The idea of hybridity has been central to the music of alto saxophonist/composer Rudresh Mahanthappa throughout his career. Most prominent, of course, has been his highly original fusion of east and west, jazz mixed with the sounds of his Indian heritage. But that’s too easy and linear a depiction of this open-eared and inventive composer, who has absorbed an enormous variety of music into his thinking and amalgamated it into a singular vision.

On his new ACT release, Gamak, Mahanthappa continues that multi-directional evolution with a bold, striking set of music that melds leading-edge jazz with innovative reinterpretations of traditional Indian and Middle Eastern approaches, shot through with an electric jolt of prog-rock complexity. Just as his personal experience is never wholly lived on one side of the hyphenate or the other, his music speaks in a voice dedicated to forging a new path forward.

Gamak, Mahanthappa’s thirteenth album as leader or co-leader, marks the debut of a new band that is both a reprise and a reinvention. The album reunites the saxophonist with bassist François Moutin and drummer Dan Weiss, the rhythm section from his long-running quartet, which was last recorded for the 2006 album, Codebook. “Dave has checked out so much music,” Mahanthappa says of Fiuczynski. “A lot of eastern music, whether it’s Chinese or Indian or Arabic, and a lot of 20th and 21st century classical music. Not to mention that he has this rock/punk aesthetic that’s evident in his band the Screaming Headless Torsos. And Dan and Francois come from a really wide perspective as well. Dan is just as much into Rush as he is Max Roach or Zakir Hussain. So I knew those guys were going to really bring this stuff to life.”

The album kicks off with the wiry prog-rock tension of “Waiting Is Forbidden” and ends with the hurtling punk screamer “Majesty of the Blues.” Fiuczynski is at his slipperiest on “Aboghi,” based on a raga that Mahanthappa describes as “one of the rare ragas that’s treated in very similar ways in both North and South India.” In the quartet’s interpretation, it’s transformed into a rubbery, feel-good boogaloo. Gamak as recorded ten years after Mahanthappa’s breakthrough sophomore release, Black Water, which he revisits directly and indirectly on two tracks. “Are There Clouds In India” was originally recorded on that album, and recently arranged for big band by Jim McNeely, which revived Mahanthappa’s own interest in the piece. “We’ll Make More” is a new piece built upon the same raga and beat cycle as “Balancing Act," the opening track from Black Water.

“Waiting Is Forbidden” came from a piece in the Brooklyn Museum, while “Wrathful Wisdom” is a concept from Buddhist philosophy. The piece to which it’s attached is one of Mahanthappa’s most challenging inventions, requiring awkward, counterintuitive alternate fingerings.

Despite the depth and breadth of his influences and his restless imagination, one thing which Mahanthappa has managed to do throughout his career is remember to “Stay I.” It’s a lesson that has continually resulted in strikingly individual statements, and Gamak is certainly no exception.