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SINCE THEIR FIRST RELEASE on the local Accurate label in 1992, Medeski Martin & Wood have been one of the cheerier stories in the marginalized world of the jazz record business. The keyboard/bass/drums outfit has shown great range, covering sounds that touch on everything from Cecil Taylor avant-piano jazz to Miles Davis–like electric jazz-rock shitstorms, Jimmy Smith bebop organ grooves, and hip-hop. Several years ago, MMW’s audience expanded exponentially when they were invited to play with Phish. So it shouldn’t be all that much of a surprise that good-humored frat-house rockers 311 asked the trio to come along on a summer tour that would also include "live" hip-hop band the Roots. The tour plays the 20,000 capacity Tweeter Center next Friday.

"311 is definitely a different audience from what we would draw playing by ourselves, so that was one of the reasons we wanted to do it," MMW bassist Chris Wood says over the phone from a tour stop in Philadelphia. The tour also gives MMW enough off dates to play other gigs, including jazz festivals and small clubs, and they’ll hit their share of rock festivals this season. "I don’t think we’ve ever had what people would call a ‘jazz audience.’ So playing festivals other than jazz festivals, it’s not really going outside the norm; in fact, sometimes it feels the other way around. Our music is sold in the jazz section, but I don’t think any jazz aficionado would call it jazz. But that word’s meaningless to me, because some people think that Duke Ellington is jazz and other people think Kenny G is jazz."

Wood seems happy to identify himself simply as "improvising musician." Playing all varieties of venues keeps the band’s shows changing from night to night. "It totally depends on the venue. The smaller club gigs allow us to improvise more and just make stuff up. Which is really rewarding for us. It’s kind of our favorite thing to do." As for the gigs with 311, "We’re playing huge places. We have no soundcheck, and we get to play for only 40 minutes, so that takes a little more planning. If nothing else, at least there’s a list of songs that we’ll play during the set, just something to fall back on in case we can’t hear each other well. That’s just really hard — to play open in that situation. So we’re more likely to have a set list. And then on a smaller club gig, we won’t even talk about anything, just go up there and start playing."

In September, the band will release End of the World Party (just in case), their fifth for Blue Note and their first with an outside producer, John King of the Dust Brothers. On first listen, it’s a 180-degree turn from the dark, Beasties-like hip-hop sound of their last album, 2002’s Uninvisible, even though King was at the wheel during the production of the Beastie Boys’ Paul’s Boutique.

"This has more of a pop clarity to it in a way," Wood agrees. "Everything is available for your ear right there on the surface." The sessions began with the trio "doing a week in the studio improvising." At first, King would narrow an improvisation to, say, a single bar of drums, make a loop, and build a rhythm track. "It’s a very pop way of building a track in a song. But I think as he heard us play more and listened more to what was on the tape, he began to appreciate how we organically get from point A to point B and started editing things together to try to retain some of that feel." Wood was happy with the results either way. "It’s always us. Because even if he creates a rhythm track that way, John and I still have to go back and improvise over it. We’re always going for that improvisational moment that sounds good."

The Billy Bang Quintet plays the Green Street Grill stage of "Destination Cambridge: The Unconventional City of Cambridge Central Square World’s Fair" next Sunday, July 25, from 3 to 4 p.m. The event, which runs from noon to 6 p.m., is free; call (617) 876-1655. Medeski Martin & Wood open with the Roots for 311 next Friday, July 23, at the Tweeter Center in Mansfield; call (617) 228-6000.