The back-to-school season is a good time to remember jazz’s greatest pedagogue, pianist and composer Lennie Tristano (1919-78). Last week, Birdland presented a quintet led by saxophonist Charles Krachy, featuring Virg Dzurinko (one of Tristano’s younger students) and an alto-tenor frontline performing Tristano-esque contrapuntal variations on standards. This week, tenor saxophonist Mark Turner – virtually the only younger well-known player to reflect the distinct influence of Tristano and Warne Marsh, brings his outstanding trio, Fly, to the Village Vanguard.

The group, which co-stars bassist Larry Grenadier and drummer Jeff Ballard, has also recently released their first CD, “Fly” (Savoy Jazz ).After years of thinking of Mr. Turner as the most prominent latter-day Tristano-ite, the first thing I noticed is that as he ages (he’ll be 39 in November), he steadily absorbs more and more influences. In fact, when I first heard tracks from his new album on WBGO, I assumed they were by one of Joe Lovano’s trios.

Fly does not follow the expected path for piano trios (at least before Bill Evans and Ahmad Jamal) of one star and two sidemen. Here no one player is more important than the others.

The most exciting thing about the trio is that it shows that three musicians can be playing essentially different things and still all be playing together. Mr. Grenadier plays mostly vamps on the bass. Mr. Ballard dispenses all manner of rhythmic patterns on the drums: marches, latin, funk. Mr. Turner sometimes plays with them, sometimes against them, but they’re always on the same page, working in unison.

Ever since Benny Goodman’s trio 70 years ago, the threesome of one horn (most often a reed) and two rhythm has generally been used as a vehicle for extended soloing. Fly, however, is a vehicle for the band’s collective efforts as composers as well as players.

Mr. Turner’s composition “J. J.” – a high point of the album, as it was on Wednesday night – exemplifies their approach. At times, Messrs. Ballard and Grenadier churn highly aggressive patterns of energy while Mr. Turner creates a contrast with cool intensity. His serene patterns focus one’s attention, and he holds the stage without ever raising his voice.

The catchiest piece on the album, alas, wasn’t heard on the set I attended, but undoubtedly they’ll play it over the weekend. “Piano Tune” (which is titled ironically, considering no piano was present), is an understated waltz reminiscent of the writing of John Lewis and Ornette Coleman’s “European Echoes.” It could be a hit single.

The set closed with “It’s Magic,” perhaps in anticipation of the Jule Styne Centennial next year. The Doris Day hit is well-suited to Mr. Turner’s style: Like many post-modern reed players, he likes to use the entire range of his horn, and here the opening line in itself descends a 14th from high E-flat to low B.

It seems to be a trend in clubs lately for a group to close a program of very intense originals with a warm and familiar standard – the Ron Carter Trio did something very similar three weeks ago with “Autumn Leaves.” I, for one, welcome it.

Messrs. Turner, Grenadier, and Ballard will be back at the Vanguard in two weeks in a quartet setting with Brad Mehldau (an appropriate point to play “Piano Tune”). It’s been 10 years since Mark Turner released his first album, “Yam Yam” (Criss Cross). Since then he’s progressed from a promising student to an emerging master. His teachers would be proud.