Are there easy methods to push a note and in standard notation are there marks made for that. I can kind of figure a swing rhythm if I hear it first but if you stick sheet music I seem to misinterpret that?

What are the marks for I guess you could call it kinds of expansion. Its like the anticipations and that kind of stuff that neighbor tones. But there is probably another dimension that musicians notice but never talk about. Akin That was what I was after.