The unity of Artie Shaw's whole concept--from his expressive development of the altissimo register of the clarinet, to the clear band arrangements, slotting the instruments perfectly and giving space for his counterpoint--is on display from this 1939 air check. Add to that an all star crew that included a young Buddy Rich drumming and chirping the band on, and you've got one of the jazz tunes everyone should hear...
[ This is not a comprehensive list, nor is it representative of the "most important" or "best." Instead, following Duke Ellington's adage that the greatest music and musicians are "beyond category", I'm starting 2020 by sharing 100 jazz tunes I feel everyone should have the chance to hear--really just tunes and performances that I love. ]