(L to R): Emerson String Quartet: Violist Lawrence Dutton, new cellist Paul Watkins and violinists Eugene Drucker and Philip Setzer. (Lisa-Marie Mazzucco/Lisa-Marie Mazzucco)

“I’d like to get past May 11th,” Philip Setzer said.

Setzer is a violinist and a founding member of the Emerson String Quartet. He’s 62 years old — something he hardly believed when he saw it in print in a recent article. He has a grueling schedule. When he made this statement two weeks ago, he was speaking by phone from a hotel room in Puerto Rico; the following day, he performed in Washington, and he played in Schenectady, N.Y., the day after that. Even for America’s leading string quartet, chamber music doesn’t yield the financial perks of some other branches of the music field; playing up to 100 concerts a year involves a lot of car travel, motels and late-night meals in diners.

What Setzer wants to get past, though, is not a tough travel schedule. It’s the quartet’s last concert with the cellist David Finckel, who, after 34 years, has decided to move on to other things. This final performance will take place at the Smithsonian’s Baird Auditorium, where the group has had a regular series since it spun off from the 20th Century Consort and applied for a National Endowment for the Arts grant more than three decades ago. The last piece on the program, the Schubert quintet, will unite Finckel and his successor, the 43-year-old Welsh cellist Paul Watkins, in a public passing of the torch.

“They’re going to be filming, recording; it’s going to be broadcast,” Setzer says. “It’s going to be like being on reality TV. I’m not looking forward to that, but to getting to the point where we’re playing the Schubert quintet, my favorite piece of music in the world. The thing about playing Schubert is that it’s so difficult it doesn’t allow you to think.”

String quartets have a pervasive mystique. They’re the essential ensemble of chamber music, the prototype of the boy (and girl) band — the Emerson’s Web site gallery includes a host of attempts to find new and funky ways to photograph four guys with instruments: backlit in dark alleyways, stalking across a wintry beach. They also offer audiences the elusive juxtaposition of profound art and the mundane forces of human interaction. It’s a spiritual marriage of four people conducted in the public eye.

Emerson String Quartet with former cellist, David Finckel (second from left). (J Henry Fair/© J HENRY FAIR)

So the end of the marriage brings a special fascination. There have been quartets whose members don’t speak (the Budapest Quartet); there are quartets that dissolve in a cloud of litigation (the Audubon Quartet); there are quartets that go out with a grand finale, as the Guarneri Quartet did in 2009. Indeed, the drama of replacing a departing quartet member has inspired at least two feature films: “Basileus Quartet” (1983) and last year’s “A Late Quartet,” in which Christopher Walken plays the aging cellist who’s leaving, and Philip Seymour Hoffman plays the ever-frustrated second fiddle.

If you want soap-opera drama, the Emerson is a snooze. Yes, the quartet went through a couple of personnel changes after its 1976 founding — the violist Lawrence Dutton replaced Guillermo Figueroa in 1977, and Finckel replaced Eric Wilson in 1979 — but those departures were perfectly amicable (“I was just at [Figueroa’s] 60th birthday surprise party,” Setzer said last week). And the group has compiled a laundry list of recordings and awards — nine Grammys! — while managing to continue liking one another. The two violinists, Setzer and Eugene Drucker, trade off as first and second violin, so there’s no jockeying for leadership. And the quartet long ago agreed never to vote on big decisions. “If somebody doesn’t want to do something, we’re just not going to do it,” Finckel said last week, adding, “It means you’re never dragging around a grumpy player.”

Indeed, Finckel’s leaving is anything but a sign of dissatisfaction; you could argue that only intense loyalty to his colleagues has made him stay this long. “David’s blueprint is to do about seven things at once, all extremely well,” Watkins says.

Finckel and his wife, the pianist Wu Han, tour as a duo (they also have a trio with Setzer); run a record label, ArtistLed; founded a festival, Music@Menlo, now in its 10th season, and run the Chamber Music Society of Lincoln Center — a full-time job in itself. It’s hard to imagine how he has continued to have time for the quartet at all.

And his departure, rather than signaling a body blow, has turned out to release the quartet from looming existential anxiety.

“When we talked about the future of the quartet and how we might end it,” Finckel says, “everybody had all kinds of good ideas” — like a 10-year plan culminating in a farewell tour. But “when we actually tried to sort of start the clock, the mood of the room would become very dark; nobody wanted to talk about it. It was kind of like planning your own funeral.

“However,” he says, “when I said, ‘Hey, I’ve gotta do something else,’ it [opened] the whole possibility . . . for them to consider a new model. It would bring new artistic blood into the ensemble at a good time, and it would also allow any member of the quartet to decide in the future when the right time is for him to leave without threatening the existence of the quartet.” Now that the decision has been made, Finckel says, “the whole dynamic of the quartet has changed, become so relaxed, become so much fun.”

Even finding a successor was pretty straightforward. Watkins had been on the players’ radar for a while. Dutton was the first of the Emersons to play with him and actually said, according to Setzer, that “if David were ever to leave, Paul would be perfect.”

Watkins is not as well known in the States as he is in Britain, but he has played here a number of times — including a couple of D.C. appearances with Musicians from Marlboro over the years — and is also familiar to many American musicians because his wife, Jennifer, is the daughter of the violinist Jaime Laredo and the late pianist Ruth Laredo. (Disclosure: Watkins and I served together on the jury of the International Competition for Young Conductors at the Besançon Festival in France in the fall of 2011.)

So when Finckel made his announcement, the other members of the quartet “decided, rather than go though a whole audition thing, which was so distasteful for us, let’s see if there’s any chance with Paul.”

Watkins, living in London with two young daughters and engaged in an active career as a soloist and conductor — he’s the music director of the English Chamber Orchestra — initially said, according to Setzer, “That’s so nice of you to think of me, but I just don’t see how I could do it.”

“That was only for about a day,” Watkins emends, speaking by phone from his new home in a New York City suburb and a little breathless from his first encounters with the commuter trains. “Then Jen and I sat down and had a seriously big discussion and realized that this was a massive opportunity, not just for the obvious professional and musical reasons, but for family as well.”

Watkins was soon completely invested in the idea of joining the quartet. Because Finckel had set a precedent for extracurricular activity, there was no need for Watkins to give up his conducting jobs (although he did have to end his longtime association with the Nash Ensemble of London, another renowned chamber group). “I would love to continue to not categorize myself,” Watkins says, noting with amusement that the critic Norman Lebrecht titled his Watkins/Emerson blog post “British conductor joins string quartet.” “Would that I had been referred to as a British conductor in the 10 years previously,” Watkins says, “when it was always ‘Cellist tries his hand at conducting.’ ”

Playing in a quartet, though, isn’t a departure for him — rather, “almost like a coming home.” As a student at Yehudi Menuhin’s school — a period that profoundly influenced him — he was immersed in the quartet repertoire. By coincidence, his first concert as an Emerson — in Montreal, at the end of May — will open with Haydn’s quartet Op. 20, No. 3, “which was one of the first quartets put on my stand at the Menuhin school when I was 13 or 14.”

“This guy’s a major artist, a major cellist, a keen intellect and musician,” Finckel says, “and his hunger, passion and desire to play this repertoire is astounding.” Last summer, after a Mostly Mozart concert in New York, “he came up to me backstage in the corridor with his hands folded like a prayer, and said, ‘Please, please don’t change your mind.’ Somebody wants my job that bad, it made me feel so good.”

So there will be no brooding animosities Saturday. But there will, of course, be a certain amount of poignancy. Finckel has been blogging on the Huffington Post about the bittersweet rituals of farewell — like putting boxes of sheet music into storage.

“There’s a part of me that definitely feels very sad,” Setzer says. “The quartet is going to continue very happily, and I have no doubts that it will work well with Paul, but at the same time it’s a hell of a long time that we’ve been doing this.”

It may be heretical to say that the Emerson could use a new beginning. I’m not the only person to observe that in recent years it has not been playing at the same peak level it established in its prime. Introducing a new point of view and a new artist to the mix could be just what it needs.

“I know I’ll be really happy when we get into next season and start playing concerts,” Setzer says. “It’s very exciting that Paul’s going to be playing these pieces for the first time. Walking out to play Schubert’s ‘Death and the Maiden,’ which I’ve played a couple of hundred times, and he’s going to be playing it for the first time . . .” His voice trailed off. But with excitement, not emotion.

The Emerson String Quartet

will play at Baird Auditorium in the Museum of Natural History at 6 p.m. Saturday. The concert is sold out.