Ed O'Brien, Colin Greenwood, Phil Selway, Thom Yorke, and Jonny Greenwood: combining boyish riddles with sophisticated musical games. Illustration by Jaime Hernandez

On a hot day in May, the city of Bilbao was shaken by a velvety roar, not unlike the sound of a jet plane waiting on a tarmac. At one end of Calle de Iparraguirre, which cuts across the town, the silver shell of the Guggenheim Museum was glistening in the sun. For a moment, it seemed as if the noise were coming from there—as if the building were about to lift off and rocket elsewhere. In fact, the source of the disturbance was a local bullring, the Vista Alegre, where a German experimental d.j. named Christoph de Babalon was testing his gear. He was the opening act for Radiohead, a five-man rock band from Oxford, England. Radiohead fans were gathered at the entrance, staring up at the sound and asking what it meant. One had on a Kafka T-shirt, and others wore shirts with a Radiohead logo, which can only be described as a demon in tears.

A side door led to a concrete corridor, where the bulls run on an ordinary day. From there, planks reached out to a temporary stage. Christoph was in the center, eying his mixer and his CD players. With ice-blond hair and black sunglasses, he looked like a young Bond villain, but he turned out to be a friendly, chatty sort of sonic terrorist. “I am familiar with dark, small clubs,” he said after the sound check. “Now it is like I am in a gladiator film.” He mentioned some of his musical influences, which included avant-garde figures like Merzbow and the composer Morton Feldman. “Sometimes I work with beats, sometimes with layers,” he said. “Tonight I do layers.”

Popular music in the year 2001 is in a state of suspense. No one can say where the mystery train is going. On the one hand, the Top Forty chart is overrun with dancers, models, actors, and the like; on the other hand, there are signs that pop music is once again becoming a safe place for creative musicians. The world fame of Radiohead is a case in point. Having established themselves with tuneful guitar rock in the nineties, the members of this band took the risk of doing as they liked, and they discovered things about the marketplace which others had missed. Last year, they released an album titled “Kid A,” an eerily comforting blend of rock riffs, jazz chords, classical textures, and electronic noise, which, in a demolition of conventional wisdom, went to No. 1 on the Billboard chart. “Amnesiac,” its like-minded successor, came out in June and is doing just as well. Radiohead’s selling point is not their identification with any one genre but their way of ranging over music as a whole. They have intensity, intelligence, a personality in sound. In Bilbao, they were present in spirit before they played. The idea of placing a German d.j. in a Spanish bullring was Radiohead to the core—a tricky, eclectic song waiting to happen.

Christoph went to his dressing room, and the stage was empty for a while. Two shirtless old men sat on stone steps, looking as though they had not moved since Franco died. Radiohead’s gear basked in the sun. On the left-hand side was a rack of guitars—twenty-three in all. Up front, in an area set aside for Ed O’Brien, one of three guitarists in the band, was a tangle of pedals, samplers, and inch-thick cords. In the center of the stage, to be shared by Colin Greenwood, the bass player, and Thom Yorke, the singer, were various keyboards, a piano, and an upright bass. Equipment for Colin’s younger brother, Jonny Greenwood, stood on the right: more guitars, more keyboards, a xylophone, a transistor radio, a sci-fi stack of analog synthesizers, and a modified ondes martenot, one of the earliest electronic instruments. The ondes martenot is controlled by a ring that slides along a wire; fewer than a hundred people have mastered it, and Jonny is one. The only really conventional-looking apparatus was the drum set, although you could tell by some distress on the edges of the drums that the player, Phil Selway, had attacked the sides as well as the skins.

Backstage, the members of Radiohead were eating dinner. Colin Greenwood hovered over the catering table, inspecting an array of Basque dishes. He is typical of the group in that he looks nothing like a celebrity who has sold fifteen million records. He is thirty-two years old, with jet-black hair and large, kindly eyes. He is easily distracted and delighted by the world around him, favoring the words “mad,” “brilliant,” and “amazing”—the last spoken with a long, liquid stress on the second syllable. He has a habit of suddenly burying his face in his hands, as if he were sinking into despair, or falling asleep; after a moment, his face lights up again. Lavishly well-read, he can talk at length about almost any topic under the sun—Belgian fashion; the stories of John Cheever; the effect of different types of charcoal on barbecued meat—but he gets embarrassed by his erudition and cuts himself off by saying, “I’m rambling.” He is not above wearing a T-shirt that says “Life’s a beach and then you shag.” You might peg him as a cultish young neo-Marxist professor, or as the editor of a hip quarterly. But he is a rock star, with several Web pages devoted to him.

“It’s full on out there, isn’t it?” Greenwood said, looking toward the bullring, which was filling up with fans. “I’m scared.” He occupied himself by talking about “Faust’s Metropolis,” Alexandra Richie’s thousand-page history of Berlin. Outside, Christoph began to play for real, and was received in bemused silence.

An hour later, Radiohead hit the stage with a confidence that had been invisible before the show. The sound was huge, but it was awash in colors, contrasts, and detail. It was grand in effect, cool in tone, dark in mood. The set was a mixture of older tunes, from the band’s breakthrough albums of the mid-nineties—”The Bends” and “OK Computer”—and newer ones, from “Kid A” and “Amnesiac.” The old songs had choruses that the fans knew by heart, but the new ones, which have been described as “anti-commercial” in the rock press, made the crowd dance harder. “Idioteque” set off fierce rhythmic clapping, even though it was dominated by jagged beats, computer-music samples, and squawks from the old-school synths. It must have helped that the singer, when he was done singing, launched into a demonically silly dance, kicking his legs as if someone were firing a gun at his feet. It may also have helped, on an unconscious level, that love-drunk chords from “Tristan und Isolde” lurked at the heart of the song, courtesy of a Paul Lansky composition called “Mild und Leise.”

In the middle of the set, Radiohead played a song called “Airbag,” which showed why this band is taken as seriously as any since the Beatles. It was a rugged ritual, full of cabalistic exchanges, with each player taking a decisive role. Jonny started off with a melody that snaked along in uneven time—one-two-three-one-two-three-one-two—and swayed between A major and F major. O’Brien added leaner, brighter curlicues on guitar. Selway came in with a precise but heavily syncopated beat. Then Yorke began to sing, in a well-schooled, plaintive voice, an oblique account of a near-fatal collision: “In the next world war / In a jackknifed juggernaut / I am born again.” At the mention of war, Colin let loose a jumpy bass line, giving a funky spin to the hymns in the treble. The music cut through a jumble of verses and choruses, then held fast to a single chord, as Yorke fell into synch with O’Brien’s chiming lines. Just before the end, Colin grinned, leaped in the air a couple of times, and seized hold of his brother’s tune, the one that had set the song in motion. The doubling of the theme had a kind of thunderous logic, as if an equation had been solved. The interplay was as engaging to the mind as anything that has been done in classical music recently, but you could jump up and down to it.