Well, if you can come up with a better name for it,
I'm open to suggestions.

The recordings and performances that come to mind
in particular
are African-American in origin,
and although not 'blues' as such,
there is a relationship to the blues,
if only 'rhythm-and-blues'.

Then there is the music that has come to be called jazz.

This stuff has always got, not just a rhythm, but a BEAT.
And often as not,
there is music in there someplace.
The vocal part may be little more than 'rapping'
but if so, then there is musical accompaniment.

This artist was from the first half of the 20th century,
and he is nothing like a household name now,
but between 1935 and 1950
many of the jazz musicians and jazz oddballs,
from Babs Gonzales to Eddie Jefferson (scat singer nonpareil)
knew who he was.

Here, Leo Watson fronts the Gene Krupa band.
He is unusually, erm, calm in this performance.
Just you wait until I link you to some of the WILD records he made.

Jeepers Creepers