In recent decades there have been any number of jazz groups—particularly the various David Murray configurations—that have sounded cutting edge (like Charlie Mingus) and ancient (like the earliest New Orleans jazz) at the same time. The Times‘ Jon Pareles coined the term avant-gutbucket to describe this phenomenon. Most of the musicians so-called were postmodernists looking backward. Banjo master Eddy Davis, on the other hand, is essentially a traditionalist who doesn’t just look forward into jazz’s future, but sideways at pop, folk, and international musics as well. Having the opportunity to lead bands two nights a week—at the most ridiculously overpriced and the most amazingly cheap venues in Manhattan—has given him the chance to forge two distinct ensembles.

The Carlyle band, fronted by Woody Allen, uses the traditional instrumentation (the lineup is typically Simon Wettenhall, trumpet; Gerry Zigmont, trombone; Cynthia Sayer, piano; Greg Cohen, bass; and Rob Garcia, drums) and sticks to the letter and spirit of such New Orleans “revival” masters as George Lewis and Bunk Johnson. Allen himself is a gifted avocational clarinetist, whose celebrity status (even more than George Segal or Conrad Janis) has done a lot to attract media attention to this music.

The Cajun band, which can be heard for the price of a $15 plate o’ ribs, combines all manner of influences. Its home turf is ’20s jazz standards à la Louis Armstrong and Fats Waller (Davis’s own vocals are indebted to both icons), but this is a starting point rather than a final destination. Davis regularly pulls out such bebop anthems as Miles Davis’s “Four” (no relation) and Thelonious Monk’s “In Walked Bud” (when some of the guys didn’t know it, they reverted to the changes to “Blue Skies”). He’ll also play Cy Coleman, bossa nova, Italian movie themes, ’60s show tunes, and his championing of the more obscure compositions of Henry Mancini could turn anyone into a Mancini fan. The group spotlights Debbie Kennedy, bass, and Conal Fowks, piano and/or bass—the major shortcoming is that Davis could use a strong drummer, such as Garcia, although he does employ the crowd-pleasing vaudevillian Joe “Mr. Spoons” Jones. The front line features two reeds, the inspired clarinetist Oranje Kellin, co-creator and musical director of the show One Mo’ Time, who comes stylistically from New Orleans by way of Sweden, and Scott Robinson. Robinson, who is also a part of the orchestra led by contemporary jazz composer Maria Schneider, plays the forgotten C-melody saxophone and is one of the great colossi—on any horn—of our time. Davis’s group hasn’t recorded, but Robinson’s all C-melody album, Melody From the Sky, which captures much of what he plays at the Cajun, was the great reed virtuoso showcase album of 2000.

Davis, who encourages sitting-in by both veteran superstars (Bob Wilber) and emerging vocalists (Heather Simmons, Joan Bender), is himself at the heart of the music. He is a great musician, whose instrument happens to be the banjo and whose basic style happens to be premodern jazz, yet who is more likely to play “Night in Tunisia” than “That’s a Plenty.” The current jazz scene could do with more like him.