He started playing trumpet in middle school, at a summer music program, and grew devoted to the instrument as a student at East High School. Mr. Miles played in the jazz band alongside the future actor Don Cheadle, who played saxophone, and soon began an apprenticeship with the respected Denver saxophonist Fred Hess.
Mr. Miles and Mr. Hess would become collaborators, making a number of recordings together and both serving on the faculty of Metropolitan State University of Denver, where Mr. Miles eventually became director of jazz studies.
After graduating from high school, he enrolled as an engineering student at the University of Denver, but soon transferred to the University of Colorado Boulder to study music. He went on to graduate school at the Manhattan School of Music, but he would spend the rest of his career in Denver, where he mentored a generation of musicians — both on the live scene and in classrooms at Metropolitan State.
On his first album, “Distance for Safety,” released in 1987, he led a hard-driving trumpet-bass-drums trio infused with equal doses of rock and free jazz. He went on to release a string of consistently unorthodox albums on various small labels, conforming to no favored format or style, including “Witness,” a 1989 quintet date, and “Heaven,” a 2002 duo record with the guitarist Bill Frisell.
As Mr. Miles’s career went on, an expansive Rocky Mountain sound seeped ever more indelibly into his compositions and his playing, which was rough around the edges but balanced and controlled at its core. In the 2000s he switched fully from the trumpet to the cornet, a slightly less glamorous instrument that seemed to suit him.
Unlike a typical East Coast trumpeter, he rarely flitted or zipped around on the instrument. He approached notes as if to disarm them, sometimes allowing tones to fill themselves out gradually, becoming wide and full and bright. The melodies he traced felt designed to be followed, even when they went fiendishly askew.