I am very interested in that subject and I would like to understand the above better; maybe I can even add a remark. But there's a problem with the language: Is it correct that ties and slurs are curved lines above or below the note 'heads' (?) and beamed means that the 'necks' (?) of the notes are connected by a straight bar? If so, what's the difference between a tie and a slur - I mean graphically? You know in my original language there's only one expression.
(?): Literal translations from german. Should be self-explaining, though.