Between the Fingers
Bradoon rein below the pinkie.
When the reins are held split, there are many different ways to hold them. The most common, and the one I don''''t use myself, is to hold the bradoon rein below the pinkie, and the curb rein between ring finger and pinkie, where the snaffle rein usually goes. But if you have learned to ride and feel the horse''''s mouth on your ring finger, you will continue to feel the horse''''s mouth with the ring finger in the double bridle. You will ride the curb like you would a snaffle, and with the same amount of contact and technique. That does not work very well, you can''''t position, lift and bend very well. Because you now need to do those things on the bradoon, and the bradoon rein is under the pinkie.
Bradoon rein below the ring finger.
True, the curb should go into the hand above the curb, so that any turning inward of the knuckles will effect the bridoon, and never reach the curb. But there''''s no need for this to be done below the pinkie. The whole reason one holds the snaffle rein between the ring finger and the pinkie, still stands when riding on a bridoon (and added curb).
The straight line to the bit from the elbow goes
via the ring finger.
The relaxed hand held straight out from the lower arm will be angled upward by the rein below the pinkie. The rein and its pressure will want to be in a straight line from the elbow to the bit (seen from the side) and this will cause the hand to tilt upwards. A straighter line goes from the elbow to the bit via the ring finger. There are enough fingers on the hand to allow the curb rein to come to the hand between long finger and ring finger. It doesn''''t matter that this finger is unused to holding a rein. It won''''t be doing much with it anyway.
The Fillis Hold
Holding the reins a''''la Fillis makes the curb a lot
sharper, so the horse tends to break off behind
the 2nd vertebra.
James Fillis, a student of Baucher, who developed Baucher''''s theories further, and who trained the Russian Cavalry and left a tradition in Eastern European and Russian dressage, also invented, or probably just named, a special hold of the reins - the Fillis Hold. The usual function of the reins in the hand does not apply to this hold. That is because the curb rein does not enter the hand above the bradoon rein. Quite the opposite - the curb rein enters the hand from below, under the pinkie. The bradoon rein enters the hand from above, like a driving rein. This places the points of entry into the hand of the both reins as far away from each other as possible. This means that a mere tilting of the hand up or down has a strong effect on the horse''''s mouth, and thus it is a very "direct" form of connection. I would say, almost a "correction connection" because the curb can be used strongly without employing the bradoon. It is not just there as a self-regulatory function, like in the 3+1 hold.

Philippe Karl holding the reins
a''''la Fillis.
Unfortunately, this spectacular look is getting popular. Unfortunately, I say, because I have yet to see a competition horse ridden in this rein hold that does not overbend at the 3rd vertebra, like the horse in the picture above. Not even Kyra''''s horses. Philippe Karl (left) uses this hold a lot, but then, he is probably the most well seated and well educated rider I have ever seen, and also one who is manic about not overbending. Not something one can say about the majority of riders...
I personally don''''t use this hold at all, since I find no use for it. Either, the horse is ready for the double bridle, and I use it 3+1 or 2+2, or he is not, and I use a snaffle. But it is very popular with for example Kyra Kyrklund, Michelle Gibson, etc.
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