Wearing an ocean-blue dress and holding recently written lyrics in her hand, Bjork sang at what may well have been her smallest gig of the year on Friday night at the Housing Works Bookstore Cafe, which was packed with about 300 people.

The music was quiet: just voices and modestly amplified acoustic instruments. But the songs were hugely complex and ambitious, announcing their destination in the lyrics: “on and on and ever onward.”

Bjork was collaborating on a suite of six new songs with Dirty Projectors, the New York City band led by David Longstreth. They had been brought together by Brandon Stosuy, from the music blog Stereogum, who supervised a Bjork tribute album and found they admired each other. No wonder: They could be musical cousins, though their songs head in different directions. Mr. Longstreth’s leaping, suddenly swelling vocal lines clearly show Bjork’s influence. And his music’s blend of classical- and progressive-rock intricacy, pointillistic backup singing and West African picking patterns rightly appeals to the equally eclectic Bjork.

Before she appeared, Dirty Projectors played acoustic versions of four songs from its next album, “Bitte Orca,” which is due for release in June. Without drums or electric guitar, the arrangements grew transparent, uncovering all their layered vocal parts — sometimes just quick, single, staggered notes ricocheting among the three female singers — and making Mr. Longstreth’s philosophical lyrics, about intention and the nature of reality, sound almost wistful.

Onstage, Mr. Longstreth said the new suite was inspired by a visit to Mount Wittenberg in northern California, where Amber Coffman, one of the singers, sighted a whale, and “the whale saw her.” Mr. Longstreth said the suite might be called “Mount Wittenberg Orca.” The lyrics, full of water imagery, contemplated humanity, love, fate and nature; the music shimmered with sustained and contrapuntal voices.

The songs were largely or entirely Mr. Longstreth’s — he took half the lead vocals, leaving Bjork only three songs — but her presence brought out their longer lines amid the counterpoint. Where Mr. Longstreth’s lead vocals can sound mannered, Bjork sings like a force of nature. The songs became ballads of innocence and discovery, particularly the delicate finale, a moment of mystical interspecies communion concluding with a line from Kurt Cobain: “All in all is all we are.” It would have been a crowdpleasing touch to follow up with a rearranged Bjork song as an encore — Dirty Projectors recorded her “Hyperballad” on that tribute CD — but they chose to leave that gentle homily in the air.

Bjork and the Dirty Projectors each chose an opening act: Olof Arnalds, a woman from Iceland, and Kurt Weisman, from Vermont. Both were songwriters who put unexpected melodic tangents and other idiosyncratic twists into sparse, folky material.