When the Grateful Deadannounced a reunion for three shows this July, Dead Heads recognized a familiar name in the band’s lineup: Bruce Hornsby. The pianist has had a longstanding relationship with the group that dates back to the ‘80s, when he was fronting Bruce Hornsby and the Range, the band behind the hit “The Way It Is.”

Hornsby opened for the Dead several times in the late ‘80s and 1990, and came to other shows just to jam. He became an unofficial-official member when the band’s keyboardist Brent Mydland passed away in...