For the last 17 years, The Bad Plus has been a model of musical cohesion. Its members — bassist Reid Anderson, pianist Ethan Iverson and drummer David King — have been an indivisible front, welcoming the occasional guest but never a substitute, according to the strictest ideal of a working band. As the saying goes, it has always been larger than the sum of its parts.

“This is one of the road bands of all time,” declared King, alluding to a tour schedule that has regularly exceeded 150 shows a year. “I would actually say, with all humility, that there is no group in jazz history that has played more gigs without a lineup change.”

But change is now on the visible horizon: Iverson will leave the band at the end of this year, as The Bad Plus announced on its Facebook page today. The group has identified a new member, the well-regarded pianist Orrin Evans, who will not only step into Iverson’s role but also bring his own style, inevitably transforming the sound of the band.

Given the history of The Bad Plus, rooted in a set of personal relationships stretching back decades, the news comes as a shock. But in separate conversations over the last few days, every musician involved described the development as a positive step.

“For us, The Bad Plus is above all this statement about group music,” said Anderson. “We want to carry that commitment forward. We really believe that it’s good for the music, and we believe it’s good to be a symbol for that, out in the world.”

An audacious power trio that also functions as a postbop combo, The Bad Plus first made its mark by reforging songs from the pop-culture consciousness. (“Smells Like Teen Spirit,” by Nirvana, was an early calling card.) But the band has also been a tireless engine for original music. Each member contributes compositions, writing for the band while preserving a distinctive signature: vaulting and sonorous for Anderson, dissonant yet often delicate for Iverson, wily and kinetic for King.

There have also been impressively focused detours through a nonstandard repertoire — including major concert programs devoted to Ornette Coleman’s Science Fiction and Stravinsky’s Rite of Spring. And the band has collaborated with a handful of kindred spirits, like vocalist Wendy Lewis, guitarists Bill Frisell and Kurt Rosenwinkel, and saxophonist Joshua Redman, who is captured here with the band at the 2014 Detroit Jazz Festival, in an episode of Jazz Night in America.

A subsequent album, The Bad Plus Joshua Redman, demonstrated the flexible strength of the band’s identity: Instead of suddenly turning into a jazz quartet with saxophone up front, the band made a place for Redman’s voice. For his part, Redman worked hard to become a functioning part of the band’s machinery, accepting its terms and conditions.

The Bad Plus has also had an influence on the postmillennial jazz landscape, especially for improvising bands made up of acoustic piano, bass and drums. The Jim Black Trio is one group that applies some Bad Plus methodology toward its own outcome. A handful of European groups, like Phronesis and GoGo Penguin, have done something similar, with varying degrees of originality.

Meanwhile, the creative energies of The Bad Plus have been unflagging: It’s Hard, released last year, is an all-covers album that shows no hint of exhaustion. Judging by all the available evidence, the band still has its musical mojo. Iverson, speaking in a proudly matter-of-fact tone, put it this way: “The Bad Plus has essentially never played a bad gig.”

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So what happened?

The answer gets a little complicated, but at root it involves long-simmering internal tensions. Iverson responded to the question with a jazz-historical anecdote, drawing from a firsthand source.

“Tootie Heath told me about the later years of the Modern Jazz Quartet, when all four members would demand to be seated in first class, in the opposing corners,” he said. “They would need two limos, because Milt [Jackson] and John [Lewis] couldn’t even rub shoulders with each other anymore. But they kept the band together because the money was so good.”

Iverson paused. “Reid and Dave are friends of mine for life,” he said, “but at the same time, I had felt like it just gets hard to keep relationships going after 17 years that are as fun and as cool as they were at the beginning.”

He had also begun to feel he’d said everything he could say within the parameters of the group. “Whatever corner of real estate I had, to be my most secret and private self in public as a player, it just didn’t feel like I could do that anymore,” he said.

Every member of The Bad Plus maintains a life outside the band, but Iverson has been the most demonstrative about stretching out in recent years. He has recorded albums with Heath, and works regularly in a quartet led by another venerable jazz drummer, Billy Hart. Last year Iverson released a trio album, The Purity of the Turf, featuring bassist and NEA Jazz Master Ron Carter. And in jazz circles, he’s known as a perceptive interviewer and critic of sorts, on his obsessive and idiosyncratic blog, Do The Math.

If you’re just vaguely familiar with Do The Math, it may be because Iverson recently found himself at the center of an imbroglio around sexist discourse and perceptions in jazz culture. (The whole mess was expertly dissected by Michelle Mercer for NPR.) That controversy had no bearing on Iverson’s decision to leave The Bad Plus, but his blog did generate some friction in the band.

“Ethan started to have an agenda, especially critically,” said King. “That was a little bit uncomfortable for us, because all of a sudden we’re in a band with a guy who’s essentially a jazz critic. We’re used to him throwing his opinions around the van, but having his opinions out there in the world so strongly all the time, it started to reflect on people thinking it was all of our opinions.”

The situation was worsened by a stubborn perception, in the press as well as the public, that The Bad Plus was somehow Iverson’s group, or a collective in which he’s first among equals. “In many ways,” King said, “Reid and I have been the artistic directors of The Bad Plus. It would actually be erroneous to state that it’s a 100% equal situation.”

Iverson’s sideline interests had also begun to raise hackles in the band. “Just frankly,” King said, “it felt a little bit like we became a bankroll for his desires to play with the old masters.”

But the biggest hurdle to comity in The Bad Plus has been a growing chasm between Iverson and Anderson, which neither musician states outright, though the signs are there. Asked about Iverson’s decision to leave the band, Anderson fell silent for 10 long seconds. When he finally spoke, it was to deliver a carefully worded statement:

“We’ve all spent so much time with each other, and had an incredible privilege to be able to do what we do,” he said. “Ethan’s been one-third of that experience and incredibly important, and made an incredible contribution in my life and Dave’s life. And now it’s time for us to move on and for him to move on and do some other things. We thank him for the last 17 years, and I guess that’s kind of the way that it is.”

King put the issue more bluntly. “Reid and Ethan were at one point very, very close in the ‘90s and early 2000s,” he said. “Their hookup has always been so heavy musically, but as people, they sort of grew apart.” He went on to compare the band to the Police, another threesome made up of strong personalities, with an undercurrent of conflict that fed the music.

“Those two have probably needed to be not creating together for a few years now,” King said, of Iverson and Anderson. “But that’s not to say that it hasn’t yielded some of our heaviest music.”

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Orrin Evans, who at 42 is a couple of years younger than Iverson, is one of the most dynamic postbop pianists of his generation. He’s also a decisive bandleader who has led small groups along with one high-test large ensemble, the Captain Black Big Band. And he’s a member of a strong collective trio, Tarbaby, with bassist Eric Revis and drummer Nasheet Waits.

“Something I always find myself saying is ‘Go for the obvious,’” Anderson said. “Orrin is an incredible pianist and a really powerful spirit, and I think we share a certain outsider-weirdo aesthetic. So this was a really obvious thing to do. We didn’t have to think about it at all.”

Reached by phone during a set break at Smoke Jazz & Supper Club, Evans described himself not only as a longtime admirer of The Bad Plus but also a member of its extended family. “Reid and I go back to when I was in high school,” he said. “Reid was one of the groomsmen at my wedding. I remember when the Bad Plus started. And Dave has always been around and he’s always been really nice. I’m not walking into a new place spiritually or emotionally at all.”

There will be a lot of material to learn, and a certain legacy to carry forward, as Evans is well aware. “I’m walking into a situation that has already defined itself,” he said. “I would never disrespect Ethan, so I have to respect the role he played and also be true to myself.”

Evans had never played with King before a recent session in Brooklyn with the new lineup, which wasn’t an audition but did have the feeling of a trial run. “And when we first got together, the second he started playing one of Reid’s tunes, the sound just exploded out of the instrument,” King recalled. “And we needed that: to say, ‘You know what? This music is alive.’ When it’s inhabited by someone who is excited to be there. It just crushed.”

Iverson, who said he applauded the choice of Evans, already has a lot of activity planned for his life after The Bad Plus. This summer he’ll record a duo album of original music with tenor saxophonist Mark Turner. He has a recent live recording made with trumpeter Tom Harrell, which he’d like to release as an album. Iverson is also writing a piano concerto for American Composers Orchestra.

And as the longtime musical director for the Mark Morris Dance Company, he’s deeply involved in Pepperland, an evening-length anniversary tribute to the Beatles’ Sgt. Pepper’s Lonely Hearts Club Band, for which he composed a score inspired by the album’s songs. (The piece will have its premiere in the City of Liverpool, England, May 25-27.)

Iverson also intends to do more writing and jazz scholarship, at Do The Math and elsewhere — something he’d always had to squeeze in from the road. “With a comparatively free calendar, I’m looking forward to practicing and thinking about music in a philosophical way,” he said.

He will be on tour with The Bad Plus this spring, reaching the Jazz Standard in New York from May 9-14. Iverson’s final performance with the band is scheduled for a neatly symbolic date: New Year’s Eve, at The Bad Plus’ customary stand at the Village Vanguard.

Evans will make his public debut with the band two weeks later, in St. Louis. By then, The Bad Plus may have an album out to smooth the transition: there are plans for the new lineup to record a program of all-original music, including pieces by Evans, in late summer.

“We want to be able to build this up into a real institution of our generation,” said King. “It’s like: This is the sound we make. It’s an idea above all. It’s an idea that you turn other things down for the sake of the group, and you create a language that can only be played by these people.”