There must be hundreds of stories like Greg Burk’s on the Boston jazz scene — the academy-trained musician who starts playing jazz in high school, studies with a couple of revered masters as an undergraduate, gets a master’s degree, and pays his dues in the clubs, gradually finding a niche, supporting himself with the luxury of a steady teaching gig, and trying to make a music he can call his own.

For the 33-year-old Burk, who brings his trio to the Regattabar on November 6, this could be his time to step out from the crowd. He’s been the pianist with the Either/Orchestra for the past three years, and his composition "Look to the Lion" is a highlight of the band’s new Afro-Cubism (Accurate). And his own new trio album, Checking In (Soul Note), shines with a quiet authority. Among its 10 tracks are a folk-inspired modal-mainstream swinger ("Sun Up"), a couple of spontaneous free improvisations ("Tutto Nudo" and "Ascent to the Strawberry Patch"), an Abdullah Ibrahim–inspired African-flavored piece ("Moasis"), a piano solo ("6 Ways"), a ballad ("Serena"), and a touch of R&B ("Sweet, My Honey Sweet").

There are several reasons why Checking In is more than just another piano-trio record. There’s the cohesion among Burk and veteran drummer/percussionist (and a formidable composer in his own right) Bob Moses and bassist Jon Robinson, a pal from Burk’s undergraduate days. There’s Burk’s own playing, his classical pianist’s sensitivity to dynamics and texture. And then there are the pieces themselves — each is stamped with the identity of supple original melodies. "Serena" has a classic ballad feel that makes it immediately familiar, as though you’d heard it before and were waiting for the lyrics to come to you. Even the "free" pieces are grounded in compositional direction, each member of the trio contributing to a sense of development and narrative expectancy. Burk doesn’t include a single "standard" on the entire 58-minute album.

"I think the least you can do if you want to sound like yourself is write your own tunes," he tells me over tea and pumpkin bread at the Trident bookstore, on Newbury Street. He adds, chuckling, "I mean, you may play like McCoy Tyner on top of them, but at least you wrote your own tunes."

"When I first listened to him play," says Either/Or leader Russ Gershon, "I heard an excellent modern mainstream jazz pianist, but that’s not nearly all that’s going on with him. He has a command of the vocabulary of jazz and classical music, but he uses them in unpredictable, non-traditional ways that are not immediately obvious. He has the skill and the ears to make his ideas fit into an ensemble, but his playing is a window into a parallel musical universe that happily intersects with other domains but retains its own integrity."

Burk began writing almost as soon as he got into jazz while a high-school student in Lansing, Michigan. "I didn’t make the basketball team, so I joined the jazz band." His parents are both classical musicians, and he says, "I was looking for a way to play music that was group-oriented that was not classical music." Although he had studied classical music with, among others, his grandmother, he found the classical demands for perfection impossible to meet. "I could never get through a whole piece without making a mistake. That was the problem: I could study something for a year and I would always make a mistake, and it would be in a different place every time. That’s the ultimate frustration for classical music, because you want to not make any mistakes."

But Burk’s high-school band teacher exposed him to the other classics — Ellington, Basie, Clifford Brown, Dizzy Gillespie. "I started writing tunes right away. It became connected with playing jazz." He cut his professional teeth working in Detroit jazz clubs with veteran musicians where, as he says in the liner notes to Checking In, "you had to know what you were doing or you’d hear about it." At the University of Massachusetts in Amherst, he had studied with Archie Shepp and Yusef Lateef. After Detroit, he studied at Berklee and worked on his masters degree at the New England Conservatory, where he studied with a stellar faculty that included composer George Russell, saxophonist Jerry Bergonzi, and pianists Danilo Pérez and, perhaps most significantly, Paul Bley.

Bley differed from his other teachers in that "they would all talk about the ingredients, you know — ‘you take three cups of flour.’ But Paul was all about presentation, he really made you think about what you wanted to do, what were your strengths, and how were you going to survive as a musician. His basic line is, ‘You have no business trying to play like somebody else, you have to come up with your own thing — and you have to record as much as you possibly can. Record your first 10 records right away, because you’re not going to like them, and then you can start learning from that.’ "

Burk has taken Bley’s advice to heart on several counts. As we converse, he mentions one album after another that he’s recorded, including three quartet records that he did in Detroit and a few that are sitting in the can. The day after our talk, he drops off several CDs — there’s a solo-piano CD, a free-duet album with Bob Moses, an album of Bach arranged for jazz quartet with Garrison Fewell, Jon Hazilla, and Paul Del Nero, and a fusiony project from a couple of years ago by a quintet called Fat Dragon (released on the local Planet Pomegranate Records) on which Burk plays electric keyboards exclusively.

For Checking In, he says he tailored his pieces — some of which are 10 years old — to the interests and strengths of Moses and Robinson. "I tried to imagine the musicians and the kind of tunes that they’d play well together. ‘Sun Up’ is a kind of folk melody, and Bob writes a lot of folk melodies, and Jon also has that quality in his bass playing — he plays a lot of other music besides jazz — bluegrass, Gypsy music."

Paramount in Burk’s writing these days is simplicity. "I like to write melodies that I can sing, or tunes and harmonies that are singable. I feel like a lot of jazz is harmonically alienating. I mean, I’m a pianist, and pianists deal with harmony all the time, but I find that generally a lot of jazz gets to a level of harmonic sophistication that only other pianists can appreciate. I listen to a lot of modern jazz that’s so harmonically rich it’s unsettling — I can’t imagine how people who aren’t musicians could hear it."

He says it’s his current gig teaching ear training and basic keyboard at Berklee that’s given him the security to record. Returning to Bley, he continues, "His question became not so much ‘What am I going to do with this music?’ but more like ‘How am I going to survive doing this music?’ But that goes back to the whole musical idea, because if there’s 10 pianists who sound like you, then it’s harder to survive than if there’s only one."

HERBIE HANCOCK is candid about music and the music business. The 62-year-old bona fide jazz superstar (there are only a handful) just came off a year or so of heavy touring with Directions in Music, a cooperative outfit with saxophonist Michael Brecker and trumpeter Roy Hargrove that’s dedicated to the work of Miles Davis and John Coltrane. The CD for that project was recorded live for Verve, and with the three musicians working on complete rearrangements of the Davis and Coltrane books, the music came across as surprisingly fresh — new, even. The live concerts were anything but a "greatest hits" package, and to judge by various reports, they got better as the tour went on. The band’s performance at the JVC-Newport Jazz Festival last August was easily the most exciting set I saw in more than two days of non-stop music.

Now Hancock is going out on tour again, with another acoustic band, this one with saxophonist Gary Thomas, bassist Scott Colley, and drummer Terri Lyne Carrington. How did the new project come about?

"I don’t go out and solicit gigs," Hancock explains over the phone from his LA office. "There’s an agent that I work with, and I guess he did research and found out that there were enough venues — promoters that wanted me to perform in their area as a trio or quartet. They didn’t care about what the project was. It was enough to put a little tour together."

So he’s embarked on a three-and-a-half-week tour that will come to Berklee this Friday. The Directions project required a lot of preparation, Hancock informs me — the CD was part of the package from the beginning, and the tour was going to be long and expensive. The current quartet, he goes on, comes mostly from his relationship with Carrington (he’s on her new CD, from Act, Jazz Is a Spirit). "We don’t plan to record, and there’s no particular focus on it. We’re kind of picking excerpts from some of my older pieces, like ‘Dolphin Dance’ and ‘Chameleon.’ I did some of the arrangements for the Future 2 Future band tour [his last electric band], and we’re taking some excerpts from some of those arrangements and playing them with this band, and some pieces where we combine elements of one piece with excerpts from another. We do that with Wayne Shorter’s ‘Footprints.’ But he says he’s determined to take the music "outside the comfort zone, to unknown areas, and see what we can discover there. That’s what this will be about."

As for future projects, Hancock is hoping to perform with symphony orchestras in the fall of 2003, beginning with a Gershwin program inspired by his Gershwin’s World (Verve, 1998) and perhaps eventually doing some of the music he and Wayne Shorter developed on their duets project, 1+1 (Verve, 1997). "Hancock-meets-Gershwin is hopefully my foot in the door to the classical audience. That has kind of a sizzle for them because they know Gershwin’s name — and some know my name. I’m hoping to get accepted in that world. . . . Once the door is open, we can do a lot of things."

The Greg Burk Trio with Jon Robinson and Bob Moses plays the Regattabar on Wednesday November 6; call (617) 876-7777. Herbie Hancock with Gary Thomas, Scott Colley, and Terri Lyne Carrington comes to the Berklee Performance Center this Friday, October 25; call (617) 876-7777.