Experiment Control: Lehman deftly plays with spectralism on his latest.

With Travail, Transformation, and Flow, alto saxophonist Steve Lehman makes a rare offering to the jazz world: a thoroughly alternative principle of improvisation. Lehman’s deeply compelling harmonies and textures sound noticeably different from anything before it, but the music doesn’t have the threat-to-everything-we-know-and-love trappings of prior upheavals.

On the disc, Lehman uses a jazz application of “spectralism”: a French school in which composers begin with a note on a given instrument, use a computer to analyze the spectrum of tones that make up that note, then orchestrate all of those tones on different instruments to create new harmonies. The physical acoustics and the musician’s attack on the instruments help determine the nuances within the tonal spectrum, but timbre is the primary element of spectral harmony.

That’s about all anyone needs to know about spectral theory and more than is needed to enjoy Travail, Transformation, and Flow. What it means in terms of the actual sound of the album is that Lehman uses a broad variety of instrumental timbres in his octet. His alto meets tenor sax, trumpet, trombone, tuba, vibes, bass, and drums, essentially a big band in a small package. It also means that the eight tracks on the album develop very slowly—with frequent repetition and lots of sustained notes and resonances. The album’s strength lies in timbre and harmony: The few melodies Lehman does compose are redundant and not very interesting. The closing “Living in the World Today” is the only melody that’s particularly memorable—and Lehman didn’t write it.

The most prominent sound on Travail is the vibraphone of Chris Dingman, whose four-mallet attack allows him to play chords, which reverberate, often for several seconds, after he strikes. Dingman could be the music’s harmonic frame all by himself, but Lehman frequently fuses the vibes with Jose Davila’s tuba so that together they sound like one pretty but alien ax, as on “Alloy” and “No Neighborhood Rough Enough.” An even neater trick happens on the short “Dub,” where the vibes fade out as trombone and trumpet fade in, using a close-but-dissonant harmony that makes the first sound seem to morph into the second. On most albums these would seem like minor touches, but on Travail, Transformation, and Flow, it’s a great deal of the point: by making notes and voicings inseparable from each other, Lehman blurs the boundary between arranger and composer and establishes relationships between sounds that should clash.

Although cutting-edge harmonies are the album’s highest priority, Lehman never short-changes the rhythmic element. More than anything, the riffs and vamps that form most of his compositions establish and reinforce the songs’ grooves, much like Sonny Rollins’ original tunes. The third track, “As Things Change (I Remain the Same),” is all groove, with Dingman and bassist Drew Gress playing together. Even the solos (from trumpeter Jonathan Finlayson, tenor saxophonist Mark Shim, trombonist Tim Albright, Davila, and Lehman) of the piece observe the same accents and pauses that the rhythm section does.

The rhythms in question, however, aren’t swing or even free. Most of what drummer Tyshawn Sorey plays draws from hip-hop and electronic dance music. The opening “Echoes” rides on the sort of steady tick-tick pulses that would ordinarily come from a drum machine; “Dub” actually finds Sorey using acoustic traps to replicate the skittery electrobeats of artists like Autechre. Not coincidentally, “Living in the World Today” is a GZA cover in which Sorey, Gress, and Dingman open on a groove that skips its final beat before repeating: a direct allusion to the realm of sampling and glitch.

But even with such innovative harmonies and rhythms, jazz’s main draw remains the improvisations, and nobody in the band disappoints on that front. Lehman himself is the most penetrating, slicing through the harmonies of “Echoes” with a jagged, self-consciously dissonant alto solo. Shim and Albright share the title of most tuneful; the saxophonist shines on “Rudreshm” and the trombonist appeals on “Alloy,” with both turning in delirious melodies on “As Things Change.” But these often microtonal solos then become part of the album’s weird harmonic matrices, and the sum total is shrouded in dark enigma. The precisely honed dissonances are fraught with tension, so that each tune presents itself as a tangled dilemma with no apparent resolution. Mix in the rhythms, and a more practical dilemma emerges: These are club beats, but how does one get down to such troubled music?

Better, perhaps, to refrain from dancing and just listen. The mysterious and open-ended tensions on Travail are a powerful lure into an advanced and challenging set of music that firmly establishes Lehman as a major force in jazz’s avant-garde without taking the music too far out for comfort. Rare as it is to rewrite the language of jazz improvisation, it’s rarer still to do so while simultaneously fusing the idiom with modern classical and contemporary hip-hop—let alone to make it this compelling and listenable.