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Determing a key from key signature


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I have them all down with one exception, the key of F. From the book in Section 8, it says you can determine the key for flats as the key is determined by the next to the last flat. I guess that doesn't hold true when the only flat is Bb, correct? Is that one that I just need to memorize?

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Flats are applied in a certain order, BEADGCF. If you look at it the same as the note names, they're circular and keep repeating (BEADGCFBEA...). Therefore in the key of F, the next to last flat is B.

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