The blistering guitar intro to Johnny B. Goode, Little Richard's high-pitched whoop and pencil-thin mustache, the whole attitude of 1950s rock and roll: much of it traces back to a saxophonist and bandleader who peaked a decade earlier. Louis Jordan was born in 1908 in Brinkley, Arkansas, had a clarinet in his hands by age seven courtesy of his music-teacher father, toured with the Rabbit Foot Minstrels as a teenager, and studied at Arkansas Baptist College before landing in Chick Webb's hard-swinging orchestra at Harlem's Savoy Ballroom, where he shared vocal duties with a young Ella Fitzgerald. But the economics of moving a 17-piece band across the country never added up, and in 1938 he walked away to form the small, agile Tympany Five.

Stripping the band down created a sonic vacuum the rhythm section had to fill, and the result was jump  ...