I am a long-time French bow user but the basic principles of French and German Bow use are not far apart in my view.
I copied the following from my response to Goodgig, 04-19-2008 re Bow Arm Weight.
"For me natural weight means weight of the arm resting on the strings through the hook formed by first finger and thumb of the bow hold. With nothing, no "crane muscles," on top of the arm holding back. To me this produces a nice earthy tone by bending the hair around the string and suppressing some of the upper partials, and sounds no more than about mf.
To use this weight smoothly and effectively from end to end of the bow without lifting I rotate the elbow up and out slightly which turns the bow hold in and throws weight forward onto the index finger. Only a few degrees, in order to align the elbow (hinge joint) movement with the bow direction. This works well for ON STRING playing.
For OFF STRING and SEMI-OFF playing I lower the elbow until bow hold fingers are parallel with the stick and I can "pat" the string with a shallow carried bounce. This works well near the balance point of the bow, that magic place that makes string crossing easy, and produces nice warm quaver speeds that I call "Haydn/Mozart" (try the opening of Eine Kleine Nachtsmusik).
SPICCATO could be as far out as the middle of the bow and require a different approach again because the string is more struck with a steeper "vee" shape by rotating the bow around the thumb. Generally bass players are allowed to produce spiccato closer to the balance point because our strings are so heavy.
So, my bow hold keeps changing according to the demands of the music. Three big variables come into play - bow speed, weight and contact point - also take into account which string you are playing on (the heavier the string the slower the bow)
The further you bow from the bridge the faster the bow must move to support and drive the vibrations. I prefer to bow closer, say near half way between fingerboard and bridge where the string is stiffer, and use a little more weight with a slightly slower bow. I listen for resonance, tone and projection while encouraging free movement of the strings even though the weight of my arm is bending the hair around them and controlling them.
Try this experiment. Wrap your fist around the frog. Crush the bow down on the D string and slowly draw a screeching BUT EVEN sounding down bow (like drawing your fingernails down the blackboard at school, remember!). Repeat this again and again, gradually reducing the weight and you will start to hear the note come out, still hopelessly crushed, from under the bow. Finally the full beautiful tone will emerge, the string will be moving freely and the bow hair will still be bent around the string!! Then go to the proper bow hold and copy. This is my model sound that I try to apply to all notes, all strings, as a starting point in sound production.
I do believe in using the natural weight of the arm for on-string playing. How I set my bow and bow arm to achieve this would take much more space to explain."
The open heavy E string vibrates at 41.7 times per second (?) and uses much less bow speed and length, maybe flatter hair and a little more weight , and some care with contact point to produce clear rich projected sounds. Faster notes progressively shorten the bow length and move the bow towards the end of the fingerboard.
Conversely, the G string requires faster longer bow with less pressure and staying away from the end of the fingerboard to produce the same clarity and projection.
As you progress up each string towards the higher positions you should maintain approximately the same ratio of contact point to string length. For example, if you bow 6 inches from the bridge for open G then bow 3 inches away for octave G. You can tweak bow speed, length and weight, and angle of hair to produce more control of sound.
If you do not move the contact point up progressively as you finger higher you must compensate by moving the bow faster and faster to support the faster string vibrations. Even so the sound becomes less focussed. Never play near the end of the fingerboard on the G string _ sound collapses too easily!
Another useful exercise is to start playing a really comfortable note, say C on A string, "on" the string with full bow length and clear rich sound. Gradually speed up the bow strokes, keeping the same quality and clarity of sound by progressively shortening the bow lengths with a little more weight until you are using about 2 inches of bow for 16th notes at 1/4 = 80. The magic place to contract to is the balance point of the bow. Then reverse the procedure, expanding to full bows as you slow down. The bow can be quite firmly on the string, not lifting at each end, because the vibrations of the bass body soften note endings so long as you keep playing. Listen for clear musical nicely separated detache sounds. Too short movements produce grunts without tone and too long produces fluffy scrubbing sounds. The aim is to play confidently hard on the the string clearly at any speed with no bow lift, just flat sideways movements. Then add in timing coordination and shifting while maintaining this clarity.
Best wishes
DP
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