The answer, IMHO, is it depends. I look at it like this, if the instrument, in your case the fiddle, has a mic or an amp I leave it where it is. But if it doesn't have a mic or amp then I move it towards where the singer was standing.

So if you are trying to emulate a true blue grass band then I would move the fiddle to a little left of the singer when it takes the lead: note this is from the audience's perspective. I do this as I have seen the singer stand directly in front of the mic but when the fiddle/instrument's lead comes in the singer will move slightly to the right and the fiddle/instrument will be slightly to the left of that mic. That is very slightly to the left. YMMV


The fitness trainer asked me, "What kind of a squat are you accustomed to doing?" I said, "Diddly."


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