Ah but let us not use what has been learned about ballistics in the past two centuries to cloud what was known back then to those who made gain twist...,
Mr. Kemp is correct, it takes a very little turn to stabilize a round ball. This was known.
It was "known" that at least a minimum 1/4 turn prior to exiting the muzzle was needed to stabilize a round ball, and that American and German rifles, especially the Germanic target rifles, had faster twists than that minimum, with the Germans often using very fast twist on those rifles. (Source
Instructions for The Formation and Exercise of Volunteer Sharp-Shooters Barber 1804) Barber also noted that such fast twist rifles had several problems including "disagreeable recoil" and tougher to keep clean, both not wanted in a military rifle, and his observations influenced the Baker Rifle.
Rifle shooters of the time, especially in Germany where target shooting was much more of an advanced competition than in the United States, wanted faster twists as they thought they were necessary..., today we know this isn't true for the patched round ball, but it was part of the idea behind the gain twist. Again not faster RPM, but their "percieved" need for a
fast twist coupled with higher MV to be accurate at very long ranges.
I'm not suggesting that the gain twist in a ML barrel has any major advantage, especially now that we have round bottom rifling, I was simply explaining what was the accepted idea behind it.
LD