2 parts to this
first is what do you aim to achieve when the martingale on a shank bit and you run one peice through the middle ring and one clipped to the shank and what do you achieve when they are both running through the shank.
I run through where my reins are attached to the bit. What I am achieving by using a German martingale is to use a tool to keep the horses nose down so they cannot hollow out their back. I can get vertical collection of the head or neck when my young horses get into a situation and panick. I can generally bring them back down and finish the run without incident therefore giving the horse confidence.
The only time I use a shank is when the horse starts bracing on the snaffle.
I also have my German martingale loose as it is a tool I use incase of a panic emergency.
If you are talking about a running or a standing martingale I have no clue what you are asking.