Forty years ago, several hundred thousand people (an exact number will never be known) gathered in Bethel, N.Y., for the Woodstock Music and Art Fair. Nearly everyone who was anyone in rock—Jefferson Airplane, The Who, Janis Joplin, Sly & the Family Stone, Crosby, Stills, Nash & Young, Richie Havens—played at that mud-soaked music fest. And nearly everyone who was in the audience got to check them all out.

But only a very few actually got to see Jimi Hendrix perform—a performance of such rock guitar virtuosity that even today, it functions as Woodstock’s keynote address.

Even for those who could say that they were there at Woodstock, most will remember Hendrix’s performance through the numerous CDs and DVDs capturing that day in rock history.

A number of factors conspired against Hendrix: poor logistical planning, crappy weather, oversized crowds—not to mention an unpolished pickup band playing backup. Hendrix’s set—the final one of the three-day weekend festival—was supposed to start at 3 a.m., but didn’t get rolling until 8 a.m. on Monday, Aug. 18, 1969. By then, most of the Woodstock Nation had to get home. The weekend was over. But those who stuck around were treated to a truly special morning—breakfast with Jimi, so to speak. Not that he was treated as anything special. As he began to play, people on the periphery of the amphitheater started to clean up behind a thinned-out crowd.

The festival organizers had anticipated 150,000 concertgoers and probably got at least twice that many (and possibly the “half a million strong” that Joni Mitchell’s song, “Woodstock” boasts), and their other logistical skills were off, too. Shows each night ran well into the dawn, and on Sunday a lengthy rain delay pushed Hendrix’s set well into the next day. It would be one of the most unusual performances of his career.

Concert promoters announced Jimi’s band as the “Jimi Hendrix Experience,” but he quickly corrected the announcer and called his group “Gypsy Sun and Rainbows.” Earlier that year, Hendrix had disbanded The Experience, the group that he formed in London in the mid-‘60s. The Jimi Hendrix Experience had recorded three discs, two of them, Are You Experienced and Electric Ladyland, rank among the greatest recordings in popular music. A few months after Woodstock, Hendrix would debut his new group, the Band of Gypsies, with bassist Billy Cox and drummer Buddy Miles.