But unlike Coleman, whose music is airy and accessible, Coltrane gravitated toward the screaming intensity of saxophonists like Albert Ayler and John Gilmore, as well as two younger players who would become his protégés: Pharoah Sanders and Archie Shepp. The opening cut of Coltrane’s 1965 Meditations, “The Father and the Son and the Holy Ghost,” featuring Sanders, is so furiously intense that the English poet and jazz critic Philip Larkin dismissed it as “the most astounding piece of ugliness I have ever heard.”

But Larkin was just stodgy. I love “The Father and the Son and the Holy Ghost” and Meditations as a whole. It has an inner logic and coherence; it justifies and contextualizes its turbulence. But as Coltrane pursued this musical direction, it sometimes became hard to distinguish exploration from parody — take Om, for example, or the part on the often but not wholly superb Live in Seattle disc when the saxophone master starts, well, groaning. “If I had been one of the musicians on the stage,” a friend once remarked to me, “I would have wanted to sink through the stage in embarrassment.”