Mr. Zorn is known for writing pieces that keep shifting styles, sometimes phrase to phrase. As performed here, the shifts in “Jumalattaret” seemed just right, as the music segued from mellow moments of jazzy piano chords, wistful folk song and strands of filigreed passagework to crazed blasts that suggested hardcore rock. Ms. Hannigan’s technical assurance allowed her to bring out the cycle’s musical subtleties and emotional subtexts. She is a remarkable musician, who has performed more than 100 premieres while also pursuing conducting.

This was the New York premiere of the piece, and it was great to hear it in the Armory’s intimate and elegantly restored Veterans Room. Will “Jumalattaret” have a future? It’s hard to imagine other artists performing it with comparable brilliance. But thankfully Ms. Hannigan and Ms. Gosling have a recording in the works.

The program on Tuesday continued with the JACK Quartet, joined by the vibraphonist Sae Hashimoto, in an episodic piece that Mr. Zorn described to the audience as “thought experiments.” Then Mr. Gosling played “Encomia,” a set of five of this composer’s dreamy, rueful and unhinged piano pieces. Ms. Hannigan, again riveting, joined the quartet for “Pandora’s Box,” Mr. Zorn’s intensely dramatic, mood-shifting take on the story of Wedekind’s femme fatale Lulu — inspired, he told the audience, by Berg’s opera on the same subject, in which Ms. Hannigan has had brilliant successes.