“Temporary Kings,” the debut album from saxophonist Mark Turner and pianist Ethan Iverson, finds these two quiet killers immersed in a deep, fragile, highly focused form of play. They sound like they’re building a house of cards in the void.

And while that kind of intimacy should feel shocking from a partnership so new, these guys go back. The duo began crossing paths at jam sessions in New York in the late-’90s — before Iverson had formally assembled his pathfinding group, the Bad Plus, in 2000; and before the New York Times called Turner the “best jazz player you’ve never heard” in 2002.

Over the years that followed, the Bad Plus steered its idiosyncrasies toward big, enthusiastic audiences, while Turner quietly became one of jazz’s greatest tenor players. On the side, Turner and Iverson collaborated in a captivating quartet led by the drummer Billy Hart. On “Temporary Kings,” it’s just the two of them.

In separate conversations, they describe playing this delicate new chamber music as “intuitive” (Turner) and “easy” (Iverson) — and you can hear it in the unlabored touch they each bring to a deliberate idea. For Iverson, who left the Bad Plus in 2017 after years of frustration, the collaboration has certainly made his musical life feel more capacious. “It’s nice to have all the space around that was taken up by working for 17 years in the Bad Plus,” he says. “Now I can double down on making the most eloquent and esoteric music I want to make.”

If eloquence was the mission, he couldn’t have asked for a more simpatico partner than Turner, a laconic player whose economical vocabulary goes against the forceful, shouty post-Coltrane way of doing things.

Iverson describes Turner as the owner of his sound, but as a “searching” musician, too. Which is it? “I would say both,” Turner says. “The more that I look, the more that I gather for this thing that I’m beginning to own. I think those go hand in hand, actually. If you don’t look [for it], then you definitely don’t own it.”

There’s plenty of eloquence, esotericism, ownership and searching to be heard throughout “Temporary Kings” — especially during Iverson’s “Unclaimed Freight,” an atypical blues inspired by Stravinsky’s “Symphony of Psalms.” (As for the title, Iverson says he spotted it on a sign adorning a gargantuan warehouse while he was road-tripping through rural Minnesota.)

“It doesn’t feel simple,” Turner says of the song. “It’s a blues that no one else would write. It just sounds like Ethan’s blues.” And Turner clearly respects that authorship, even in the song’s liveliest moments, by taking the lead in a way that mysteriously sounds more like following.

Then, in the tune’s stunning finale, another switcheroo: the music downshifts its mood without really altering its structure. Turner sinks into a low, long note like he’s trying to extinguish a stubborn birthday candle. Iverson lightly bumps the table with his twinkling right hand. The card house collapses into silence.

Mark Turner and Ethan Iverson launch their tour Sept. 13 at An die Musik Live, 409 N. Charles St., Baltimore. andiemusiklive.com. $10-$20. “Temporary Kings” is out Sept. 7.