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Bit of a n00b, I'm afraid. I'm just getting into this, and very much from the perspective of folk fiddle (cajun and bluegrass), rather than any kind of concert/classical aspirations!
I'm aware of the huge diversity of approaches to holding the bow (and, indeed, fiddle) in folk (thumb over frog, thumb under frog, thumb bent, thumb straight, holding way up the bow nowhere near the frog, etc, etc)
On the one hand I don't especially want to limit myself later on, and on the other, I suspect it's always possible to re-address and correct technique later. My general thoughts at the moment are, I guess, if it sounds ok, feels comfortable and doesn't hurt, go with it.
Equally, it would be daft to proceed without checking in with folks on here, and seeing what you all think. I guess there's a pretty sensible school of thought about 'proceeding as you mean to go on', so maybe it's not a bad idea to get it right at the beginning..?
My teacher has been spending a lot of time working with me on the bow hold, so it would appear she regards it as something important to get right from the start. The hold I'm learning looks very much like the pictures at the following site:
This is a beginner bow hold, and the thumb will later move inside the frog.
The most difficult part for me is learning to avoid putting the bow weight on the pinky finger. The little finger should be able to lift up freely and tap the bow.