String crossing can be a confusing topic. Here are some reasons why:
So... how does one figure this out?
First, you need to understand the 4 hinges of your arm.
Start with the largest muscles first. Play a staccato note on one string. After your bow comes to a stop, raise or lower your whole arm as one unit (be careful not to raise the shoulder). You also have to move your arm a bit forward when you go to a higher string, or a bit closer to your body if you are going to a lower string. This allows the bow to be perpendicular to the new string before playing the new string.
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Sometimes (especially students who learn cello without a teacher) students will lift the bow when they change string. This is BAD because it is not spiccato, it's a lifting which takes away the arm weight and tightens the arm muscles.