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I'm not a teacher, but as an amateur player I faced with this problem (described below) and overcame this successfully.
Every online tutor mentions that we should use left hand elbow to cross the strings. Unfortunately, none of them say how much important is this and what are the consequences of not following the advice. In this post I intend to analyze the rule.
First, suggest that there is nothing about the violin in the whole world. You are the first person in the world who take a violin in hands. You will definetely spend a lot of time optimizing the bow hold and other things related to posture and performance. But now concentrate on string crossing with your left hand. You will probably find that it is difficult to play on G string. How would you make playing on G string much more comfortable? There are two ways. One of them is wrong and one is right. Let's condider the wrong first!
A wrong route is to cross the string with your fingers only or with fingers + wrist. The point is that you just vary angle between a finger and a fingerboard. It looks like that:
As you can see what I do on these photos is trying to cross the strings with minimum elbow's movement. I fix my elbow at the same spot for every string! I cross to E string by varying angle of fingers to a fingerboard and by movement of a wrist. Look attentively! Can you see that the wrist at the photo No 1 is not straight!!??
Positive consequence of this approach:
- you can play the violin
Negative consequences of this approach:
-your hand is not relaxed
-this position of a wrist (picture 1) makes vibrato impossible
-you cannot play in tune
Last point must be considered in details. Everyone knows how difficult to play on the violin in tune. It is easier when your fingers move in three ways: 1) vertically up and down; 2) up and down through the fingerboard when you do vibrato; 3) up and down through the fingerboard when you shifting between position. So, the picture below show this:
A-B is a vertical movement (1 way). C-D is a horizontal movement (2-3 ways).
BUT fourth horizontal movement between the strings must be limited to a necessary case (e.g. when you play on the E string). There must be greater care with this movement and it should not be used to cross the string. The movement is shown below:
Movement from point E to F or from E to somewhere in between E and F or from F to somewhere in between points E and F must be used only when this is objectively neccessary! If it is used to cross the string and elbow stay at the same place you must guarantee that your finger goes straight and under angle from, let's say string E to G string. And you'll never be able to guarantee that. To understand what I'm talking about try to fix your elbow and cross from F note at E string to A note at G string. You will get a bit sharp or a bit flat A. So, you will be out of tune!
So, the point is that the fourth type of movement of your fingers must not be used to cross the strings unless you do it with elbow movement at the same time. If you do this without your elbow, there is a serious risk that you won't be in tune. Above I tried to analyze and prove this point.
This part is much more shorter. Elbow should be free and ready to move, if you gonna play violin in a right way. It is important to move your elbow to the right when you wish to play on G string. But it is important to move yor elbow to the left when you play on E string as well. This is extremely important.
Many tutors say that that the wrist must be straight. They generally mean this:
It is important point. But your arm must be straight in this way as well:
This second point of straight hand rule will be satisfied if and only if you use your elbow to cross the strings.
P.S. Good luck! As I said, I had problems with this kind of things. The aim of this article is help to beginners to recognize how important is good left hand technique related to the elbow and why it is important.