Madrid's teachers during this time included prominent trumpet artists and educators such as Conrad Gozzo, James Stamp, Claude Gordon, Donald Reinhardt, and Bud Brisbois.

[5] In early 1969 he joined Woody Herman's big band on a European tour, splitting the lead trumpet book with Bill Chase.

In 1973 he joined Louie Bellson's big band in Los Angeles and played lead with the Orange Co.

Late in 1973, he was asked by former Herman band member Tom "Bones" Malone to replace Lew Soloff with Blood, Sweat & Tears.

By early 1974 Madrid moved out to Hawaii, working with major musical acts that included Don Ho and many others.