Why does the German layout arrange timpani from high to low, left to right?

Why are the timpani in the German timpani layout arranged with the smaller ones on the left, going up to the larger ones at right? Actually, drums, which are believed to have been the ancestor of the timpani, were originally used to send signals in the military. Apparently, when the drum was sounded, the troops would march forward or advance. Since two drums, a small and a large drum were carried on the back of a horse, it is said that the smaller drum was placed on the left side, as the rider need to lift his right leg to mount the horse without the drum getting in the way. This is a practice that has carried on into modern times.