So far I've been able to find standard notation for the hi hat hit and hi hat pedal hit but it its not clear to me what is the closed hi hat notation. As i understand, normal hi hat hit is on the G2 spot, while the hi hat played with foot is a circled x sign on the D1 spot. Any help?
Well, normal hihat IS closed hihat, ain't it?
Google tells me that an X note sitting on top staff line (that'd be G5 for a piano player) is normal hihat (closed). If you want to SPECIFICALLY state that it's closed (not open) put a + on top of it. Open having an o on top of the X note.
according to page 3 of http://web.mit.edu/merolish/Public/drums.pdf
I don't think the notation standard is settled on that. Every genre has a different shortcut but Stephen's
Also putting a legend is a widely used solution. The main reason for the ambiguity is that there are too many percussive details to be fitted on the staff. Especially if you have lots of toms to transcribe and all the different types of splashes, crashes and chinas (where we decided to put a chinese character for cymbal to communicate) makes it pretty hard to read after all details are included.
The drumset notation is usually an approximation of the actual sound. Unlike other instruments, it's very hard to reproduce the exact replica of the transcribed music without extrapolating what it might have sounded like.