The baritone saxophone was once the furniture of the horn section, a heavy anchor in the back row. Gerry Mulligan gave it a light, airy voice and changed the trajectory of jazz. This episode follows him from a nomadic childhood as an engineer’s son, through a nanny’s house in Marion, Ohio filled with Fats Waller player-piano rolls, a confiscated arrangement of Lover at a Kalamazoo Catholic school, and dropping out of high school in Philadelphia to write charts for Tommy Tucker.

The conversation traces his move to New York in 1946, arranging for Gene Krupa and Claude Thornhill, living in Gil Evans’ basement apartment on West 55th Street, and helping architect the Miles Davis nonet that became Birth of the Cool. It then moves to Los Angeles, Stan Kenton’s band, and the tiny Hollywood club where a missing piano led to the pianoless quartet with Chet Baker, followed by his 1953 narcotics arrest, Baker’s refusal to reunite, his relationship with actress Judy Holliday, his classical work with Zubin Mehta, and the gold-plated horn now at the Library of Congress.

• Why bebop’s claustrophobia pushed arrangers to slow down and stretch out
• How implied harmony let bass, baritone and trumpet outline chords without a piano
• The architect and the free climber: Mulligan’s rapport with Chet Baker
• Rebuilding the quartet with Bob Brookmeyer after Baker walked away
• Commissioning concertos for baritone sax and recording with Astor Piazzolla