Trumpeter and singer Chet Baker became the definition of cool jazz. His brilliant improvisation and tender tones were like nothing else and his matinee idol good looks got him plenty of attention. He worked with Stan Getz and Charlie Parker and created a sensation playing counterpoint solos with Gerry Mulligan and his baritone sax. hear Chet Baker sing and play tonight on the 9 O'clock Special. Chet Baker was introduced to music by his dad who was a professional guitarist in Oklahoma. He played trombone but moved on quickly to the trumpet. Chet studied music for a few years in college and was in the army band, but told people he didn't read music and played by ear.