Yeah, the German is better for switching between long passages and the French for switching quickly within the same phrase. I can put the bow down and pick it up just as fast as the rotation in the hand the German takes to get into "pizz" position, so I tend to just do that. I have either a small table or chair at concerts or a quiver.
There was a period in the US when French was preferred for classical. In that time I had some young students who were primarily French players. I advised them to get a cheap German so they could continue practicing when the French caused pain early on.
It seems like there is less of that preference now.
I can play the French grip painlessly and use Rabbath's grip. Still, there is no real way to get there out of the gate.
Yes, having a table/stand for the French bow is very helpful, but sometimes the transition to pizz is too fast to set the bow down. If the bow remains in hand, it limits my pizz technique. If the pizz passage is slow, it's no big deal. But if it's fast, it's a lost cause; I have to find some way to get rid of the bow. My observation is that bass sections often cover such transitions with a phased approach, I.E. different players agree to transition at a different point to ensure everything is covered.
Never been a fan of quiver, but I suppose that is a personal problem
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With the German bow, the pizz grip is totally different and my plucking fingers are not restricted by the bow. I don't feel it's ever necessary to put the bow down. This is one of the factors that I found very appealing about the German bow.
To this day I own a German and French bow.
As far as the grip I use on French...I have no idea what to call it. I think one important factor is finding the point where the bow has the right balance in your hand. Text book grips will often put you behind the balance point, so the bow is too tip heavy and the player has to muscle it around too much. Each bow is different and the grip must be adjusted accordingly.
The other part is getting confident with a very light grasp and gaining the ability to manage the pressure points, rather than clenching equally with all fingers all the time. The player must learn to apply strength only when and where it is needed, and this is a very tricky concept for inexperienced players to grasp and master. I must confess that I sent a few French bows flying due to losing control while exploring this concept.
I think it's also important to realize that the problem is beyond learning how to hold the bow properly. The use of gravity is relevant. The ability to pull energy from one's core is relevant. A nuanced understanding of how to pull sound from the instrument is relevant. In short, there are lots of little factors that eventually must come together so one can play the French bow without pain, and some of the factors are not directly related to bowing. I suppose this is why a good instructor can be invaluable.