Juan Tizol came to the United States in 1920 from San Juan, Puerto Rico, to play in the pit band at the Howard Theater in Washington, D.C. where he met Duke Ellington. Tizol had studied both valve and slide trombone with his uncle and was a master of both. Most players preferred the slide because of its sound and greater tonal accuracy. But the valve trombone offered greater fluidity and was favored by Tizol. He joined Duke Ellington’s orchestra in 1929 and became the soul of its ensemble section over the next 15 years. He frequently rehearsed the band for Duke, who wrote arrangements that took advantage of Tizol’s mastery of his instrument, pairing him with saxes and trumpets.

Two of Tizol’s compositions, written while with Ellington, became ja...