Can't be done? Any good tool room lathe, such as a Hardinge or 10" South Bend with a change box can cut as few as 32 different pitches, from 4 TPI to 224 TPI. My Galicop (South Bend, Belgium) can cut 96 different pitches. New machines can cut whatever the programer tells them to cut.
As for profile, that's what tool grinders do when they are looking as those big ole optical comparators.
A common lathe in the UK is a Myford, and they use south bend gears in many of their smaller machines.
Having foundries and machine shops both here and in the UK, I kinda got an idea what they can do (Especially when they loose their "Not Invented Here" attitude).
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