Answered in PM, but as you'll have gathered it isn't a complete answer because I could only relate what I remembered when I saw it being done many years ago.
What I said was:
It depends on the height of the pillar.
You need to divide the height by the number of full courses to give you the number of turns to get the top aligned with the bottom (can't remember whether you deduct one course from the total to give you the actual number, you'll need to experiment).
Many years since I saw this done. I'm not a brickie but it fascinated me to see it done and I was amazed to see the technique on that animation, which I never expected to find via a google search.
I remember that the amount of turn had to be adjusted slightly to get the right effect on the twist, but that can be established by the time you get to the first point of alignment of all the sides. Difficult to describe in words, but from what I remember of that animation there is a point where it becomes obvious.
See if you can find 'brickie' on the forum and send him a PM. You can search for him by putting his username in the search box at the top of the forum page and choosing 'Members' then hit the magnifying glass. Perhaps he can give you more info.
Fascinating to have this raised after all these years. I remember the old brickie I saw doing it say that the most difficult part of it was keeping the pole dead vertical because it was that which kept it all plumb, but at least it gives you something to put a level against!
Edited by joiner, 08 October 2014 - 09:30 PM.