for me on that level. Then I looked at the painting and remembered it was the view Van Gogh saw from the asylum, and I started to feel much more connected to Van Gogh and what he was going through as a person. And I started thinking of words to express what he was thinking. I had never written lyrics before but I suddenly knew I was going to tell his story.

Q You mentioned how "Starry Night" is an iconic image, as are all the paintings that inspired you in this project. Because these paintings are so familiar, did you worry about the danger of running into people's preconceptions about how the music should match what they thought of the painting?

A It was a danger I embraced and a risk I was willing to take. I wanted preconceived ideas of who this artist is to the listener; that way it is a challenge to them and for me to get them to accept my perception. People have told me, 'I always loved that painting but now I appreciate it in a new way.' And that was the goal. If I had chosen paintings nobody knew, it would have been OK, but everything would just be taken at face value, without the risk of the interaction. Sometimes it won't work. But mostly it seems like the risk has paid off.