The legendary Gerry Mulligan-Chet Baker Quartet of the early 1950s wasn’t just a great band; it was a great idea for a band. The idea of allowing trumpet and saxophone to improvise freely and interact without the harmonic constraints of a piano gave the foursome both a playful quality and a seriousness not found in other modern jazz combos. The absence of a dominant chordal instrument motivated the four players to work harder, to avoid the clichés and familiar patterns that were already settling into bebop. Everything that the quartet did sounded fresh and original, and it still does more than 50 years later.

Since Mulligan and Baker played together for only two years, they hardly had the chance to grow stale. Both men tried to keep the idea going with different partners and slightly different instruments — Mulligan with Bob Brookmeyer and Baker with Stan Getz — but it wasn’t the same. Remarkably, no other regularly working ensemble picked up the slack, and the two-horn, two-rhythm concept had to wait until Ornette Coleman (a mere six years later) to give it new life.

For the last few years, the Brooklyn-based trumpeter John McNeil has been exploring the possibilities of Mulligan’s original concept: trumpet and sax with bass and drums and no piano or guitar, playing essentially a bop-based music based on traditional chord sequences. On his most recent album, last year’s “East Coast Cool” (the title of which refers to how the West Coast Cool School sound of the ’50s was largely invented by New Yorkers like Mulligan and Miles Davis), Mr. McNeil worked with the baritone saxophonist Allan Chase. This week, between Tuesday and Sunday, at the Village Vanguard, the other half of the frontline is the tenor saxophonist Bill McHenry.

Whereas the album offered mostly original compositions, at the Vanguard (where the two horns were supported by the bassist Joe Martin and the drummer John Rueckert) the quartet played mostly lesser-known works by instrumentalist-composers associated with the West Coast Cool School. The opening set on Tuesday night included Mulligan’s “Soft Shoe,” which featured a creeping blues line reminiscent of “Misterioso,” and three pieces from Chet Baker’s orbit: “Headline” by Jack Montrose, the “Rhythm”-esque “Batter Up,” and “A Dandy Line,” which continually slows down and speeds back up. The rarest piece was “Caprice,” an undocumented tune by Dizzy Gillespie that began with a “Salt Peanuts”- style intro. There also was an attractive original by Tommy Flanagan, “Solacium.”

What makes this group special, like the original Mulligan-Baker group, is the constant interplay between the two horns. In most mainstream modern jazz, the only interaction is between the rhythm section and the soloist; even the obligatory trade-of-fours with the drummer (usually heard in the last tune of the set) often seems perfunctory. But Messrs. McNeil and McHenry are constantly playing off one another — even when one is taking a solo, the other is either supporting or answering him, the way a pianist would customarily be expected to do. The interplay is built into the melodic statements as well as the improvisations, and totally drives the music, much the way it does in a traditional New Orleans band.

Messrs. McNeil and McHenry only played one pop tune in the opening set, “Moonlight in Vermont,” and likewise, there is only one jazz standard on the album, “Bernie’s Tune.” Both were part of the Mulligan canon. Taken together, they lead one to the unexpected conclusion that Mulligan’s music was more like Ornette Coleman’s than I had previously realized. Messrs. McNeil and McHenry spaced out “Moonlight in Vermont,” beginning with the sax and bass in a unison pedal drone, and generally rendering it as if it were from the soundtrack of some horror movie about a werewolf who meets his fate in a skiing accident. It reminded me that Mulligan and Baker played “My Funny Valentine” in a dirge-like fashion that actually anticipated a lot of Mr. Coleman’s music, particularly “Lonely Woman.” And the McNeil-McHenry treatment of “Bernie’sTune”had a distinctly schizophrenic, frenetic quality of the sort that one associates more with Mr. Coleman and Don Cherry.

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Having threatened to put pianists out of work in the early part of his career, Mulligan went on to collaborate with many of the greatest during the next 40 years. In 1993, I was fortunate to hear him in a quartet setting at a Highlights in Jazz concert — perhaps the best of the many times I heard him live — co-starring the celebrated jazz spokesman and pianist Dr. Billy Taylor. Thankfully, one of their performances together from that year was recorded and has been released as “Live At MCG (Manchester Craftsman’s Guild, Pittsburgh).”

Mulligan and Mr. Taylor’s heavy reliance on basic ur-standards, such as “Indiana,” “Body and Soul,” and “Just You, Just Me,” indicates that this was a special collaboration rather than a working unit. There’s a tricky arrangement of “All the Things You Are,” on which Dr. Taylor takes the lead in re-conceiving the Jerome Kern tune as if it were a Bach fugue. Elsewhere, there’s just room enough for one of the most famous tunes each by Mulligan (“Line For Lyons,” taken faster than he usually played it at this point), Dr. Taylor (“Capricious,” not to be confused with Dizzy Gillespie’s “Caprice”), and Duke Ellington (“Come Sunday”). The latter is the most reverential piece on the album, and fully illustrates the incredible esteem in which Mulligan held the Maestro.

However, if you download only one track from this album on iTunes, “Darn That Dream” is the one to nab. Mulligan first arranged the Jimmy Van Heusen song for Miles Davis’s Birth of the Cool band in 1949, and continued to play it through the years with Chet Baker and Bob Brookmeyer. This late-in-life performance shows both a sensitivity and a capriciousness worthy of Lester Young, another of Mulligan’s guiding stars. He and Dr. Taylor begin as a duo, with bass and drum (Chip Jackson and Carl Allen) refraining until the bridge. Mulligan phrases the opening eight bars more eloquently than I have ever heard any great singer do the words, pondering every note and presenting it as if it truly meant something to him. Just before he gets to the title phrase, he pauses and laughs, then resumes playing.

He’s presumably hearing the lyrics in his head, and the phrase “Darn That Dream” suddenly strikes him as funny — being a leftover euphemism of a more innocent age when only Rhett Butler was allowed to say “Damn” (not that “Damn That Dream” would make a great title for a song, anyhow). Mulligan is completely in the moment, yet creating something for the ages. The dream has been thoroughly darned.

wfriedwald@nysun.com