Just a thought……..Are you looking at a "Serrated" shaft or a "Splined" shaft ?
I have always described what you have in the photo as Serrations, so you might find more information using that terminology perhaps.
My B.S. A19 from 1941 cover aircraft Serrations, but it jumps from 16 to 20 with no mention of 19.
Serrations are generally straight sided, but your do look to have some curve on the sides, so maybe the involute suggestion is a good one.
The standard method of measurement is with two pins in the grooves and a dimension taken across them, but again with an odd number this does not make life easy. All the one listed in the BS are even numbered.
Sorry I cannot be of more help.
Phil