Filmmaking is a difficult job of distillation, but nothing has prepared me for winnowing down nearly 19 hours of film—my new PBS documentary, Jazz —to a single CD. Still, I’ve done it, and of the 20 cuts on the album (released by Columbia/Legacy), these are my absolute favorites.

1. Star Dust, Louis Armstrong, 1931.

Armstrong is to music in the twentieth century what Einstein is to physics and the Wright brothers are to travel: the most important person there was. He liberated jazz, taking it from being an ensemble music to a soloist art, with his horn and his voice. I think this masterpiece of virtuoso singing and playing is the best way to start any consideration of jazz.

Armstrong at the height of his powers transforms W. C. Handy’s familiar standard into a virile, driving, utterly dramatic showcase for his trumpet genius.

3. The Mooche, Duke Ellington, 1928.

Ellington saw as clearly as anyone that African-American history is at the center of our culture, and his compositions reflect that in nearly every note and gesture. Listening to them is like listening to the pronouncements of an Olympian god. This one is from his early days as the bandleader at the Cotton Club in Harlem.

4. Hotter Than ‘Ell, Fletcher Henderson, 1934

Henderson and his arranger, Don Redman, helped create a new way of playing jazz—big band swing. As his incomparable tenor sax player, Coleman Hawkins, said, theirs was “the stompingest, pushingest band I ever heard.”

5. Begin the Beguine, Artie Shaw, 1938.

A beautiful, moving, and lyrical composition filled with both technical virtuosity and an intellectual approach to swing. It endures as one of the great anthems of the swing years.

6. Cotton Tail, Duke Ellington, 1940.

Ellington molded his orchestra into his own personal instrument, and no member of the band ever played more beautifully than his great tenor saxophone star, Ben Webster. One of Webster’s best-known performances is in this up-tempo tune, which his boss wrote specially for him.

7. Jumpin’ at the Woodside, Count Basie, 1938.

Basie brought to the nation a new kind of music, pulsing and suffused with the blues. If you had to pick one Basie tune to characterize that driven “Kansas City” sound, this would be it.

8. Solitude, Billie Holiday, 1941.

No female singer has had a greater impact on jazz than Holiday. “Solitude” is her masterpiece, an Ellington melody performed so beautifully and with such humanity that it is hard to imagine anyone else singing it.

9. Groovin’ High, Charlie Parker and Dizzy Gillespie, 1945.

After World War II, a new, risk-filled music began to dominate: bebop. The two great pioneers of bop combine here to rework completely an old standby, “Whispering,” into something entirely new.

10. So What, Miles Davis, 1959.

Trying to represent the scope and variety and restless experimentation of Davis’s career with one piece