Swing the changes: A new generation of musicians will be turning the joint upside down at this month's London Jazz Festival

What's been happening to jazz? There's hardly a sharp-suited bopper to be seen in the line-up for the 17th London Jazz Festival, which begins on Friday. The great tradition is there if you want to look for it, with appearances by the veteran saxophonist Sonny Rollins and his contemporary equivalent, Branford Marsalis. But this year, such performers are in a conspicuous minority on an outrageously wide-ranging bill that takes in more than 1,500 musicians and 750 hours of music over 250 events at 50 venues in 10 days. The sense of stylistic openness is not only due to the presence of customary jazz festival performers who aren't really jazz at all, such as the Blind Boys of Alabama or Brazil's former Minister of Culture, Gilberto Gil. This year, even the card-carrying jazz acts are getting frisky and mixing it up. That model of the modern jazz pianist, Chick Corea, for example, is appearing with a country-twanging banjo virtuoso, Béla Fleck.

In part, these changes are historical and were already in train long before the LJF was established in 1992. When the modernist line hit the final terminus of free improvisation in the 1960s, jazz went sideways. The postmodern era that followed saw jazz dalliance with rock, soul and funk; make new investigations into classical, folk and ethnic music (especially in Europe, which became the centre for recorded jazz); and form experimental partnerships with other media.

What's different now is that, 60 years down the line from bebop, the original "modern jazz", there's not many of the original performers available any more. And with a jazz recording industry that had been helping to bankroll tours by visiting US stars, now close to ruins (even the estimable Blue Note label barely exists as a truly active concern), the distant jazz past is increasingly that: gone, deceased, expired. Except, that is, as the subject for retrospective festival projects such as Friday's opening Barbican concert, Jazz Voice: Celebrating a Century of Song, and the continuing experiments of new musicians investigating old styles.

For John Cumming of Serious, which organises and programmes the festival, the shape of the LJF is also due to the shape of London itself. "The challenge has always been to create a festival of music that is tied to one genre, but to make it work for this massively diverse city," he says. "If you like, the festival is a cypher of the city, an image of what London is today. We've accepted that it has to be a sprawl and so the music reflects that. Anyone trying to define what jazz is now would have a problem, and we need to celebrate that."

What remains amid the sprawl of the city and the ruined monuments of a near-mythical past, is a sense that, for jazz musicians today, stylistically at least, almost anything is possible. Just listen to the three pianists interviewed on this spread. They're less encumbered by the weight of the great tradition, and with fewer expectations about how they should sound or what they should look like. Emerging jazz stars are once again able to relax and make it all up as they go along.

www.londonjazzfestival.org.uk

The new jazz trio

Zoe Rahman

For the Mercury Prize-nominated pianist Zoe Rahman, who is performing solo concerts in three different venues as part of the Festival on the Move strand, it's knowing how to stop that's the problem. "I play in so many contexts – with my trio, with Courtney Pine, with Jerry Dammers' Orchestra – and they're all different, and all really busy," she says. "But when you're playing solo, when you stop playing, that's the end of the music! You can't rely on someone else to take over. You just have to be aware there's an audience, and to use variety to make it interesting to them, so that it's a real journey."

Rahman was classically trained before specialising in jazz. "All music is a language," she says. "You begin by stringing sentences together, then you make paragraphs. With jazz, it's a completely different way of learning to classical piano; a lot of it is just listening, learning to use your ears."

After Oxford University, Rahman went to Berklee in Boston and studied for two semesters with Joanne Brackeen. Although she can play lyrically if she wants to, as in her recent album of Bengali songs Where Rivers Meet, what Rahman does unusually well is hard, rhythmical swing. "Julian Joseph [who preceded her at Berklee, and became an informal mentor] helped me in getting that real swing sound," she says. "He turned me on to Mulgrew Miller, Herbie Hancock, Oscar Peterson and Chick Corea. Swing is so different to classical music. You can feel the time and pull it around, playing against yourself. When you hear Thelonious Monk or Sir Roland Hanna playing solo, it's complete in itself. Because I listen so widely, and to music from around the world, my own solo concerts will feature a lot of other people's tunes, and I'll run them into each other. It's good to know it's not just me and the piano!"

Zoe Rahman is in Festival on the Move at Charlton House, SE7 (020 8858 9497) on Friday; The Red Hedgehog, N6 (020 8348 5050) on Saturday; and TARA, SW18 (020 8333 4457) on 21 November

Tord Gustavsen

Many jazz musicians have been inspired by sex, but Tord Gustavsen must be the first to have written a dissertation about it. "The Dialectical Eroticism of Improvisation", as an English language abstract of his University of Oslo post-graduate thesis is called, deals with the parallels between musical and erotic performance, using psychoanalytic theory derived from academic studies of relationships and childhood. "It's about the ongoing paradox between closeness and distance," Gustavsen told me last week, before going on stage for the last date of his UK tour. "The way you improvise is to be in every moment but also to shape things over time. You have to be present but you also have to be able to deal with deferred gratification, preparing for the climax that is to come."

Those who have heard Gustavsen – and he's the ECM label's best-selling artist of the last decade – will know that he's a foreplay man rather than a wham-bam-thank-you- ma'am kind of guy. His music builds with exquisite slowness towards a transfiguring release that is all the more powerful for being withheld for so long. "It's the tension between elegance and passion that you deal with and struggle with every night on stage. I want to be elegant but I also want to fill every little note with the rawness of passion. The pleasure lies in all the small details you create the grooves from."

The Tord Gustavsen Ensemble play the Queen Elizabeth Hall, SE1 (0871 663 2500) on 21 November

Robert Glasper

In the 1990s, the fusion of jazz and hip-hop became the scene of some terrible crimes to each art form, as musicians from one field of endeavour proved they had little feel for the other. "Many people have heard an attempt to mix hip-hop and jazz, but not necessarily in a good way," says the Texan pianist Robert Glasper on the phone from Baltimore, where he's playing a concert in the band of the R&B star Maxwell, with genius-rapper Common as the support act. "I mix it together as much as I can and I do feel I'm doing both forms justice." When he made his UK debut at Soho's Pizza Express two years ago, the jazz fans applauded the solos while the hip-hop heads cheered the ensemble grooves.

As the pianist for projects by Mos Def, Q-Tip, J Dilla, Erykah Badu and the R'n'B singer Bilal (who appears with him at his LJF date), Glasper has good form, while his jazz albums for Blue Note are pleasingly supple affairs. Here, the hip-hop elements aren't clichéd adaptations of electronic grooves, more the application of a whole sensibility. "It's not a technical thing, because you can teach technique," he says. "Hip-hop is more of a feel, and you can't teach that. My feel when I play is that laid-back-ness, the behind the beat thing that's reminiscent of a sample. I love to lay on the vamp, to stay in the groove, and that's very much within the spirit of hip-hop."

Glasper, who met Bilal at New York's New School for Jazz and Contemporary Music in 1997, doesn't feel his work with Maxwell is doing him any harm. "The good thing is that I'm playing in front of people who wouldn't come to a jazz club. In jazz, everyone does the same thing at the same festivals every summer, playing to the same people year after year. I'm sure that if John Coltrane came back he'd find the same people in the audience who'd been seeing him the last time. But I think he would want to see some new people."

Robert Glasper and Bilal are at the QEH on 15 November