I haven't looked into this yet but is the added note you are talking about like the added note of the Major bebop scale between Sol & La? Or is it the sharp Fa of the Lydian sound?
But wait there's more! Not only does this function harmonically, it also functions melodically. The added scale tone makes it so that a chord tone ends up on every down beat when playing in eighth notes. I've actually found that it doesn't matter where you add that extra scale note, you can do it all the way up and down the piano anywhere you like as long as you get chord tones where you want them.