The act of making music is exhilarating for the performers in both bands. Illustration by Joanna Neborsky / Photographs by Corbis

The historian John Lukacs, in “A Thread of Years” (1998), his collection of vignettes from across the twentieth century, imagines a few jazz fans listening to a cocktail pianist in New York in 1929. Then he talks about how this music—melodic swing at the beautiful, blurred boundary of jazz and popular song—defined a state of mind before the Second World War. Everybody “who responded to that kind of American music,” Lukacs states categorically, “hated the Nazis.” It’s a nice rejoinder to the Marxist philosopher Theodor Adorno’s insistence that the “monotony” and rhythmic seductions of jazz were a friend to fascism. And it trails a question. What was in this dance music, heard in short takes on scratchy 78s, that left its devotees devoted to some larger set of humane values?

The question is at the heart of Terry Teachout’s searching new biography, “Duke: A Life of Duke Ellington” (Gotham), which touches on the mystique of the great bandleader’s music as much as on its notes and measures. Ellington was a dance-band impresario who played no better than O.K. piano, got trapped for years playing “jungle music” in gangster night clubs, and at his height produced mostly tinny, brief recordings. (His finest was made on a bitter winter night in 1940, in a Fargo, North Dakota, ballroom.) How did he become a dominant figure of modern music and, for many people, an exemplar of art? The typical answer used to be that he was really a master composer on the European model, all score paper and seclusion and suites. On inspection, this doesn’t hold much water. Ellington’s best music turns out to be the crystallized collective improvisation of an exceptionally ornery group of musical malcontents. To explain it all, we seem to need new categories of value, and another kind of meditation on what originality is.

This is Teachout’s second big jazz biography. His first was “Pops,” an excellent volume on Louis Armstrong, which he turned into an even better play, “Satchmo at the Waldorf.” Teachout inhabits right-leaning places where riff-loving men seldom wander, but his writing seems all the better for his distance from liberal piety; some of the best jazz criticism has always come from less than liberal precincts, as with the apolitical Whitney Balliett and the Tory Philip Larkin. Apologetics are the enemy of art criticism, and the conservative critic has the advantage of distance from the ideological passions that can encumber jazz: not everything has to be seen as an allegory of persecution and salvation—there are just good and worse musicians and music. (In the same way, the unbelieving biographer of a great Roman Catholic thinker isn’t oppressed by the need to show that he was always right.) Yet Teachout is a sensitive writer, and one reason his biographies are moving is that he has obviously been giving himself an education in the realities of American racial history as he writes them. We are reminded, alongside him, on almost every page, just how brutal, demeaning, and absolute bigotry against blacks was for so long in America.

Armstrong is easy. He was not just a genius but an irresistible lion. Even the old complaints about his having sold out no longer seem credible: he simply went from making most of the best jazz records ever made to making some of the best pop records. Though Armstrong could articulate his sources—Joe Oliver, the lost Buddy Bolden—the Armstrong sound emerges early and whole. As with Elvis, though on a far roomier artistic scale, it just happened.

Ellington, by contrast, was a slow starter and a slow learner, whose first hits now sound dated and chi-chi. The son of Washington, D.C., domestics who passed on a high sense of style and a fastidious desire for elegance, he was a city man. There was something self-constructed about him, as there had to be with so many African-American figures of the era—he was a Duke in the same way that Father Divine was divine. Unlike Armstrong, he had a platonic idea of the kind of music he wanted to make, and of the kind of musician he wanted to be, which preceded his actually making any. Early Ellington oscillates uneasily between a kind of “primitivist” growling and stuttering, and tepid impressionistic effects, as in “Creole Love Call.” But the idea that possessed him—rhythmic adventure, unafraid of seeming too “African”; lyric embroidery, unashamed of emotional delicacy—was powerful, and capable of being realized in a more complete way. He spent the next fifty years realizing it.

Well before Ellington made his permanent music, he was the man even people who didn’t like jazz were allowed to like. Dignity demanded that he never take off his dinner jacket, and then it became a straitjacket. As Balliett pointed out, Ellington knew from the beginning that he needed a sound, more even than a beat or a style. The individual players he employed weren’t up-to-date urban players but, often, less sophisticated New Orleans musicians, whose great gift was a distinctly human tone, often achieved with the use of homemade mutes and plungers. They never suffered from the homogenized, driving tone of the white bands.

Over the years, Ellington cultivated those kinds of players until, with the 1940 band, he achieved something extraordinary—an all-star band that played together, soloed luminously, and never sounded competitive. As critics still remark in proper wonder, at least five of the musicians—Jimmy Blanton, on bass, Ben Webster, on tenor sax, Johnny Hodges, on alto sax, Harry Carney, on baritone sax, and Tricky Sam Nanton, on the trombone—are in the running for the very best ever to have picked up their instrument.

Yet a residue of disappointment clings to these pages: Ellington was an elegant man but not a very nice one, Teachout concludes, exploiting the musicians he gathered and held so close. He used his musicians (not to mention his women) often quite coldly, and his romantic-seeming life was really one long cloud of shimmering misdirection. Teachout reveals that Ellington was rarely the sole composer of the music associated with his name. Nearly all his hit songs, Teachout explains, “were collaborations with band members who did not always receive credit—or royalties—when the songs were recorded and published.” It’s long been known by fans that many of the most famous “Ellington” numbers are really the arranger Billy Strayhorn’s, including “Take the A Train” and “Chelsea Bridge,” and that the valve trombonist Juan Tizol wrote most of “Caravan.” But much of “Mood Indigo” was Barney Bigard’s, while “Never No Lament” (which became the hit “Don’t Get Around Much Anymore”), “I’m Beginning to See the Light,” and “I Let a Song Go Out of My Heart” began as Johnny Hodges riffs and then became songs. “Sophisticated Lady,” “Prelude to a Kiss,” and “In a Sentimental Mood,” in turn, are melodies originally blown by, and rarely credited to, the alto-sax player Otto Hardwick.

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None of these are obvious, all-purpose riffs, or simple blues phrases. They’re rich, melodic ideas, as complex as anything in Gershwin or Rodgers. Ellington owned them, but they didn’t start in his head, or take form under his fingers. Teachout says all the right things about how, without Ellington’s ears to hear them and his intelligence to fix and resolve them, these might have been butterflies that lived a day, fluttered, and died. But you sense that he’s shaken by the news. It seems like theft. It certainly bothered the musicians. Hodges used to make a sign of counting money when Ellington was playing the medley of his tunes.