Mariss Jansons, conductor of the Royal Concertgebouw Orchestra in Amsterdam. (Marco Borggreve)

The greatest living conductor is bringing the greatest orchestra in the world to the Kennedy Center this coming week.

Don’t take my word for it. When a panel of international critics was polled about orchestras, Amsterdam’s Royal Concertgebouw Orchestra came out on top. As for its music director, Mariss Jansons, he leads both No. 1 and No. 6 — the Bavarian Radio Symphony Orchestra — in that 2008 ranking. He turns down most other conducting invitations. The only two other orchestras he works with regularly are Nos. 2 and 3 — the Berlin and Vienna philharmonics.

“I don’t really have much time to have guest conductings,” he says. “All these orchestras constantly invite me, and I feel a little embarrassed that I am not coming.” But, he adds, “you can’t do everything. You can have a thousand wishes, and you can’t fulfill them.”

Jansons, 70, is speaking by phone from his hotel in Amsterdam, where he spends 10 to 12 weeks a year. His life is mostly on the road. This year, the Concertgebouw is celebrating its 125th anniversary with a world tour that will take it to six continents, including its first performances in Australia (in November) and Africa (in March), as well as the current U.S. appearances — Tuesday’s concert will be his first in Washington since 2010.

Add to that his commitments in Munich with the Bavarian Radio Symphony and that ensemble’s touring schedule — Jansons recently went with the group to Asia — and he’s left with very little time in the city he technically calls home. “I am in St. Petersburg so short a time, you can’t say that I’m living there,” he says.

This kind of punishing schedule makes some conductors jaded. But Jansons doesn’t let anything become routine. In Asia with the Bavarian Radio Symphony, he did a cycle of Beethoven symphonies — warhorses, chestnuts or, depending on your outlook, revelations. Jansons’s gravelly voice brightens at the memory. “It was musically extremely exciting,” he says. “We did a video from Suntory Hall, a DVD — wonderful hall, very good public. It was one of the highlights, I must tell you, of my life.”

There’s the hyperbole again. It’s hard to write about Jansons and avoid it. He’s a brilliant musician, and everybody likes him.

“I think he makes, fairly consistently, deeply felt and committed performances,” says Henry Fogel, the dean of Roosevelt University’s Chicago College of Performing Arts, who earlier in his career ran the Chicago Symphony Orchestra and the New York Philharmonic — not at the same time. “Any orchestra he plays with, the musicians seem to fall in love.”

Fogel adds, “The CSO musicians . . . kept asking me why we didn’t bring him more often. The issue was, you can’t get him.”

You can’t get him — because he’s too busy and because of his health issues. The latter represent what appears to be the sole tension in Jansons’s biography. His story closely parallels that of his father, the conductor Arvid Jansons, who moved the family from their native Latvia when his son was 13 because Arvid was offered a post at the Leningrad Philharmonic assisting the great Yevgeny Mravinsky. Arvid Jansons died of a heart attack on the podium in Manchester, England, in 1984.

Mariss Jansons, too, had a post at the Leningrad Philharmonic early in his career, before his steady international rise through a 20-year stint as music director of the Oslo Philharmonic and a seven-year tenure, from 1997 to 2004, as music director of the Pittsburgh Symphony Orchestra. And Jansons, too, suffered a heart attack on the podium; it happened in 1996 in Oslo, as he was finishing a performance of “La Boheme.” He had another heart attack a few weeks later.

By all accounts gregarious and fun-loving, Jansons also has iron-clad discipline when it comes to the most important things in life — including life itself. Ever since the heart attacks, he has kept a quiet focus on his health. It’s one reason he keeps a reasonable cap on his activities, rather than giving in to the temptation of conducting in a different city every week. He’s even managed to restrict his diet.

In Pittsburgh, says Robert Moir, the symphony’s senior vice president of artistic planning, Jansons “had a passion, an ardor for sugar like nothing I’d ever seen. Gideon [Toeplitz, the orchestra’s late managing director] would bring him bricks of halvah . . . Mariss’s eyes would open wide when he saw it.” Now, Moir says, “he doesn’t touch it. It’s unbelievable.”

Jansons doesn’t eat dinner after concerts anymore, either, and focuses on staying fit. As a result, Moir says, “even though he’s had a long history of illnesses and heart problems, at 70 years old he looks [amazing].”

The other most important thing in life, of course, is the music. Jansons has a fierce allegiance to both of his musical homes: the Concertgebouw, steeped in tradition and rich beauty; the Bavarian Radio, a streamlined precision instrument.

“The Concertgebouw is a very delicate, very transparent orchestra with a very beautiful sound and very good feeling of musical styles,” Jansons says, observing that it has a particular flair for French music. The Bavarian Radio, by contrast, is a “very spontaneous, very lively orchestra, very full of emotions, and such dark, German, full sounds.”

Jansons’s job in Munich has an extra component of questing; since he arrived there in 2003, he’s been trying to get a new concert hall built in the city. No luck yet. In January, Jansons was announced as the winner of the Ernst von Siemens Music Prize, sometimes called the Nobel Prize of music; he’s pledged to put the $270,000 in prize money toward the construction of a new hall. “If the concert hall will not come,” he says, “of course, there are plenty of other things to support.”

If there’s been any criticism of Jansons over the years, it’s that his repertory isn’t very broad. He’s been best known for late romantic and 20th-century music; his Shostakovich cycle, recorded with several different orchestras and completed in 2005, is a benchmark and a cornerstone of any record collection. And certainly the current Concertgebouw tour isn’t calculated to change perceptions: It consists of works that are traditionally associated with the orchestra, such as the Mahler symphonies.

Tuesday’s Kennedy Center concert includes Mahler’s First Symphony, a familiar part of Jansons’s repertoire; he toured it a number of times with the Pittsburgh Symphony. But Moir observes that unusual works are appearing more and more on Jansons’s programs — such as a performance of Varese’s “Ameriques” in Lucerne, Switzerland, not long ago. “He’s in a different phase of his life now,” Moir says. “He’s experimenting.”

And the real point of the exercise is less what he plays than how he plays it. The real drama of Jansons’s life lies here, in the never-ending pursuit of excellence. “Nothing was ever good enough,” Moir says of Jansons’s performances in Pittsburgh. “It was a constant quest for that impossible, elusive perfection.”

He adds, “No matter how blazingly outstanding the performance was — and they all were; I don’t remember a bad concert in the time he was here — I don’t remember him being satisfied.”

How does Jansons think he’s evolved? He can answer only specifically, talking about the Mahler First. “I myself feel I am more deep in going inside the atmosphere and mood,” he says, “so that I make more dramatic, more expressive what is behind the notes. Especially, I think, in the third movement and finale, I think I put these dramatic and expressive moments almost to their border.”

Hyperbole? From some people, it might be. But Mariss Jansons really is that good — as Washington’s audiences will have another chance, on Tuesday, to hear for themselves.

Mariss Jansons

will lead the Royal Concertgebouw Orchestra in Bartok’s Second Violin Concerto, with Leonidas Kavakos, and Mahler’s First Symphony at the Kennedy Center Concert Hall at 8 p.m. Tuesday. Visit Web site for tickets.