The "pianoless" quartet has always had a special place in jazz — the original Ornette Coleman Quartet, Gerry Mulligan with Chet Baker, and, a variation on the theme, Charles Mingus with Eric Dolphy. Without a chording instrument — a guitar or a piano — these bands have a spareness, almost an austerity. But they also offer tantalizing ambiguity: harmonic structures can be implied rather than stated explicitly. Horn players can engage in free counterpoint without tripping over piano voicings. In Coleman’s case, it meant inventing a whole new language. But even the most mainstream of these bands offer a pleasure that’s among the deepest of abstract art — transforming the familiar into something new that can’t quite be named.

Now come Guaranteed Swahili, the Boston-born quartet with Jason Hunter on tenor and soprano sax, Eric Rasmussen on alto, Tim Luntzel on bass, and Eric Thompson on drums. Although everyone but Hunter currently lives in New York, the band have been together since late 1995, when they emerged from the remnants of the Venus Band, of which Luntzel and Rasmussen were a part, a quartet that had held down a lengthy early-’90s residency on, of all places, Lansdowne Street, in the since-renamed Venus de Milo club, where they drew an avid following of young alt-rockers and music-school kids.

Guaranteed Swahili — with two independently released CDs and a third planned for spring release — have all the hallmarks of their pianoless ancestors. Hunter and Rasmussen are a classic tenor/alto match-up, with an uncommon expressive range. Rasmussen spins out endless skeins of melody in the manner of Lee Konitz, while Hunter’s tenor likes to explore the outer reaches of the chord changes — Coltrane by way of Joe Lovano. Hunter brings to the table the requisite expressive shrieks, split tones, vocalisms, and "false" registers that are the legacy of the tenor-sax avant-garde. But he also has a solid upper register, so he can honk and slither alongside Rasmussen’s melodic deliberations, or they can both take off, Konitz/Warne Marsh–like, on extended flights of airy, lyric counterpoint.

But that’s only the half of it. Rasmussen, as the band’s primary composer, loves to mess with time. Listening to Guaranteed Swahili, you’re aware of a strong rhythmic pulse you can’t quite count. Think of the surge of free jazz organized in a tight metric scheme. Rasmussen will literally write a piece with a different time signature in every bar. The classic tension/release of verse/chorus and key changes is transfigured in rhythm, with the solos arranged to bring out each player’s strengths. Or, as Hunter explains to me over coffee at the Trident Café on Newbury Street, "Eric will get the solo section that has a bar of seven, bar of five, bar of four, bar of three, bar of five — and then I’ll get the solo section that’s like a four-bar vamp in seven and then I can lose my shit and play kind of freely over it."

It’s a tribute not only to Hunter and Rasmussen, but especially to Luntzel and Thompson that Guaranteed Swahili can play this kind of music and have it come off not as a dry academic exercise but rather as highly charged, swinging jazz. Hunter points out that the common denominator even in Rasmussen’s most complex charts is still the eighth note — a guide for both players and listeners.

Another appeal of the band is its work with longer forms. "I’m trying to make a tune longer," says Rasmussen on the phone from New York, "so it’s not the listener hearing a ‘head’ and then five solos on the same form, but trying to have it so you have some material, have a soloist play on that material, have some new material, have a soloist play on the new material." A piece might start out with a rubato section for a single horn and drums, and gradually build to an exultant, bopping unison theme statement by the band. Mystery and narrative surprise abound in this music.

Rasmussen is all too aware of the pitfalls of writing exercises for blowing. "When I first started delving into this music, there was some exercise point to it, like: I want to be able to play in this time signature." He compares it to Coltrane, who "wrote something like ‘Giant Steps’ so he could learn how to play in those chord progressions." But another influence was a teacher who told Rasmussen to stop worrying about writing in eight- or 12-bar units, and instead to use more natural phrases that fit his horn playing. "I’m trying to write singable, hummable melodies that are challenging," he says, adding, "I see people tapping their feet. Or they’ll see me the next day and say, ‘Yeah, that was a really catchy tune,’ and actually whistle some of it back. They don’t realize that it’s a bar of 5/8 going into a bar of 3/4."

Guaranteed Swahili play the Regattabar this Tuesday, February 18; call (617) 876-7777.