Typically, the accidental alters the pitch of the note that it is attached to as well as any subsequent occurence of the same note (identical line or space) in the same measure. Notes with the same pitch name, but higher or lower octave should not be effected. Any note with an accidental that also has a tie across a barline carries the accidental to the note on the other side of the barline. Notes in the new measure that are not tied to altered notes from the previous measure are performed using the current key signature.
Often, notation can get very complicated and composers or editors will use a courtesy accidental (cautionary accidental or reminder accidental) to remind the performer that the accidental attached to a previous note has been added or removed.
Also [Eng.] accidental; [Fr.] accident (f); [Ger.] Vorzeichen (n); [Ger.] Versetzungszeichen (n); [It.] accidente (m).
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