There's an intriguing, good-humored wariness in the playing of the tenor saxophonist Bill McHenry. His tone is dry as cardboard but smooth and rarely stern, and as an improviser he treads meaningfully, choosing his moments, guarding against wasteful expenditure. As a bandleader he prefers soft direction, presenting loose guidelines and then letting the chips fall. This can make for a Zen logic of care and surrender, rigor and relinquishment. But it can also yield an aimless disconnect and a sense of vaguely unfulfilled intention.
All of those outcomes played out to one degree or another on Tuesday night at the Village Vanguard, where Mr. McHenry has brought a quartet with an expressive elder, the drummer Andrew Cyrille, and a couple of well-bonded peers, the pianist Orrin Evans and the bassist Eric Revis. This group made its debut last November in the same room, and had one of its sets broadcast by WBGO (88.3 FM) and npr.org. There hadn't been any other gigs until this week's, which will be documented in more traditional fashion: Sunnyside is recording two nights of the run for future release.
If much of the opening set felt provisional, it wasn't just a matter of settling in. The band began on firm footing, with 12:30 a.m.," a newly minted blues featuring a loping feel and a lightly pecking melodic line. Mr. McHenry articulated that line with maximum terseness, as if to underscore its teasing syncopation. Then he began his solo with a foghorn squawk, holding it for almost four barstension, meet releaseand moved on to a relaxed and mischievous style, somewhere between Dexter Gordon and Charlie Rouse. The rhythm section cruised and simmered behind him.
It was casually enchanting, as was a later perambulation through a Gershwin standard, Love Walked In." Mr. McHenry phrased that one in a soft, honking mode, like a muffled emulation of the young Sonny Rollins.
The set's more open-ended moments felt hollow, as if lacking a motive. A ballad called Today" was pretty but never tapped into a deeper current. An abstract piece that began with saxophone and piano, and then yielded to an ecstatic, free-form bass solo, left an unfinished impression. A modal groove piece seemed to trail off midstream during Mr. Evans's solo, and what was probably meant as a flourish registered instead as apathy.
On their own time Mr. Evans and Mr. Revis make up half of Tarbaby, a fine and provocative post-bop unit; they know how to bring gravity to a situation. And Mr. Cyrille is one of the great percussive engines of the jazz avant-garde, at home with textural license. So it makes little sense that the band struggled where it did.
Whatever the issue, it had no bearing on the set closer, So That Life Can Endure ... P.S. With Love." A ballad by Mr. Cyrille, introduced on record more than 15 years ago, it brought out Mr. McHenry's imploring side, and the band snapped into focus.
The Bill McHenry Quartet performs through Sunday at the Village Vanguard, 178 Seventh Avenue South, at 11th Street, West Village, (212) 255-4037, villagevanguard.com.