Just as Lee Morgan seemed poised to break the cycle of drug addiction that had plagued him for years, the 33-year-old jazz trumpeter died in 1972, the victim not of an overdose, as so many similar stories have ended, but a bullet. The documentary “I Called Him Morgan,” which charts his brief life and career, offers classic tunes and a vivid history of the New York jazz scene, while never quite managing to sell the drama inherent to its tale.

Morgan’s musical career, which included a stint with Art Blakey’s Jazz Messengers, is recounted by such colleagues as saxophonist Wayne Shorter. But it is Lee’s personal life that takes center stage, as the bulk of the film is built around an audio recording of a 1996 interview with Helen Morgan, his common-law wife and the woman who shot him. 

Helen came into the musician’s life at a time when he was struggling with heroin and a stalled career. Thirteen years his senior, she nursed him off drugs and set him back on the right track. But the relationship was rocky.

The film’s most arresting images are the black-and-white photographs of Francis Wolff, who documented recording sessions for Blue Note Records. “I Called Him Morgan” itself has a jazzlike approach to storytelling, offering variations on its theme of lost promise in interviews, archival performance footage and misty re-creations of the snowy Manhattan night Morgan died. 

Filmmaker Kasper Collin — who directed “My Name is Albert Ayler,” another documentary about a jazz figure who died young — hasn’t quite found the sweet spot here between true crime and musical biography, but the story that plays out in “Morgan” is still an intriguing one.