Idler,
As Eddie says, the included angle for the fitting is 60 degrees.
The thread, at least as used at the timing cover end, is 7/16-20. It was probably intended to be from the 20 threads per inch Cycle Engineers Institute (CEI) series (more familiar for there 26tpi series). This later turned into the British Standard Cycle (BSC), though the 20tpi series seems to have dropped from usage. It used a 60 degree thread angle, and is pretty much the same as 7/16 US Fine thread (USF).
If the nut you have is BSF, that is 18tpi and may account for the 'tight' feel on a 20tpi nipple.
Doug