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E=Fb

A Fb can be technically correct. For example, in the key of Db minor, the 3rd would be a Fb, not a E. My music theory teacher was a symphony player (viola), and we had this discussion in class 1 day. He said he would have to make microtonal adjustments on the fingerboard in these cases. that is parts of the shortcoming of our 12 note scale. Granted, we cant do much about it on a fretted instrument, but that is also the reason for tempered tuning on a piano
 
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