The tune is "Tootsie Roll" by Marty Paich who composed it in the smooth, perhaps "cool," style of the John Kirby group and features Dave on clarinet, Benny Carter [a close associate of Kirby's]on alto saxophone, Ray Linn on trumpet, John Williams [of yet to come "Star Wars" fame] on piano, Lyle Ritz on bass and Frankie Capp on drums.
Kirby was nearly forgotten when he died in 1952, but according to Richard Cook in his "Jazz Encyclopedia: "The Kirby sextet hinted at things to come - Tristano, West Coast neatness, perhaps the whole wave of cool Jazz itself - without really influencing any player or school too much."