If music can be called "suspenseful," there was something about the music that Rez Abbasi premiered at the Painted Bride on Saturday that held as much edge-of-your-seat tension as the best film thrillers. In part that could be chalked up to the fact that his stellar band, Invocation, was performing new, incredibly complex music for the first time. But more often the sensation came from the same place all great suspense comes from: daring risk-taking coupled with sheer unpredictability.

The music that Abbasi presented is destined for his next album, Unfiltered Universe. With Invocation, the Pakistani American guitarist creates a unique fusion of jazz with music of his South Asian heritage. In the past, that's encompassed Pakistani Qawwali and the Hindustani music of northern India. Now he's drawn inspiration from the rhythmic traditions of South Indian Carnatic music.

Those inspirations should feel particularly familiar to Abbasi's longtime collaborators, pianist Vijay Iyer and saxophonist Rudresh Mahanthappa. Both have explored their South Indian heritage distinctly, together and separately; while they were frequent partners early on, this show was an increasingly rare opportunity to see them share the stage.

Mahanthappa's tart, wiry alto took careening turns and molten flurries, an ideal foil for Abbasi's overdriven leads. Iyer provided more severe and cerebral delights, with captivating shifts between stabbing chords and delicate, angular musings.

Drummer Dan Weiss envelops tabla techniques into his own stunning approach. Playing Abbasi's music, he coupled rhythmic patterns with disruptive (in the best sense) surprises. Bassist Johannes Weidenmüller maintained a crucial, understated tension, while the ensemble's newest member, cellist Elizabeth Means, contributed swoops and scrapes and added enticing color to the melodic palette.

Unlike many experiments with jazz and world music, there was nothing explicitly Indian about Abbasi's music. Instead of facile quotations, he's melded techniques and concepts into an idiosyncratic, compelling sound of his own. Hard-rock guitar gods were as relevant as South Asian classical music to his solos, which could be jagged or contemplative. His compositions ranged from the stutter-step of "Propensity" to the prog-funk of "Dance Number," offering ample opportunity for bracing improvisations even as the band was finding its way in this new music.