On an August night in 1981, the German band Kraftwerk played at the Ritz, on East Eleventh Street in Manhattan, in support of its latest album, “Computer World.” The only instruments onstage were actually machines: reel-to-reel tape recorders, synthesizers, keyboards, and a calculator. All four members of the group had short hair and dressed identically, in black button-down shirts, black pants, and shiny shoes, which made them look more like valets than like musicians. That didn’t bother them, as they didn’t like the idea of being a band—or even musicians—and often referred to themselves as “operators.”

Kraftwerk at MOMA: the band’s exploration of the relation between man and machine underlies much of what you hear on the radio today. Photograph by Pari Dukovic

For the song “Pocket Calculator,” one member triggered percussion with a drumstick. Another used a Stylophone, a metal keyboard played with a small stylus. Florian Schneider, a founding member, played the calculator, which was wired into the sound system, so that pressing the keys made audible beeps. His partner, Ralf Hütter, who is the only remaining original member of Kraftwerk, sang the lyrics of the song in a monotone—an approach that he calls Sprechgesang, or “spoken singing”—and played a small Mattel keyboard. “By pressing down a special key / it plays a little melody,” he intoned. Schneider responded by playing something sort of like a melody with the calculator. At one point, Hütter bent down and let the audience play the keyboard. Recently, Hütter said, “I wanted to show them that anyone could make electronic music.”

That year, songs from “Computer World” were played on “urban” radio stations in New York, such as Kiss-FM and WBLS. The Bronx d.j. and hip-hop pioneer Afrika Bambaataa was in the audience at the Ritz. He had found Kraftwerk’s 1977 album, “Trans-Europe Express,” in a record bin several years earlier. “I was just looking at these guys on the cover and saying, ‘Whoa, whoa, what the hell is this?’ ” he told me. “Wow! Something’s here that’s very funky, and I got to play it for my audience.” He added that Kraftwerk’s battery of gear at the Ritz made it look as if they were playing “washing machines.” (Because of the difficulty of re-creating their recordings with such complicated equipment, the band has visited the U.S. only seven times in its forty-two-year history. Now they use laptops.) The following year, Bambaataa, along with the musician John Robie and the producer Arthur Baker, combined the beat of “Numbers,” from “Computer World,” and the melody of the title track from “Trans-Europe Express” to create “Planet Rock,” an early hip-hop song that spawned a small clutch of genres, including electro, Miami bass, and Brazilian baile funk. “Computer World,” Kraftwerk’s masterpiece, sold less than a million copies, yet its influence has been surprisingly broad—even Coldplay, for its single “Talk,” from 2005, has used a melody from the album.

One song on “Computer World,” called “Home Computer,” has a distinctive, ascending arpeggio that feels a bit like bubbles rising quickly through mercury. That arpeggio shows up in LCD Soundsystem’s single “Disco Infiltrator,” from 2005. It’s also referenced in Missy Elliott’s “Lose Control,” from the same year. A few days ago, I was walking through SoHo and passed the Uniqlo store, with its painfully fluorescent lighting, which illuminates only slightly less fluorescent clothing. Nicki Minaj’s hit “Starships,” a savvy combination of dubstep and traditional house, was bleeding onto the street. When I listened closely, I realized that this version was actually a mashup with one of the many songs that has used “Home Computer” ’s arpeggio. Maybe it was Kraftwerk, or LCD Soundsystem, or Missy, or someone else entirely. It didn’t matter—the sound still signifies newness, joy, and some kind of ascent.

It turned out not only that anyone could make electronic music but that almost everyone wanted to. Kraftwerk is perhaps the only group that played the Ritz in 1981 that sounds entirely current today. Plenty of people saw the machines coming, but nobody else has listened as carefully to them, or documented their strengths as lovingly.

This month, the Museum of Modern Art opened a retrospective of Kraftwerk, its first for a musical act. In the six-story atrium, Kraftwerk played an abbreviated version of its repertoire, in chronological order of its albums, on eight consecutive nights. The shows cherry-picked from each, followed by an hour or so of the group’s best-known songs. “These aren’t concerts,” Klaus Biesenbach, the chief curator at large for the Museum of Modern Art, who organized the exhibit with the curatorial assistant Eliza Ryan, explained. “It’s a retrospective; it’s curated. They aren’t playing everything they ever recorded, any more than we could fill the museum with every photo Cindy Sherman has ever taken.”

Demand for tickets overloaded the Web site of the third-party vender, ShowClix, minutes after they went on sale. Buyers were limited to two tickets each, and ticket holders had to show identification to obtain a wristband required for admission, to prevent scalping. Still, listings on Craigslist showed up immediately, offering entry in exchange for more than two thousand dollars and, in one instance, for an evening with a “hot, swinger couple.” Animatronic robots designed to look like the band members were on display in the lobby, and listening stations loaded with the band’s albums were in place near the atrium. Hütter said that seeing these robots was no better or worse than seeing the band members themselves. “The robots are members of Kraftwerk,” he added.

Four consecutive Sundays have been dedicated to d.j.s playing the music of Kraftwerk over a surround-sound system set up in a geodesic dome in the courtyard of MOMA PS1, in Queens. Bambaataa is scheduled to play the last Sunday, May 13th. The first weekend at PS1, April 14th and April 15th, showed how wide Kraftwerk’s influence has been. That Saturday, Juan Atkins, who is often credited as the first practitioner of Detroit techno, played a set that began with Kraftwerk, then moved into pop songs that reflected the band’s influence, like Yaz’s hit “Don’t Go,” from 1982. The next day, Hütter performed. While the beat from “Numbers” thumped along, and the band’s album covers were projected onto the walls of the dome, Hütter sang into a Korg vocoder, which processes speech and combines it with the notes of the keyboard. “I feel at home in the dome,” he sang.

How did a pop band end up in a museum? Hütter and Schneider began collaborating in the late sixties, in Düsseldorf, and in 1970 opened a studio, a loft that they called Kling Klang, near the railway station. Düsseldorf was a center for avant-garde art; Kling Klang shared a wall with Gerhard Richter’s studio, and, for breaks, they would all play foosball with Joseph Beuys. First calling themselves the Organization, they later chose Kraftwerk (“power station”), because of its implications—“energy,” “art work,” “craft”—and also because of the ubiquity on German highways of signs for power stations.

In addition, the name and its industrial aesthetic seemed like a subtle affront to the earthy English hippies who were popular at the time, bands such as Cream, the Yardbirds, and Led Zeppelin, who performed versions of American blues, complete with long guitar solos. The guitarist Michael Rother, who played in an early version of Kraftwerk and later formed the influential rock band Neu! with the drummer Klaus Dinger, told me that Hütter was the first musician he had met who “had the same feeling about melody and harmony that I’d held inside me that was not based on blues or the structure of American-British pop music.” Living in postwar Germany, and alert to the problems of the immediate past and the proximate present, musicians were trying to establish a German pop language from thin air. Mimicking Anglo-American musical poses was cheesy, but anything that sounded overtly Germanic evoked dangerous historical memories. What the groups of Kraftwerk’s cohort settled on, in common, was reduction and repetition: no guitar solos.

Kraftwerk’s early records were not particularly melodic and only intermittently rhythmic. Pieces were built around keyboard tones, flute, guitar noises, the sound of breathing, and occasional stretches of drumming. “Autobahn,” the band’s fourth album, from 1974, was its first to move decisively toward pop, though not as it was practiced at the time. Bits of flute and guitar remained, but most of the music was generated by drum machines and synthesizers, which Hütter and Schneider had begun to modify themselves. By the time “Radioactivity” was released, in 1975, the guitar and flute were gone, and the machines took over for good. While the chorus of “Autobahn”—“Wir fahr’n fahr’n fahr’n auf der Autobahn”—was a reference to the Beach Boys and their “fun fun fun,” Kraftwerk rarely sang in harmony, and almost every vocal was processed through some kind of machine.

They saw their work as “confronting the mirror of the tape machine” and representing Alltag—everyday life. Their shows, which often took place in art galleries, were rarely traditional. Hütter sometimes rubbed a microphone across his face. “Depending on the length of my beard, it would make stronger sounds,” he said. At one show, their collaborator Emil Schult circled a gallery space on roller skates and beamed wireless signals into the sound system while Hütter and Schneider played keyboards. At another, the band set up a drum machine and weighed down the keys of a synthesizer before leaving the stage. Hütter told the Rolling Stone reporter Mike Rubin that “the audience at the party was so wild they kept dancing to the machine.”

But the band’s passion was for recording, and it did so obsessively, with the gifted engineer Conny Plank. In Dave Tompkins’s “How to Wreck a Nice Beach,” a history of synthetic voice processing, Schneider says, “The mysterious thing about these machines, sometimes when you use them, you feel like a secret agent of sounds. We closed our studio—nobody could go inside. We were very paranoid.” The work paid off. As democratic and empowering as drum machines may be, there are very few pop records that sound as exquisitely balanced as Kraftwerk’s.

At the time, electronic music was a curiosity in pop. In 1968, the composer Wendy Carlos released an interpretation of Bach, played on a Moog synthesizer, that won three Grammys. Compilations keyed to the novelty of the Moog appeared in the early seventies, featuring chirpy versions of songs such as “Yummy Yummy Yummy” and “Popcorn.” There was already substantial academic and commercial work being done on synthesizers in places like Stanford University’s computer department, the BBC Radiophonics Workshop, and the West German Broadcasting studio, in Cologne. Tangerine Dream, from Berlin, Kraftwerk’s contemporary, was making entire albums using synthesizers, though it fit more comfortably into what would one day be called “ambient music,” rather than pop.

Early reactions to Kraftwerk were often hostile, and sometimes verged on xenophobic. In an interview published in Creem, in 1975, the critic Lester Bangs asked the members of Kraftwerk if their machines were “the final solution” for pop music. “No, not the solution. The next step,” Hütter responded, and he was right. Pop’s non-narrative phrases, glittering, brief melodies, and reliance on technology can be traced directly to Kraftwerk’s concept of Mensch-Maschine, or “man-machine,” which was not just the name of the band’s seventh album but also a guiding principle. The sound is rooted in the interaction between computers and people—which, for many of us, is what now fills our waking hours. Kraftwerk’s melding of machines and everyday life is far from eugenic, though; it’s remarkably gentle, even a bit melancholy. The bicycles and cars and computers and radios and calculators that inhabit their albums are a friendly lot. When Bangs tried to provoke the band by citing William Burroughs’s assertion that one could start a riot with two tape recorders, Schneider responded, “A person doing experimental music must be responsible for the results of the experiments. They could be very dangerous emotionally.”

After “Autobahn,” Kraftwerk’s music became increasingly syncopated and propulsive, and, without intending to, the band began laying the foundation for electronic dance music. Hütter’s explanation is simple: “Machines are very funky.” With remarkable consistency, each album referred to a mechanical process that the music mimicked, a simple concept that reflected a culture increasingly defined by the machines around it. “Radioactivity” echoed Geiger counters; “Trans-Europe Express” imitated the rhythm of wheels on train tracks and the descending tone of the Doppler effect; and “Computer World” was made by computers and about computers. The albums embodied both the simplicity and the richness of electronic signals.

Last year, MOMA presented an Andy Warhol exhibition, which felt like a natural precursor to the Kraftwerk shows. The band is the Warhol of pop—apolitical, fond of mechanical reproduction, and almost creepily prescient. While Warhol, with his silk screens and lithographs, was criticized for ignoring the idea that an art work is a unique object, traditionalists decried the anonymity of Kraftwerk’s machines, and implied that using synthesizers was somehow cheating. But, for both artists, it was not limiting that anybody could paint a soup can that someone else had designed, or that anybody could push a button on a keyboard that someone else had made. One could modify the image of mass-produced objects as needed, and both Warhol and Kraftwerk did, repeatedly. Making copies of things made them democratically available but didn’t preclude the individuality of the modifiers.

The exhibition at MOMA was Kraftwerk’s first appearance in New York since 2005, when the group played a volcanic show at the Hammerstein Ballroom. (Schneider was still with the group; he left the band in 2006. Hütter says that Schneider was tired of touring.) Whereas the Hammerstein show was ecstatic, a loud moment of catharsis for the dance audience that remains the band’s core demographic, the MOMA shows were controlled presentations for a diverse crowd that seemed only to want to lay eyes on these legends. As Kraftwerk, in various forms, has done for decades, four band members stood in a line behind podiums that neatly hid what they were manipulating. Hütter stood stage right and worked with a keyboard, playing most of the lead melodies live. At other times, he said, “I read e-mails. I have an iPad. I have a text prompter for the lyrics.”

Henning Schmitz and Fritz Hilpert, later additions to the band, stood between Stefan Pfaffe and Hütter, working on synchronized laptops, while also triggering rhythmic elements. Pfaffe controlled the visuals. Since it was a retrospective, the shows were not allowed to vary substantially—“you can’t change a painting for a retrospective,” Biesenbach said—so each one began with a deep vocoder voice speaking in German and English, introducing the “ladies and gentlemen” to the Mensch-Maschine. After a brief spray of notes, a white scrim fell, revealing the band members, each wearing a skintight bicycling outfit covered with luminescent white lines in a grid formation, as if they were being tracked on a green screen for later animation. Hütter is fit—he takes bicycling trips through Europe—but he has a small paunch, which slightly deformed the grid.

For several nights, the band opened with a song called “The Robots.” Hütter recited in Sprechgesang, “We’re charging our own battery, and now we’re full of energy.” Behind the musicians, on a screen, robots sported red shirts and black ties, as they had on the cover of “The Man-Machine.” The crowd, which included musical adventurers such as Yoko Ono and Michael Stipe, had been given 3-D glasses. In 3-D, the robots turned and dipped their heads, and their enormous arms seemed to float over the band members. The visuals for many songs were simply the lyrics rendered in a kind of ticker-tape typeface, crawling across the screen as lines undulated in the virtual background. “Autobahn” opened with the sound of an engine turning over and introduced a visual rendering of the Autobahn running through the Rhineland. (The band’s appearance at MOMA was sponsored by Volkswagen.)