British Tools and Fasteners gives:
0.5 (1/2) inch 26 Tpi 0.0385 0.4590 ins 0.4606 inch
But in their data section it also says :
Most people think that all cycle threads are 26 tpi pitch. Whilst this is true of all the most popular sizes from 1/4" to 3/4" diameter, other pitches were also used as shown in the tables seen in the CEI section
So depending upon where you look you will find different answers. 24 TPI is also used.

The ICSCUTTINGTOOLS.com site gives 26 TPI for CEI and BSC. Only ADMF (Admiralty) is 20 TPI.

There is only one thread form, 60 degree with radiused crests and valleys. The only information I found on the radius is from Whitworth forms which are 55 degree.
With the changes from BSC to SAE around '68 I did not know if the cam thread changed. Just giving 1/2" BSC does not give the thread pitch.
Phil, could it be your pattern 24-7000 was UNF, not BSC? UNF has truncated peaks, not rounded which may have interfered with the BSC cam thread.