Claude Debussy died a century ago, but his music has not grown old. Bound only lightly to the past, it floats in time. As it coalesces, bar by bar, it appears to be improvising itself into being—which is the effect Debussy wanted. After a rehearsal of his orchestral suite “Images,” he said, with satisfaction, “This has the air of not having been written down.” In a conversation with one of his former teachers, he declared, “There is no theory. You merely have to listen. Pleasure is the law.”

To mark the centenary of Debussy’s death, which fell in March, two handsome boxed sets of his complete works have been issued. They befit a man who treasured pretty things. One, from the Deutsche Grammophon label, is decorated with Jacques-Émile Blanche’s portrait of the composer, in which he assumes an aristocratic, lapel-grasping pose. The other, from Warner Classics, displays Hokusai’s woodblock print “The Great Wave Off Kanagawa,” which, at Debussy’s request, was reproduced on the cover of one of his most celebrated scores, “La Mer.” Physical recordings are no longer a fashionable way of listening to music, but you will probably get closer to Debussy if you shut down the Internet and give yourself wholly to his world. The D.G. set has the libretto of his only finished opera, “Pelléas et Mélisande,” and the texts of his large output of songs—necessary resources in approaching an acutely literary composer whom Stéphane Mallarmé and Marcel Proust recognized as an equal.

It is best to start where Pierre Boulez said modern music was born: with the ethereal first notes of the orchestral tone poem “Prelude to ‘The Afternoon of a Faun.’ ” Debussy wrote it between 1892 and 1894, in response to the famous poem by Mallarmé. The score begins with what looks like an uncertain doodle on the part of the composer. A solo flute slithers down from C-sharp to G-natural, then slithers back up; the same figure recurs; then there is a songful turn around the notes of the E-major triad. Yet, in the fourth bar, when more instruments enter—two oboes, two clarinets, a horn, and a rippling harp—they ignore the flute’s offering of E. Instead, they recline into a lovely chord of nowhere, a half-diminished seventh of the type that Wagner placed at the outset of “Tristan und Isolde.” This leads to a lush dominant seventh on B-flat, which ought to resolve to E-flat, but doesn’t. Harmonies distant from one another intermingle in an open space. Most striking is the presence of silence. The B-flat harmonies are framed by bar-long voids. This is sound in repose, listening to its own echo.

Debussy accomplished something that happens very rarely, and not in every lifetime: he brought a new kind of beauty into the world. In 1894, when “Faun” was first performed, its language was startling but not shocking: it caused no scandal, and was accepted by the public almost at once. Debussy engineered a velvet revolution, overturning the extant order without upheaval. His influence proved to be vast, not only for successive waves of twentieth-century modernists but also in jazz, in popular song, and in Hollywood. When both the severe Boulez and the suave Duke Ellington cite you as a precursor, you have done something singular.

The music is easy to love but hard to explain. The shelf of books about Debussy is not large, and every scholar who addresses him faces the challenge of analyzing an artist to whom analysis was abhorrent. The latest addition to that shelf is Stephen Walsh’s “Debussy: A Painter in Sound” (Knopf), which places proper emphasis on Debussy’s myriad links to other art forms. The composer may have been the first in history to become a fully modern-minded artist, joining a community of writers and painters, borrowing ideas and lending them in turn. Admittedly, before Debussy there was Wagner, whose impact was sufficiently seismic that the term “Wagnerism” had to be coined to describe it. With Wagner, though, the influence tended to go in one direction: outward. Debussy was receptive. He saw, he read, he pondered, and he transformed the ineffable into sound.

“He was a very, very strange man,” the soprano Mary Garden said. With his piercing eyes and jutting forehead, he could make a rough first impression—like “a proud Calabrian bandit,” according to the pianist Ricardo Viñes. François Lesure, the author of the definitive French-language biography of Debussy, portrays him as “withdrawn, unsociable, taciturn, skittish, susceptible, distant, shy.” He was said to be “catlike and solitary.” He “lived in a kind of haughty misanthropy, behind a rampart of irony.” He had a tendency toward mendacity in his professional and personal relationships. He was conscious enough of his limitations: “Those around me persist in not understanding that I have never been able to live in a real world of people and things.”

Debussy was born in the Paris suburbs in 1862, to an impoverished family. His father, Manuel, held a string of jobs, including china-shop owner, travelling salesman, and print worker. His mother, Victorine, was a seamstress. In the period of the Paris Commune, in 1871, Manuel served in the revolutionary forces, as a captain, and when the Commune was defeated he spent more than a year in prison. Fortuitously, when Manuel told Charles de Sivry, another inmate, about his son’s musical interests, Sivry mentioned that his mother, Antoinette Mauté, was a pianist. Mauté, a well-connected woman who was said to have studied with Chopin, began teaching the boy, and helped to arrange his admission to the Paris Conservatory, in 1872. Another notable thing about Mauté is that her daughter Mathilde had the misfortune of being married to Paul Verlaine. At the time, that ill-fated couple was living with Mauté, and Arthur Rimbaud, soon to become Verlaine’s lover, was an increasing source of tension. Although Debussy never spoke of meeting either Verlaine or Rimbaud, he must have been at least vaguely aware of the chaos in the household.

At the conservatory, Debussy was a restless student, exasperating his teachers and fascinating his schoolmates. When confronted with the fundamentals of harmony and form, he asked why any systems were needed. He had little trouble mastering academic exercises, and, after two attempts, he won the Prix de Rome, a traditional stepping stone to a successful compositional career. But in his early vocal pieces, and in his legendarily mesmerizing improvisations at the piano, he jettisoned rules that had been in place for hundreds of years. Familiar chords appeared in unfamiliar sequences. Melodies followed the contours of ancient or exotic scales. Forms dissolved into textures and moods. An academic evaluation accused him of indulging in Impressionism—a label that stuck.

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Perhaps Debussy’s central insight was about the constricting effect of the standard major and minor scales. Why not use the old modes of medieval church music? Or the differently arrayed and tuned scales found in non-Western traditions? Or the whole-tone scale, which divided the octave into equal intervals? Debussy had a particular fondness for the natural harmonic series—the spectrum of overtones that arise from a vibrating string. If you pinch a taut string in the middle, its pitch goes up an octave. If you pinch it at successively smaller fractions, the basic intervals of conventional Western harmony emerge. So far, so good: but what about the notes further out in the series? These are more difficult to assimilate. In the chain of intervals derived from a C, you encounter a tone somewhere near B-flat and another in the vicinity of F-sharp. Debussy favored a mode that has become known as the acoustic scale, which mimics the overtone series by raising the fourth degree (F-sharp) and lowering the seventh (B-flat). That those notes correspond to blue notes helps to explain Debussy’s appeal to jazz musicians.