In 1960, Leonard Bernstein introduced a work by Pierre Boulez, the classical music titan and longtime Chicago Symphony Orchestra guest conductor who passed away yesterday, to a New York audience as part of a series on 20th century music. His message: please just stick around until the dessert course is served.

I want to tell you that we’ve arranged to play you an extra piece at the end of this program, a sort of “bonus” for braving the perils of this strange and experimental music you’re about to hear. This will be La Valse by Ravel.

The program seems to cry out for one good old-fashioned sound of orchestral glamour. On the other hand, if you should suspect that we’re merely offering you a sop, or trying to send you home in a more genial and contented humor, you’re absolutely right.

After a piece featuring five orchestral groups by another composer, Bernstein spoke about Boulez's little Improvisation sur Mallarmé. He did not get any less foreboding.

Boulez composes with a system, a terribly complex one, which is vaguely related to the serial systems we know from Schoenberg and Weber, but so different and advanced as to make the 12-tone systems seem quite old-fashioned.

I won't try to describe this system to you, because, partly, it's mathematically so involved (as well as in terms of physics), and partly because I myself cannot analyze its patterns without knowing the secret original number patterns—that is, the mathematical model on which Boulez has constructed his piece. It's like needing the secret map to get to the buried treasure.

But none of that really matters. In fact, what emerges when the music is played, is curiously unsystematic in its effect. The quality seems at first hearing rather impressionistic, improvisatory, and instinctual. There's even an Oriental atmosphere as there is in so much older impressionistic music by Debussy and Ravel and so on.

So going in, Bernstein has already told the audience he doesn't exactly know how this piece that he's about to conduct, you know, works. And he's just getting warmed up.

There's absolutely nothing you can feel as a beat, nothing you can tap your foot to, or recognize as either symmetrical or asymmetrical. It seems simply to improvise rhythmically … And yet the metrical construction of this little piece is of enormous complexity and difficulty of performance. The mathematical relations of one tempo to another are extremely detailed and subtle. In other words, the rhythm seems to have become so complicated that it has disappeared entirely.

Remember, we're talking about a "fascinating little five-minute work." But sometimes it's the little things that can break a culture.

And perhaps this disintegration of meter is also a symptom of our age, an age in which everything seems to be fragmentized, or reduced to molecular proportions of some sort … Sometimes I wonder if turning in toward molecular dissection isn't the logical outcome of the great decline of religious spirit in our time, that spirit that naturally turns outward toward the unknown, secure in and confident in our faith … The atmosphere he generates is one of great innerness and mystery. Perhaps what it is is a new kind of mysticism borne of scientific insights.

Bernstein may as well have said: "God is dead. You are alone. Ravel will be offered at the end as an opiate."

Even if you don't buy Bernstein's analysis—and according to Boulez, the complex structure of the piece is just a mirror of Mallarmé's poems—it's a pretty weird piece.

That composer, about whom Bernstein felt he had to warn audiences, whom his mentor Olivier Messiaen described as "like a flayed lion," nonetheless quickly became one of the grand figures of classical music.

Nine years later he made his debut with the CSO, with which he became a fixture beginning in the 1990s. "What happens when an iconoclast becomes an icon?" Terry Gross asked a decade ago, when Boulez turned 80. "He was once the avant-garde's most outspoken critic of the establishment, and is now one of the most admired figures in the classical music world." And how do you transform from one into the other?

As is so often the case when I want to understand classical music, I turn to the work of my late friend Lee Sandlin, who in 1998 called Boulez "the best orchestra conductor alive." And the reasons for it came through when he performed Bartok that night at the CSO. Sandlin writes:

His music ordinarily makes the hardiest modernist blanch: his hyperabstract approach to composition, his bizarre taste for backcountry Hungarian folk music, and the off-the-scale spookiness of his sensibility make him a byword for everything that's most unnerving about modern music …

So how is it that Boulez was able to make Bartok's music sound so lovely? Maybe it was an accident—Boulez might be so used to dissonant exercises in avant-garde audience alienation that he can no longer tell that Bartok is supposed to sound weird. Or maybe his being saturated in the compositional logic of modernism has let him get past the surface strangeness of Bartok's sound to reveal an extraordinarily luminous inner design. Boulez isn't fazed by Bartok's love of grotesquerie or his Einsteinian approach to form. Where other conductors see an eerie parody of lyricism, Boulez simply sees lyricism; where they find a broken maze of internal construction, he sees a lucid through line.

Here it loops back to Bernstein's introduction of Boulez almost four decades before, when Boulez was a flayed lion, not a lion of the form. He created a musical framework of staggering complexity, beyond even the comprehension of Leonard Bernstein, to produce a five-minute piece that sounds like an improvisation.

"His own music has a great amount of surface beauty that the people who followed him don't necessarily have," composer Nico Muhly told The New York Times. "That decadence. The Frenchness to it. You can feel the butter swirling in that pan."

Muhly, like Bernstein, points back to the sound of Ravel, the composer meant as an apertif to Boulez's improvisation. He found the old beauty within the avant-garde, and established himself within the establishment.