A key signature is a group of sharps or flats at the beginning of the piece located after the treble or bass clef.
These symbols could be confusing to interpret, especially in a sight-reading situation, so a system of ordering both sharps and flats was formed.
The order of sharps is : F,C,G,D,A,E,B.
The order of flats is : B,E,A,D,G,C,F.
If we look at a piano keyboard the note C sharp for instance could also be D flat.
This confusion is avoided by designating a key signature all sharp or all flat, a decision determined by the majority of accidentals in the key of the tune.
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