Accidentals are no accident! An " Accidental " is just the term used to describe the symbols such as Sharps, Flats or Naturals which alter the pitch of the notes they are placed in front of in a bar, which are not part of the key signature. A Sharp raises the pitch a semitone (up one fret). A Flat lowers the pitch of the note a semitone (down one fret), and a Natural cancels the effect of a sharp or flat and returns the note back to its natural state. Accidentals are also very useful for locating any temporary new Keys. If the notes aren't part of the songs key signature it will either indicate that the chord is altered or that the song has moved into a temporary new key even just for one chord.
Sometimes it is necessary to raise the pitch of a note by a tone (up two frets) this is indicated by placing a double sharp in front of the note. The same applies to a note which must be lowered a tone, ( two frets down ) indicated by the double flat symbol.
One of the most important points to remember is that these " Accidentals " only affect the notes they are placed in front of. Notes of the same name, in octaves above or below are not affected.
Sharps and Flats in a Key Signature however, do affect all notes of the same name regardless of whether they are in other octaves above or below. This is the theory most musical reference books adhere to. A popular method in recent times, which I recommend, is to indicate in brackets any sharps, flats or naturals where the music may be complex or note values could be misinterpreted. For the sake of the music and the musicians, always clarify what the correct notes should be, make comments next to a complex passage, do whatever you need to make your music understood. It makes no sense to blindly stick to antiquated rules that are often confusing, if people are going to misinterpret your music.
A good example of confusing use of Accidentals is whether you use one or two naturals to cancel a note that has been Double Sharped or Double Flatted ? ? The rule books say that you would use two naturals to cancel the effect of a Double Sharp or Flat. Using only one natural would still mean that the note is affected by one of the remaining sharps or flats.
Not everyone abides by this rule though, it has become very popular to only use one natural to completely cancel the effect of Double Sharps or flats. Personally I agree with the latter method. The natural should cancel any Double Sharp or Double Flat, if the note is reverting back to a single Sharp or Flat, place a sharp or flat after the natural, indicating that the natural has cancelled the Double Sharp or Flat completely and that the new Flat or Sharp has come into effect. Clear as mud eh!!!!
Well here are some examples to help sort things out.