These days, it isn’t enough for a jazz instrumentalist and bandleader to be a virtuoso player with a distinctive style. It’s equally important to come up with a band sound that’s different from what everyone else is doing.

That challenge is a formidable one for tenor saxophonist Chris Potter, who is most often heard in New York clubs with the bands of Dave Holland, a master at assembling groups that sound like no one else’s. Yet Mr. Potter has achieved something special – and unique – with his quartet, Underground, which is performing this week at the Jazz Standard and released a new CD, “Underground” (Sunnyside 3034), last month.

It’s hard to think of another tenor player of Mr. Potter’s generation who is in his class. At 34, he is well on his way to joining the elite ranks of such venerated veterans as Joe Lovano and Dave Liebman. As a student, Mr. Potter began on alto saxophone before upgrading to the bigger, deeper sound and wider canvas of the tenor. At times, he toys with a thinner, more alto-like tone, but at other points he plays with a big, wide, celebratory tenor sound.

The Underground quartet seems at first to be oriented toward fusion or even smooth jazz. The rhythm section – Craig Taborn, Rhodes piano; Adam Rogers, guitar; and Nate Smith, drums – is completely electrified and features a lot of funky backbeats. But some of Mr. Potter’s music is so dark and dense and austere that it could create a new genre label: “heavy jazz.” When his tenor stops playing, the other musicians don’t solo so much as provide an electronic soundscape.

The third tune of Wednesday night’s set at the Jazz Standard, “Arjuno,” opened with a slow, stately introduction, and as it gradually proceeded to the central melody, I imagined an ancient walled city with its gigantic gate slowly opening. In the way the beginning sets up the rest of the piece, I was reminded of John Coltrane’s religious works like “Song of Praise,” “Peace on Earth,” and “India.”

Virtually all of Mr. Potter’s compositions for the group are dark; the rare moments when Underground lets a little light in occur when the quartet plays someone else’s music. Radiohead’s “Morning Bell,” the Beatles’s “Yesterday,” and Billy Strayhorn’s “Lotus Blossom” are all on the album, and the latter was played at the Jazz Standard as well.

It opened with a long, celestial starscape painted by the Fender Rhodes, after which Mr. Potter set himself the task of personalizing the melody without actually improvising on it, treating it to a variety of tones and textures and playing with the tempo. He finished with a long, unaccompanied cadenza that led directly to the climactic piece of the set, the funky and extroverted “The Wheel.”

Other highlights included “Train,” a long and complex melody that, like a freight train, comes in many sections; and a piece called “Brues,” which alludes to the blues but isn’t in strict blues form.

***

Gary Smulyan, the outstanding baritone saxophonist of his generation, is honoring two distinct aspects of his horn’s heritage this week.Through Sunday, he is playing alongside trumpeter Jeremy Pelt at Dizzy’s Club Coca-Cola, re-creating the Donald Byrd-Pepper Adams Quintet, and on Wednesday, he starred in a program of Gerry Mulligan’s music, accompanied by the excellent student orchestra Jazz Band Classic.

Mr. Smulyan is the rare musician who could do justice to both these remarkable – and extremely different – player-composers. Take, for instance, that staple of jazz composition, the major-key blues, which was a highlight of both shows. In playing Byrd’s “Hush” at Dizzy’s, Mr. Smulyan was earthy, visceral, almost gruff. His version of Mulligan’s “Blueport,”though no less aggressive, was much more airborne, belonging to the sky rather than the earth.

Mr. Pelt’s playing was at its usual high standard, but the driving force of the beautiful program at Dizzy’s Tuesday was Mr. Smulyan. At one point, he surprised everyone by introducing a Charleston dance figure in the middle of a hard-bop blues. At Symphony Space, he impressed with a crafty exchange with Christian Contreras, Jazz Band Classic’s teenage baritone saxophonist, on the rare “I Know, Don’t Know How.”

At its best, the baritone is a dancing bear of an instrument, but Gary Smulyan is so “all over” his horn, as musicians say, that it sounds more like a tenor on steroids.

Potter until March 12 at Jazz Standard (116 E. 27th Street, 212-576-2232). The Music of Donald Byrd until March 12 at Dizzy’s Club Coca-Cola (Broadway at 60th Street, fifth floor, 212-258-9595).