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i came across a sign on my notation where a note is being played that is G after that there is a note in between e that is open but we first play it and then hammer on it... what is it called ?

Small quaver with stroke through flag and stem

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This is called a grace note. Its duration can be stolen from either the note before or after it, depending on the stylistic context. I think the slash is intended to indicate "as fast as possible".

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    This particular grace note is an acciaccatura, or crushed note. It is played very rapidly. – Old Brixtonian Jan 17 at 19:56
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    It is an acciaccatura, just one kind of 'grace note'. The idea is to play it and get off it as soon as possible. the word translates from Italian as 'crushing'. Hence on guitar, an immediate hammer-on is a nice simple way to perform it, and the following G. – Tim Jan 17 at 20:06
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    That slash line isn't cancellation! – Tim Jan 17 at 21:51
  • @ibonyun: I don't agree with the as fast as possible part. The note value (an eighth here) clearly indicates the intended length in relation to the main note. – guidot Jan 19 at 21:33
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    @guidot I don't think the fact that the engraver used an 8th note has much to do with the actual intended duration of the grace note. The precise duration of grace notes is a subject rife with debate, so I don't think there is a "correct" answer here. Other commenters pointed out it is an acciaccatura -- because of the slash I think -- which in Old Brixtonian's words "is played very rapidly", and in Tim's words "play it and get off it as soon as possible". – ibonyun Jan 20 at 2:14

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