Miles Davis and John Coltrane onstage in 1960, in Chicago. Photograph by Ted Williams / Iconic Images / Getty

There’s a great story behind “Miles Davis and John Coltrane—The Final Tour,” the sixth volume in Sony’s “Bootleg Series” of live recordings by Davis (it comes out March 23rd), and that story makes itself heard in the music. In 1960, the trumpeter Miles Davis, along with his regular band, was booked to go on a concert tour in Western Europe as part of the ongoing, and internationally famous, “Jazz at the Philharmonic” concert series. However, at exactly that time, Coltrane, who played tenor saxophone, was preparing to leave Davis’s quintet and form his own working group. Coltrane had been a sideman with Davis on and off since 1955; they were both born in 1926, but their careers took drastically different paths. Davis was already a minor star in 1945, at the age of nineteen, when he recorded with Charlie Parker. Three years later, at twenty-two, he led a nonet, featuring intricate arrangements, that proved vastly influential. (They’re gathered under the title “Birth of the Cool.”) Davis had a huge and significant discography as a leader by the time he hired Coltrane, an unheralded musician best known as a rarely soloing sideman, who’d never yet led a record date. With Davis, Coltrane quickly found his voice, and expanded it during a stint in 1957 with Thelonious Monk. Coltrane had led dates on several labels; recorded the influential “Giant Steps,” in 1959; and was ready to go out on his own.

Davis’s group, featuring the pianist Wynton Kelly, the bassist Paul Chambers, and the drummer Jimmy Cobb—which had been a sextet for several years, featuring Cannonball Adderley’s alto sax alongside Coltrane’s tenor—was now depleted. Adderley left in the fall of 1959, and Coltrane was feeling his oats. On club dates, Cobb said, Coltrane “would play an hour solo himself, and we were only supposed to be on the stand for forty minutes or something.” Prior to the European tour, Coltrane told Davis that he wouldn’t join him there, and even recommended another tenor saxophonist to Davis, Wayne Shorter, who was only twenty-six. (Davis actually hired him—in 1964.) But, because Coltrane was familiar with the band’s material, Davis prevailed upon Coltrane to join him one last time for the European tour. Coltrane agreed, grudgingly; according to Cobb, Coltrane displayed his discontent throughout the tour: “He sat next to me on the bus, looking like he was ready to split at any time. He spent most of the time looking out the window and playing Oriental-sounding scales on soprano.”

In fact, Coltrane made exemplary use of his time on that tour, working out his musical ideas more fully, audaciously, and radically than he had ever done in his previous studio recordings. Davis is in fine fettle throughout the tour; Coltrane plays with fury. As he did in American clubs, he plays longer solos (often much longer) than Davis does (not hour-long, though) and often gets much more applause than Davis does. By bringing Coltrane back into the group for this European tour, one of the band’s most prestigious showcases, Davis in effect relegated himself to the role of a sideman in his own band.

Coltrane’s solos range from the overwhelming to the astonishing to the devastating to the outrageously playful. He developed ideas that he had been working on throughout the late fifties, ideas that took the harmonic complexities of bebop to a new level. What he had been doing in the late fifties was, essentially, playing every note of the chords that provided the tune’s harmonic structure—and when he substituted (in the classic bebop form) new chords for familiar ones he played all of those notes, too. It made for lots of notes that he played very fast, in long breaths, with a vibrato-free, hard-steely tone that led one critic of the era, Ira Gitler, to immortalize Coltrane’s style at that time as “sheets of sound.” In “The Final Tour,” the sound is of Coltrane ripping the sheets to shreds. He played plenty of high-velocity rushes of notes here, too, but also broke off and fragmented those long lines. He wrenched them apart with low-end blasts, mid-range cries, and high-pitched shrieks, moving away from the musical sense of notes and chords toward pure sound—a dramatic tendency that he took to ecstatic extremes with his own groups.

Before this release, the music from the quintet’s European tour was available—exactly as the “Bootleg Series” suggests—through unauthorized releases. (Several of these concert recordings, including the ones in the Sony set, were officially made for radio broadcast.) They’re already familiar—mainly to fanatics trawling used-CD shops. (I’ve collected bootlegs of the tour for decades; there are about eight disks full of them, and they’re among my favorite jazz recordings.) “The Final Tour” offers three of the group’s concerts, including the two crucial ones from the tour. In their Paris performance, on March 21, 1960, the first night of the tour, Davis starts playing full-throated and elbows-out, and Coltrane responds by going wild, throwing down a gantlet, not to Davis or even to his audience but to himself. His performances were received as a succès de scandale. During and after several long and furious solos, members of the audience can be heard whistling (the local equivalent of booing). But there are also plenty of boisterous cheers. (I heard, anecdotally, from a friend who attended the concert, as a teen-ager, that even the passionate cognoscenti—meaning he and his friends—were Davis aficionados who came in knowing little about Coltrane but took him up as a new hero that night.)

The next night, in Stockholm, Davis seems somewhat guarded, not struggling to keep up but wary, as if he were defending some border of musical order. By contrast, Coltrane followed his Paris outburst with some lofty philosophical playfulness, picking a pair of notes from the melody and repeating them, rocking back and forth between them as if examining their gleam in the light, working them out bit by bit, line by line, until they build to an outrageous complexity that seems to astonish even him as it rushes by.

For that matter, the entire band is a delight. Kelly’s solos, following Coltrane’s, have a ripplingly songful, easygoing but intriguingly varied lyricism; Chambers offers a firm melodic and percussive counterpoint, and Cobb displays a rhythmic foundation that’s as foot-tappingly strong as it is polyrhythmically supple. Yet, as great and essential as “The Final Tour” is, its four disks tell only part of the story. I wouldn’t want to be without Coltrane’s furious outbursts from Frankfurt, Germany, the following week, or the concerts from later in the tour, in early April, when Davis seems to come out from Coltrane’s shadow, as in three tracks believed to have been recorded in Munich. By the end of the tour, Coltrane seems somewhat transfigured—his playing seems at times not appeased or tamped down but burned away to a spiritual essence, foreshadowing the mood and the content of much of his music from his own classic quartet, which finally began to coalesce in the summer of that year. As for Davis, he sought bold new musical directions as well; it took a new quintet, which he assembled in 1963-64, for him to find them.