How do you describe the music you make?
Maybe the best way is a Venn Diagram. I do vocal jazz. I think this Venn Diagram shows how I define that.
I would assert that most performances that include three of these elements qualifies as vocal jazz for me. Having all four elements strengthens the argument and certainly some vocal jazz includes only two of the four elements.
The Singers Unlimited typically had three of the four and occasionally included the fourth. The New York Voices almost always include all four, if we view the Great American Songbook expansively.
Does Barbershop include all four? It has some Extended Harmony (especially more contemporary Barbershop) and often uses songs from the Great American Songbook, but almost never includes improv and the rhythmic feels tend not to true swing or jazz feels. My interpretation: vocal jazz-adjacent but not vocal jazz.
Is Eric Whitacre’s output vocal jazz? Well, definitely not but his extended harmony makes his music adjacent, too.
Is show choir vocal jazz? Well, we virtually never have improvisation and almost never advance past triadic harmony, so it’s also adjacent but not vocal jazz.
I think that having a Venn Diagram on paper – or at least in your head – helps you to clarify your thoughts about new music, helps you program effectively (make a Venn Diagram for every ensemble you direct!), and helps you communicate about your values and genres clearly.