But on that August day, Hendrix was still trying things out, hitting the stage that morning with a group that included Cox, drummer Mitch Mitchell from The Experience, guitarist Larry Lee and two percussionists.

The band was the largest that Hendrix had ever performed with, but it was also the least polished. The situation forced Hendrix to play more out front than usual. That was especially evident in the searing peaks and ringing chords of the bluesy “Red House,” at the end of which Jimi broke a string. Lee sang lead on “Mastermind” while Hendrix attended to the instrument malfunction, then Jimi returned with an equally stunning “Foxy Lady.”

When Woodstock organizers realized how far they had fallen behind schedule, they had offered Hendrix a midnight slot, but he turned them down. By then it had become apparent that history was being made, and Hendrix wanted to preserve his spot and the climactic performance. Now, he was playing as if he was trying to put an appropriate finish to the three days of remarkable music that preceded him.

About midway through his two-hour set, he launched into a medley of tunes including “The Star-Spangled Banner.” The national anthem had long been part of the Hendrix repertoire; he played it nearly 50 times in his career, but never as long and with as much riding on it as at Woodstock. His performance, filled with blasts of feedback that mimicked the sound of fighter jets, which had become familiar from news coverage of the Vietnam War, was backed only by Mitchell, who changed deftly from routine accompaniment to a more propulsive approach akin to the late Rashied Ali backing John Coltrane, as Jimi’s sounds grew more abstract. Forty years later, it still ranks as one of the greatest guitar performances ever.

“I’m an American, so I played it,” he explained to TV talk show host Dick Cavett in an interview weeks after the performance. When Cavett tried to characterize Hendrix’s take as unorthodox, the guitarist corrected him. “It’s not unorthodox; I thought it was beautiful.” And indeed, to all those on the wrong side of the generation gap who denounced Woodstock Nation as un-American, Jimi had the proper retort; they were embracing freedom, not their opponents who yearned for conformity.

Woodstock was one of the last great Hendrix performances. He spent the last 13 months of his life struggling with lawsuits relating to contracts signed long before his first recording was released, and with the rigors of trying to keep a post-Experience band together.

Musically, he was moving in many directions at once: Aspects of jazz, art-rock and other styles filtered through the many sessions and live shows from Hendrix’s post-Woodstock phase. But Jimi’s performance at Woodstock in general and his urgent reclamation of the National Anthem in particular, is a great coda on his career. In a nutshell, it is what Woodstock was all about. It’s why this 40th anniversary is worthy of celebration.

Martin Johnson is a regular contributor to The Root.