Let’s get one thing clear from the start. The Maria Schneider rapidly becoming America’s most acclaimed big-band composer, and the one who is to appear in London on July 9, did not star in Last Tango in Paris. According to Schneider the composer, there have been fans and musical colleagues who have laboured under the delusion that somehow, in an earlier life, she offered carnal comfort to a clapped-out Marlon Brando.

The late, great Teo Macero, Miles Davis’s producer, was one such. “On one level it’s quite funny,” says Schneider with a shrug. “On another it’s frightening that people can hear something, absurd as it is, and take it for real.” It did not help when a New York paper published a scandalous story about Schneider the actress and put Schneider the composer’s picture on it. One can only assume that a hapless picture librarian is now on the streets.

If any artist does not require fame by sleazy association, it is the woman sitting opposite me in her diminutive but stylish apartment just off Central Park, New York. Living here, down the road from the Dakota Building since 1992 (“it’s rent-controlled – the neighbours pay three times as much”), she has mas-terminded the progress of a 17-piece group that has become one of the wonders of jazz. And she has done it by herself, without grants or major label support.

Her 2004 album, Concert in the Garden, full of delicately nuanced textures and inspired melody, became the first internet-only release to win a Grammy. Her 2007 album, Sky Blue, won another and has just swept the board at the US Jazz Journalists Association awards. Financed by fans through the Artist-Share scheme, it has already virtually recouped its $170,000 costs, after which sales become almost pure profit.

“A couple of years ago somebody from a major label came to me at a gig, a nice guy, and said, ‘Maria, maybe you would consider coming over to our label when you’ve done with your little internet thing. Then I gave him the figures; how I’d financed recordings, paid musicians. I could just see his face. It was like: ‘I could never do that for you.’ ” Schneider leans forward conspiratorially. “I heard through the grapevine how many copies Herbie Hancock’s Joni Mitchell album sold before it won the Grammy [for best album of last year, beating Amy Winehouse] . . a tiny, tiny amount. If Herbie Hancock with Tina Turner singing can’t do well on a big label, then what can a label do for me?”

Instead, the fans chip in – with someone paying as much as $18,000 to become “executive producer” of Sky Blue. “With so much music around for free, who’s going to go out and buy another CD?” Schneider says. “Fans have to feel a connection, that they are involved in the process. That may involve documenting the making of the album on the website, or producing limited special editions, or just replying to e-mails.

“Yeah, it’s scary. There are the expectations. You are sitting there writing, thinking, ‘I do not want to disappoint these people’. It’s a constant hot poker up your rear. But it works.”

It might also seem perverse that Schneider writes for the big band – a unit declared uneconomic since the 1940s unless your name was Ellington or Basie. She is a rare female in a macho world and Schneider’s intricate creations could not be more different from those of, say, Jools Holland, one of our few current practitioners, and his boogie merchants. “I don’t write for sections – trumpets, trombones, saxes – I write for individuals who each have a different sound. The trumpets might include a flugelhorn, have different mutes . . . it’s about subtlety of colour. It’s a more complex blend and it sort of liberated me from being bound by the jazz tradition.”

It means also that Schneider won’t work with pickup bands. “It needs to be my musicians on the road, who have lived and breathed the music.” There is a weary smile. “So we probably won’t make money with the European tour. I’ll probably be losing money.”

Schneider, as you’ll have gathered, is a workaholic. “My parents were pretty driven; both type-A personalities. Plus, growing up in Minnesota, it’s all Scandinavian Protestant work ethic there.”

She doesn’t do weekends and had one brief holiday last year – going birding in the Brazilian wilderness – which she recalls as exhausting. She works out, has a racing bike parked by a bookshelf, and looks ten years younger than her 47 years.

In her teens, living in Windom, a farm town three hours from the nearest big city, Schneider had limited contact with jazz. She may have composed jazz for the school band, may have worked with the late Gil Evans, but even now seems to have a rather wary relationship with the form. “If you look at what CDs I listen to, it’s mostly classical or Brazilian.”

Too many modern groups, she feels, are trying to push jazz too hard. And nobody ever shuts up. “I feel like someone’s coming at me with a sledge-hammer . . . More often than not I’ll be at a jazz concert and I’ll go ‘Oh my God, I can’t take any more of this. Is there going to be another solo?’ If I’m feeling that, with all my knowledge and experience, imagine what the average person that walks into the club feels.”

One day, Schneider says, she would like to produce small group albums, forcing the performers to play less. “I could help someone to make a record that would feel like a proper record, not a documentation of their expertise.”

Perhaps it’s significant that the latest project to hog her time for six months has been a classical piece commissioned by her friend, the soprano Dawn Upshaw. Setting nine works by Carlos Drummond de Andrada, the Brazilian poet, Schneider has written for a chamber orchestra for the first time. She laughs. “When they gave me the work, I said, ‘I’ll do it under the condition that if it’s a total disaster I can say I told you so’. I set out with the lowest expectations possible – but now I love it.”

The next day, I watch the first run-through at a studio down by the Hudson. Even allowing for the musicians’ unfamiliarity, the sound is frequently ravishing. There are plans to record it for radio in October. And after that? “Right now I’d like to go and lie on a beach and just read a book.” Somehow, with Schneider, you suspect that won’t happen.

Maria Schneider Orchestra, Barbican EC2 (www.barbican.org.uk), July 9 2008

Explore Music

• CD Reviews

• Live Reviews

Editor's choice

• Burning Bush with W
• Revolution at the new Saatchi Gallery
• Boy George on sex, drugs and Amy Winehouse