Czerny - The Art of Finger Dexterity Op.740, Book VI - No.48

[@protte225]

I was wondering why some of the trills, such as the first one, are written as though they are to begin before the beat. In measures 13 and 14, for example, there really isn't time to do that, anyway, But why on earth would one want to? I wondered if it might have been a way Czerny used to indicate he didn't care if there are a precise number of notes per beat. Also, it could have been simply a way to emphasize the trill starts on the principal note instead of above.