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In the below sheet music B is marked as flat however the only notes played are g g g d e c C. Is that just a typo on the part of the person who made this image and it should be on the upper C or am I missing something else?

staff

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Sharps and flats in the key signature are one indication as to the key of a piece. Lacking those notes in the actual music is irrelevant. For example, play all the white notes on a keyboard in order from C to the next C an octave higher. Now do the same from F to F. Hear how it sounds weird on the 4th note (B)? That's because you need to play it in the key of F. Now try playing F to F again but this time play Bb instead of B.

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I replaced "accidentals" with "sharps and flats". An accidental is a sharp or flat in-line with the notes, where a note deviates from the key signature. –  slim Sep 21 '12 at 12:35
    
I didn't know that. Thanks. –  mjibson Sep 21 '12 at 16:18
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It also tells accompanists to use chords that do not contain B natural. –  neilfein Sep 21 '12 at 19:38
    
@neilfein I think that's true only for simplistic music. Music that an accompanist would play (songs, for example) modulate. A common modulation is to 5 of 5, which has a raised 4th. In this case, that's to G, which uses B natural. –  mjibson Sep 21 '12 at 20:12
    
Speaking as a working musician who uses notation for traditional folk tunes: Your jab at "simplistic" music aside, modulations away from the basic key should be noted in the notation, either in this staff or other staves in the same work. (If they're not, someone did an incomplete job of transcription.) –  neilfein Sep 21 '12 at 21:20

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