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I've had a problem for a good while with getting clean notes on the G string.
I know what the problem is - my hand isn't curled far enough over the neck to be able to come down on the string from straight up (which is somewhat to the left of straight up as the floor sees it.) Coming at it from the side (rather than straight down) results in muddy notes, sometimes out of tune.
I know about moving your elbow further to the right, but that's both painful and tiring, so I'm not up to keeping it that way all the time, and it's a big motion I tend to forget about until it's too late, and/or I make a big, semi-violent motion (trying to get it there in time), which tends to make it even more painful.
My teacher came up with a simple and easy method of handling this. For me, at least, it's intuitive (meaning I think of doing it in time to get some good out of it), fast, and not painful.
Just raise the violin (with your left hand) an inch or two. That automatically pulls your elbow in, and you only need about 8 or 9 mm in first position for your finger to be angled right.
If you've had that problem, try it and let me know what results you get.
We should just not go often where the fingerboard hand is suffering and accept our limits. If you're a right handed player, it starts to get harder on the D string and when you have been on the D string a lot and finally reach the G string the fingerboard hand may be too tired. If you watch classical violin players on YouTube, you understand the violin mostly uses A and E string in sheet music. And people are not all the same, some have longer fingers which are more flexible, others have not. So we have to accept those limits. To play in Eb is by the way harder than in D#! So maybe you wanna stay away from hard to reach strings in b-keys the more b the harder.
In my case it's about A and E string because I'm left-handed. So the D string is supposed to me my home base and I can nicely play on the G string. But I have moderate the use of the A string a bit and very much the E string. Me playing on the E string too long leads to losing relaxation and then the sound on all other strings will be worse too.
Actually I had searched that G string issue in December but didn't get any results. I then discussed it on the tread where I've mostly been posting. I just learned, I have to search headlines to find topics like this.
My violin is a 3/4 violin, made for right-handed players, though I play it left-handed. As I felt she was the best in the shop of all 3/4 violins I tried and the luthier agreed. I prefer Obligato strings together with Eudoxa E string. Self-made bow, weight: 24 g / 0.85 oz