I have a score for a guitar music here, which has these strange hollow circles between notes; also before the first note:
They don't look like notes, and playing them makes the music ugly, so they have some other function.
What do they mean?
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They indicate open-string notes (E,A,D,G,B,E); note that they are in the same position of the numbers that indicate which fingers to use to fret the notes.
This is a badly notated 'open string', this should be a zero instead of a circle because it makes it hard to differentiate between open strings and open harmonics.
On guitar, there are often several places to play the same note. For example, the top E could be fretted on the 3rd string, 9th fret, 2nd string, 5th fret or open top string.The circle, as stated in the previous answer, indicates that the composer wants that E played on an open top string.The circle by the bottom E says the same thing, although I can't think of another way to play that note! As it's probably a study for a beginner, the composer has just been helpful.As the font is different, think 'open' rather than 0 fret, but it's the same difference.
In writing for the violin family, a small circle also means harmonic, which is produced by lightly touching the string enough to stop it vibrating but not enough to play the note. Sometimes the string is stopped lower down as well, in order to play a different range of harmonics.