The Dude abides. Not for long, though.

After spending a fortnight with the Los Angeles Philharmonic, opening the season with his usual aplomb, Gustavo Dudamel is in Milan this week to begin a nine-performance run of Bizet’s “Carmen” at La Scala. After that he’ll be in Gothenburg, Sweden, conducting his other orchestra in three concerts in late November, then, according to his web site at least, take a few weeks off before end of the year performances with the Berlin Philharmonic.

Over the summer, he conducted the Vienna Philharmonic at the Lucerne Festival, then, just before the L.A. Philharmonic opener, took the Viennese to the U.S. for high profile performances in Kentucky and at Carnegie Hall.

He records for Deutsche Grammophon with the Simon Bolivar Youth Orchestra of Venezuela, his old and current mates. Their latest recording, released in June, features “The Rite of Spring” and “La noche de los mayas” by Revueltas.

In other words, Dudamel is in demand the world over. He visits us when he can.

In all fairness, he conducts the L.A. Philharmonic as often as most music directors do these days, and I do not question Dudamel’s devotion to the local cause. The difference, I think, is in the long gaps between his performances here.

Last season, his first as music director of the L.A. Phil, he didn’t conduct the orchestra between the end of November and April. This year, the gap lasts from mid-October to January.

Last season, after the gap, he took the orchestra on a U.S. tour. The critical reaction was decidedly mixed. A case could be made that Dudamel and the orchestra went on tour too early in their relationship, before a true and distinctive musical bond had been cemented.

This season, after the gap, he’ll take the orchestra on an extensive European tour. Dudamel and the orchestra will perform the tour programs here in L.A. first, but the same question arises. Have they spent enough time together?

When he’s on the podium, there’s no question that the orchestra plays with tremendous energy and commitment for him. But is there a Dudamel sound, a personality, that the orchestra and conductor are forging together? And, if not, is that even important?

Last weekend, the Philharmonic gave performances of Berlioz’s complete “Romeo and Juliet” with guest conductor Charles Dutoit. On Friday, when I heard it, the orchestra sounded uncomfortable, and perhaps unmotivated, and displayed little evidence of a distinctive “Dudamel sound” just one week after the maestro’s departure.

For me, the jury’s still out. I have almost invariably enjoyed and been inspired by Dudamel’s performances here. But where is it all headed?

It will be interesting to hear the orchestra again in a few weeks, when Esa-Pekka Salonen returns for the first time as conductor laureate to lead two sets of concerts. Will the old Salonen sound make a reappearance with him? And if so, what does that mean?