Original show tune composed by Morgan Lewis, lyrics by Nancy Hamilton; from the 1940 musical revue "Two for the Show"
"How High the Moon" is a jazz standard with lyrics by Nancy Hamilton and music by Morgan Lewis. It was first featured in the 1940 Broadway revue Two for the Show, where it was sung by Alfred Drake and Frances Comstock. In Two for the Show, this was a rare serious moment in an otherwise humorous revue. Wikipedia