If we're talking about fiction, you couldn't get better than Alan Plater's Bix Beiderbecke Affair, broadcast on BBC in 1985. From a review:

With as little plot as its creator Alan Plater could get away with and as much jazz as he could manage, the 1985 television drama The Beiderbecke Affair had a far-reaching impact, inspiring sequels, novels, albums and even jazz tours. Much like its Bix Beiderbecke-style soundtrack, Plater's quietly joyous drama was unconventional, free: its narrative following the lives and relationships of its leading characters – teachers-turned-amateur detectives Trevor Chaplin (James Bolam) and Jill Swinburne (Barbara Flynn) – with a gentle, whimsical humour.

I remember it well.

Phil