The discovery and release of a previously unknown recording by the saxophonist John Coltrane, who died at the age of forty in 1967, is cause for rejoicing—and I’m rejoicing in “Offering: Live at Temple University,” the release of a tape, made for the school’s radio station, of a concert that Coltrane and his band gave on November 11, 1966, a mere nine months before his death.

I knew and already loved this concert, on the basis of a bootleg of three of its five numbers. But the legitimate release offers much better sound and contains the pièce de résistance: a climactic performance of “My Favorite Things,” the Richard Rodgers tune that Coltrane turned into a jazz classic in 1960. Yet this 1966 performance of it is very different from that of 1960, and, indeed, even from Coltrane recordings from a year or two before the Temple concert. In the intervening years, Coltrane’s musical conception had shifted toward what can conveniently be called “free jazz.”

The term started as the name of an album by one of the form’s key artists, Ornette Coleman, from 1960, even though that recording only hinted at the further extremes of free jazz, some of which were in evidence in Coltrane’s final two years. The idea, roughly, involves playing without a set harmonic structure (the framework of chords that lasts a pre-set number of bars and gives jazz performances a sense of sentences and paragraphs), without a foot-tapping beat, and sometimes even without the notion of solos, allowing musicians to join in or lay out as the spirit moves them. Lacking beat, harmony, and tonality, free jazz cuts the main connection to show tunes, dance-hall performances, or even background music to which jazz owed much of whatever popularity it enjoyed.

There’s a temptation to consider free jazz as a freedom from: freedom from structures and formats and preëxisting patterns of any sort. But it’s also a freedom to: a freedom to musical disinhibition of tone, a vehemence and fervor, as well as a freedom to invent. The very word “freedom” meant something particular to black Americans in the nineteen-sixties. They didn’t have it, and there’s an implicit, and sometimes explicit, political idea in free jazz: a freedom from European styles, a freedom to seek African and other musical heritages, and, also, a freedom to cross-pollinate jazz with other arts. In the process, jazz musicians developed new forms and new moods that reflected a new generation’s experiences and ideals. The politics of free jazz were inseparable from its aesthetic transformation of jazz into overt and self-conscious modernism.

Coltrane’s turn to free jazz, in his last two years of performance, gave rise to a more overtly transcendent yet frenzied yearning. His playing on “Offering” is even more fervent and, at times, furious than it had been, even two years earlier, on the celebrated album “A Love Supreme.” Yet his heightened, trance-like playing has a core of stillness, of devotional tranquility; his music is like a whirlwind with an eye of serenity.

The difference in Coltrane’s own playing goes hand in hand with that of his group over all. In his last years, he radically changed his very conception of his band, and what resulted was a new musical tone. Coltrane’s former group was a classic quartet (featuring the pianist McCoy Tyner, the bassist Jimmy Garrison, and the drummer Elvin Jones). His new band, heard in “Offering,” was a quintet, augmented by the saxophonist Pharoah Sanders, in which Coltrane’s wife, Alice Coltrane, replaced Tyner and Rashied Ali replaced Jones. (Garrison stayed in the group, though in the “Offering” concert he was replaced by Sonny Johnson.) Also, for the Temple gig, Coltrane supplemented the band with four more percussionists and two guest alto saxophonists, Coltrane’s longtime acquaintance Arnold Joyner and the teen-ager Steve Knoblauch, whom Coltrane invited to solo on “My Favorite Things.” (The liner notes, by Ashley Kahn, feature their accounts of the concert.) The big group, playing free of harmonic structures and foot-tapping rhythm, gives the succession and shift of musical events a tumultuous, organic flow. In the grand scope of its development and in the tumble of its frenetic incidents, the performances make perfect, natural dramatic sense.

Not everyone seems as enamored of this recording—or, for that matter, of Coltrane’s later performances in general. Geoff Dyer, writing at the New York Review of Books site, describes the music as “shrieking, screaming, and wildness.” He loves Coltrane—the works of the classic quartet, featuring Elvin Jones and McCoy Tyner. But Dyer calls late Coltrane “catastrophic”; and Dyer is an honorable fan. He tells the story of Coltrane’s musical transformations around 1965, and, demeaning the recording of “Offering,” cites approvingly Jones’s view of them:

Well, the sleeve notes by Ashley Kahn are extremely informative, but I would question the assumption that there is something “spiritual” about this last phase of Trane’s musical journey. If it’s there I can’t hear it. What I do hear is the momentum of what he’d done before—and a situation he’d helped to create—carrying him towards a terminus, a brick wall, a dead-end or, in the cosmic scheme of things, some kind of interstellar void. Or, to bring things back down to earth with Elvin’s reasons for quitting, “a lot of noise.”

Dyer calls Jones “Elvin,” calls Coltrane “Trane”; this sense of false intimacy is significant. Dyer is the author of “But Beautiful,” from 1991, a fictional gaze at classic-era jazz greats, in which he writes about “Lester,” “Bud,” “Chet,” “Ben,” and, for that matter, “Hawk” and “Trane.” He writes like a club patron who insinuates himself into the company of the musicians between sets, extracts their confidences, observes scenes of intimate horror, and then passes them along—using first names and nicknames—as if to flaunt his faux-insider status. But, when the musicians are back on the bandstand, he never lets them forget that they’re there to entertain him.

The epilogue of “But Beautiful” is an essay in which Dyer makes clear that free jazz altogether was already his bête noire—pun entirely intended. He asserts the centrality of “tradition” in jazz—as if it needed his defense—and relies on this principle to justify the limits of his taste. In this essay, too, he writes in veneration of Coltrane’s classic quartet, only to assert that, in Coltrane’s later performances, “there is little beauty but much that is terrible.” Dyer is so bound to his own idea of what jazz is, and to its popular and classical roots, that he can’t hear the ideas of one of its greatest creators. He listens to jazz like a consumer or a patron rather than like an artist; he doesn’t enter into imaginative sympathy with the musicians, and he can’t conceive or, for that matter, feel what the creator of “Spiritual” or “Dearly Beloved” finds necessary in “Interstellar Space” or “Offering.”

In “Offering,” there are astonishing, deeply moving moments in which Coltrane uses his voice—he cries out during a solo by Sanders, and twice sings in a sort of vocalise, pounding his chest to make his voice warble. Dyer writes condescendingly in his review that “these eagerly anticipated moments actually sound a bit daft—which is not to say that they were without value.” They don’t sound “daft” at all; they sound like spontaneous and ingenuous expressions of rapturous joy. But they are gestures that would have had little place amid the prodigious musical strength of Coltrane’s classic quartet. On the other hand, they’re right at home in Coltrane’s open-ended quasi-hangout band, in the familial intimacy that gives rise to its vulnerable furies.