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The band takes the stage. The drummer and the bassist start a funky rhythm, with a guitarist and saxophone player riffing along. You assume this is a contemporary jazz piece.

But then the vocalist takes the mic, and you wonder if your ears are deceiving you. Is she really singing, “I have only one burning desire/Let me stand next to your fire”? Is this really a jazz version of Jimi Hendrix’s “Fire”?

It is. Welcome to the world of Robert Miller’s Project Grand Slam.

For the past two years, Miller and his ensemble have been mixing original compositions with jazz versions of songs by Hendrix, the Kinks, Cream and other classic rock artists.

“This is my homage to the great music I grew up listening to,” said Miller, the group’s leader and guitarist.

Project Grand Slam has opened for a host of rock artists, including Yes and the late Scott Weiland of Stone Temple Pilots, besides playing jazz festivals.

The group currently is opening for Blues Traveler, the Grammy-winning blues-rock act from the Princeton area. The two bands’ next stop will be the Mayo Performing Art on Saturday.

Sharing the stage with the members of Blues Traveler pleases Miller. “I’ve been a big fan of theirs for a long time,” he said. “I love John Popper. We can’t thank them enough for giving us this opportunity.”

The roots of Project Grand Slam date back about a decade. Miller had put together a contemporary jazz ensemble that gradually was gaining some fame. (For example, the group played on an episode of the TV series “Lipstick Jungle.”)

However, the members lived in several countries.

“The logistics made it difficult for us to play out for any length of time,” he said. “We could get together for a couple of recordings, but that was it.”

Eventually, Miller decided that he needed to disband the group. But the itch to play never left him, and in 2015 he decided to put together a new lineup of Project Grand Slam.

“The idea was to put together a group of young, really talented, university trained jazz musicians,” Miller said. “I found these musicians who had great talent and great enthusiasm.”

Several of these new players came from Hispanic countries, and Miller was especially excited at the way they would work Latin rhythms into the performances.

At the same time, Miller had the idea of arranging classic rock songs — the music he grew up with — for the group. “I never liked musicians who just copy a recording of a song note-for-note,” he said. “I like musicians who do something different.”

His approach is evident on the group’s new CD, “The Project Grand Slam Experience,” which was released at the end of June. (The title is partly a tribute to the Jimi Hendrix Experience.)

The album consists of five studio tracks and five live performances.

“We wanted to capture the band in its totality,” Miller said. “Half of the songs are originals, and half are covers.”

The covers include “Fire,” “You Really Got Me” by the Kinks (which earned the appreciation of Kinks co-founder Dave Davies), and “I’m So Glad,” popularized by the band Cream.

Miller added that he is proud that jazz-rock saxophonist Mindi Abair is featured on one track of “The Project Grand Slam Experience.”

Crossing the worlds of jazz and rock may seem unusual, but Miller feels that he and his group are carving out a distinctive identity that is able to draw audiences.

“We’re not smooth jazz. We’re not rock. We’re not 1970s fusion,” Miller said. “We’re a different kind of band, but we are a band that make people listen.”

Article written by Bill Nutt.