It was a delight to read, in Tuesday’s New York Sun, of the existence of “Star Trek: New Voyages,” the production of a group of Enterpise-ing writers, actors, and producers who are taking it upon themselves to extend the legacy of the celebrated 1960s TV series by creating their own new episodes online. It’s not as if they decided that there weren’t enough installments in the original 1966–69 series, but rather, that there remained plenty to be done with Kirk, Spock, and company.

The collective band One for All, which is appearing this week at Dizzy’s Club Coca-Cola at Jazz at Lincoln Center, could be regarded as the jazz equivalent of the New Voyagers. The genre known as “Hard Bop” flourished briefly (it was the bread and butter of Blue Note Records during the label’s mid-century glory years) before it was essentially deserted in favor of modal jazz, free jazz, and soul jazz.

One for All is a sextet consisting of Eric Alexander on tenor sax, Steve Davis on trombone, Jim Rotondi on trumpet, David Hazeltine on piano, John Webber on bass, and Joe Farnsworth on drums — all of whom appear regularly in this and other combinations uptown at Smoke, on 106th Street. The nearest I can remember the group making it to Midtown was an appearance earlier this summer at the 92nd Street Y, which qualifies as a journey across town rather than downtown.

One for All’s recordings are even less mainstream: The group has recorded 12 albums in 10 years, but only four are on an American label (including last year’s “Lineup”), the independent Sharp Nine Records. The remaining entries were all done for overseas operations and are not available Stateside, much like Bill Charlap’s New York Trio and Cyrus Chestnut’s Manhattan Trinity — two New York-centric threesomes whose releases are only available in Japan.

One for All’s appearance at “Jazz in July” didn’t do the group justice because the members were impelled to recreate the very baroque early bebop of Charlie Parker and Dizzy Gillespie rather than the more expansive hard bop of a decade later (the difference is real, not academic) and because they were not playing their own music. Though I’m sure the sextet gets requests for “Moanin’,” “Song for My Father,” and “The Sidewinder,” what One for All does better than anyone is create original works in the old tradition, through a combination of completely new compositions and new arrangements of existing songs that have never before been hard-bopped.

On Tuesday night, the sextet made it clear that its strongest inspiration may be John Coltrane’s 1957 record “Blue Train,” his sole album for Blue Note. Mr. Alexander, who is the group’s standout player (and that’s really saying something, since Messrs. Rotondi, Davis, and Hazeltine are all tremendous soloists), sounds more like Coltrane in his bebophard bop period than anyone else, and it’s this classic album, more than any other, that offers the perfect representation of the hard bop sextet with tenor, trumpet, trombone, and three rhythm.

Like the classic Blue Note albums, there’s as much of an emphasis on writing as on marathon soloing. All four of the principal soloists here could spend a whole set spinning variations on chord changes, but harnessing their improvisations to a larger composition gives their music greater depth and meaning. During the opening set, they offered two pieces from their latest album, a set of jazz versions of Motown songs, which is about to be released by the Japanese Venus Records, but which sounds so good it may well be worth whatever exorbitant price Amazon.com is demanding to fly it in from Tokyo.

On “Moon Blue” (from Stevie Wonder’s most recent album, “A Time To Love”) and the Isley Brothers’ hit, “For the Love of You,” One for All made Motown melodies sound as though they were written by Jackie McLean or Sonny Clark. Both tunes were invested with such niceties as reharmonized melodic lines, and “A Time To Love” included the authentic touch of having Mr. Alexander’s tenor take the bridge all by itself. Mr. Alexander came off especially well (he’s almost better in a sextet than the customary saxophone quartet); he expressed himself in the bop vocabulary as a native speaker. In between these two pieces, he offered a comparatively mellow original, “Little Lukas” (from “The Lineup”), in which Mr. Rotondi showed what a pretty tone can be achieved with Harmon mute.

Although, as per the custom, the night’s big, exciting drum solo and percussion trade was reserved for the finale, to me Mr. Farnsworth’s best feature was “For the Love of You,” which made use of the classic Blue Note Latin beat — a southof-the-borderrhythmthatseemed equally Cuban and Brazilian. Mr. Davis received the most extensive solo feature in a new quartet arrangement of J.J. Johnson’s classic “Lament” (which most jazz fans remember from Miles Davis’s masterpiece album, “Miles Ahead”), which is as close as hard bop gets to a ballad. Even at the group’s most romantic and intimate, Mr. Davis still played in a hard-driving tempo that’s better suited to kicking butt than kissing anything.

The set ended with an explosive treatment of “The End of a Love Affair,” which has been part of the jazz repertoire since April 5, 1956, when, coincidentally, both Art Blakey and Frank Sinatra recorded it on the same day. Where Blakey’s arrangement was surprisingly Latinate, One for All’s was much more straight-ahead and aggressive. Mr. Alexander took charge with a device I’ve often heard in blues-based jazz playing but rarely in standards: He soloed in a variation of stoptime, in which the rhythm section pounced behind him on the first beat of every measure, then laid out for the next three beats. It was a dazzling technical and emotional feat, and elicited a wild response from the crowd.

When I returned home from Dizzy’s, I caught a little of “Star Trek: New Voyages.” I liked the show a lot, but it paled in comparison to Mr. Alexander and the rest of One for All in terms of professionalism and success. As with “Star Trek,” hard bop is a music that exists within a definite timeline — you know where it came from and where it’s heading. One for All may be going where man has gone before, but it’s going boldly just the same.

wfriedwald@nysun.com