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I play guitar and for one of my songs, the sheet music shows sharps for only higher notes and not the lower notes. Do I apply the sharps to the lower notes? For example, G on string 1 is a sharp but it doesn't specify that G on string 6 is a sharp.enter image description here

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That's the key signature, which tells which letter name notes are sharpened. There's only need to put a sharp sign there on the F line, and musos will assume all F notes throughout the piece are sharpened, regardless of which octave they're in., unless cancelled by the natural sign (♮). The same goes for the other sharps, and all flats, in flat keys.

In fact, just playing the piece with only the top line F sharpened, and others played as naturals, would sound rather strange, wouldn't it?

However, if you find a stray sharp, flat or natural sign in front of a note somewhere else, that only lasts for the bar, and is known as an accidental. The ones you ask about aren't accidentals, they're put there on purpose!

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What you showed us is a key signature. It sharpens all F, C, G and D notes in all octaves.

But there are also 'accidentals'. They persist only until the next barline, and only at that exact pitch.

But, when that strict rule could cause confusion, a reminder 'cautionary accidental' is sensible. Required, even.

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