"Tune Up" or "Tune-Up" is a composition written by Eddie Vinson, but is traditionally credited to Miles Davis, who first recorded and popularized it.
"Tune Up" was first recorded on May 19, 1953, with John Lewis on piano, and first appeared on the Miles Davis album Blue Haze, released in 1956, for the Prestige label.
John Coltrane was a member of both Vinson's band in the late 1940s and the Miles Davis Quintet and performed the tune on numerous occasions while with Davis.
[1] According to Jack Chamber in his book Milestones: The Music in Times of Miles Davis, both "Four" and "Tune Up" were always credited to Davis for decades, and nobody objected to the false crediting until decades later.
It has been cited as a good example of a standard with ii-V-I progressions in three different keys, making it valuable to musicians learning to play jazz.