When Gustavo Dudamel walked on stage last month at Walt Disney Concert Hall to conduct a pair of concerts with the National Children’s Symphony of Venezuela along with YOLA, the youth orchestra that Dudamel founded for the Los Angeles Philharmonic, he had a look on his face we hadn’t seen for a while. Not pride and joy, exactly. His body language was more of belonging, of being precisely where he wanted to be and doing what he was meant to do. With his musical progeny in Frank Gehry’s concert hall, Dudamel had the unmistakable appearance of having come home.

Those concerts were the first thing Dudamel brought up when I sat down with him last week in a Salzburg café. He had just arrived to conduct one of the most anticipated Vienna Philharmonic programs at the Salzburg Festival. That would include Strauss’ “An Alpine Symphony,” a grandiloquent ascent into the great mountains that grace Salzburg’s surroundings. He has been conducting the storied Vienna Philharmonic regularly for 17 years, and his performance, which opened with an intense and moving performance of the composer’s “Four Last Songs” sung by Asmik Grigorian, proved to be a sensation. Dudamel conducted with spectacular fluidity, ascending Strauss’ magnificent musical alps with the ease and grace of a world-class climber. With performances like this, Dudamel has reached the pinnacle of his career, but he didn’t look at home the same way he had in Disney Hall.

Home has a profoundly complicated and essential meaning for Dudamel. I’ve seen him appear utterly at home having a beer in Sweden with musicians of the Gothenburg Symphony or rehearsing Japanese youth in Tokyo. It was once joked about Herbert von Karajan that wherever he got off an airplane, they would want him to conduct. That’s become true for Dudamel — and no joke.

His main residence is now Madrid, where Dudamel lives with his wife, the Spanish actress María Valverde, and where his son and extended family now reside. He said he will always call his native Venezuela home. But ever since becoming the L.A. Phil music director in 2009, he has also considered L.A. home.

“I was talking to a friend yesterday,” Dudamel told me, “and I said, ‘L.A. is home.’ I am going to New York, of course, but L.A. is home.”

In his first dozen years as music director of the L.A. Phil, he happily cruised L.A. in his Aston Martin convertible, delighting in its diversity of neighborhoods. He knows all the good restaurants. He has many Angeleno friends from many walks of life. He loves Hollywood and movies. Our climate reminds him of Caracas. His son was born here, and he learned L.A. as a father.

Even so, Dudamel, made Europe a base when he accepted the invitation in 2021 to become music director of the Paris Opera, telling the New York Times that after spending a month and a half guest-conducting with the company, “I was feeling I was at home.” When it no longer felt like home, a place where he could engage as deeply and personally as he had been led to expect, he resigned, saying that he wanted to spend more time with his family at home.

Early last year, Dudamel also announced that after his L.A. Phil contract ends in 2026, he would become music director of the New York Philharmonic. The Big Apple immediately claimed ownership, hailing Dudamel as the savior whose star power couldn’t fail to revitalize America’s oldest and historically most celebrated but these days troubled and less vital orchestra.

Despite all his protestations of everlasting devotion to L.A., Dudamel’s relationship with the L.A. Phil began to change. The orchestra’s chief executive, Chad Smith, left last summer to run the Boston Symphony, effecting a year’s vacancy at the top. Dudamel hasn’t seemed as present as usual. The orchestra summarily ended it’s 2023-24 season three weeks early in mid-May. Dudamel wasn’t on hand in July to elatedly propel the Bowl season, as he had the previous 15 summers.

After a three-month absence, Dudamel finally returned Thursday, taking over the orchestra’s last two weeks at the Bowl with six different programs. But he’s only around for the first four days of October to open the orchestra’s new season, then gone again until late in the month, when he returns for his last two weeks of concerts in the year. Is that a foot out the door?

The schedule, Dudamel explained, is deceiving.

The L.A. Phil 2023-24 season may have ended abruptly in Disney Hall but only because Dudamel took the orchestra on a boldly ambitious (and expensive) European tour, which included bringing the full production of Beethoven’s “Fidelio” with Deaf West Theatre he had remounted in Disney to Barcelona, Paris and London. Dudamel was not in L.A. to open the Bowl, he said, because he had originally planned to mount a new production at Paris Opera in preparation for the Olympics.

On Oct. 1, Dudamel will lead his 16th opening night gala with Lang Lang as soloist at Disney, followed by two staged performances of Shakespeare’s “Midsummer Night’s Dream,” with Mendelssohn’s incidental music and Valverde as narrator. He then takes the orchestra to New York to open Carnegie Hall’s season with the L.A. gala program one night and the “Midsummer” production the next. The tour will continue with those concerts to Bogota, Colombia.

In fact, Dudamel pointed out that since the beginning of May, his main activity for the year is the L.A. Phil. His only guest conducting was the Vienna Philharmonic concert in Salzburg and, the weekend before Christmas, leading “The Nutcracker” in Rome with the Orchestra of the National Academy of Santa Cecilia.

“It’s not like I have a relation with the orchestra and then say goodbye,” he said. “No, no, no. This is something that we have been building for 15 years.” And he has no intention of it not continuing well into the future.

“There has been an evolution, and maybe there can now be a space for creating new things. Of course, I am wishing that what is the best orchestra will find the best decision for a music director.”

In that regard, Dudamel said that he stays in close contact with the players whether his is in town or not, and that includes discussions about conductors. The final decision will fall on the new president and chief executive, Kim Noltemy, who began in July, along with the orchestra and board. But unlike almost all major orchestras, which tend to move on, leaving the old guy out of the discussion (they’re still almost always guys), Dudamel’s input is said to be valued, just as Esa-Pekka Salonen’s was in Dudamel’s appointment.

With a Cheshire cat smile, Dudamel said to expect a big announcement in a month, but he isn’t allowed to say what it is. Noltemy, who came to Salzburg to spend some time with Dudamel, will add only that it won’t be a music director announcement. She said she has time to get to know the orchestra before having to make a decision.

As far as Dudamel is concerned, he said is never leaving L.A. Maybe the New York Philharmonic can, as Paris Opera couldn’t, become a new family. But he launched his career in L.A. He grew up and matured with the L.A. Phil, where he learned much of the standard repertory. In L.A., musical vistas opened up in ways it could nowhere else. He said he has lost count of how many world premieres he has conducted with the orchestra (the incomparable figure is said to be close to 300). There is no better way to build a relationship than to share the experience of learning new music together.

“If something have changed in my life after Paris,” Dudamel said, he realizes, “it is the quality of time that I’m now having. I feel very calm. I think when you are 40-something, you change. There was a very busy period of my life that I had to cultivate the relations that I have.” Now, at 43, he has more time to spend on projects dearest to his heart.

Spending time with family also means working with actual family and friends, something Dudamel pointed out has always been the case. When I hunted for the voice memos app on my phone to record our conversation, Dudamel immediately pointed it out. “I’ve been using it every day to record music,” he said. He’s composing a score for a new movie, not yet titled, in which his wife will star.

“My wish,” Dudamel said, reflecting on his childhood in Barquisimeto, “was never to conduct in Los Angeles. My wish was to play music with my friends. I remember when they moved me to Caracas, I didn’t want to move to Caracas. I wanted to stay in Barquisimeto. But they said, no, you have to move, because the orchestra is here. We cannot take the orchestra to you.”

Dudamel claimed that he never lost that ultimate urge to stay home and play music with friends. That is, for him, the essence of being a music director. “I have created in Los Angeles is this unique connection,” he said, “a unique human artistic connection that will never end.”

To that end, he is already making post-music director plans for L.A. in 2027 and 2028. He wants to return four weeks a year. including a week at the Bowl. He also has proposed joint projects between the L.A. Phil and the New York Philharmonic, just as he has united YOLA with young players around the world, creating a giant international family of future musicians. A Paris Opera and L.A. Phil collaboration also had been a dream.

At the moment, however, Dudamel is faced with a New York Philharmonic that is hardly a happy family. Two members accused of sexual misconduct, which they deny, have been dismissed and are suing the institution. The president and CEO has recently resigned.

But Dudamel remains optimistic and said he welcomes the challenge of bringing together his two orchestral families, old and new. “I believe we can build a beautiful bridge between New York and Los Angeles both artistically and socially. It can be a beautiful thing not to be in competition.”

If he succeeds, it will be a first. If, like Paris, it doesn’t, Dudamel still has “family” in L.A. That bridge does not appear flammable.