John Coltrane’s creative flame was burning at its brightest in 1964. The saxophonist had recently let go of his fixation on complex, layered harmonies, and he would soon pioneer a dry, squalling approach to group improvisation — nearly abandoning Western harmony altogether, and changing the course of jazz history.

Amid the transition, that year he recorded what would be his two most potent albums, “Crescent” and “A Love Supreme.” These works thrive at the crossroads: They are in touch with the driving, cohesive sound that his so-called classic quartet had established, but push into a blazing beyond.

Yet history is not this simple. Even for Coltrane — a symbol of tireless creative momentum, who is said to have never stopped hurtling forward — detours came up.

That spring, Coltrane was approached by Gilles Groulx, a young Canadian filmmaker at work on his first feature, “Le Chat dans le Sac.” Groulx asked his musical hero to record the film’s soundtrack, and to his surprise, Coltrane said yes.