This isn't my area of specialty, but I know a little bit about it. General, Chinese notation is tablature in nature, serving as an aid to memory. I took a class on this a couple years ago. A lot of this stuff is covered in Frederick Lau's Music in China.

Going to use this image as my example. The notation is read right to left. On the far right will be stuff like the title, tempo, and key signature.

The characters correspond to different pitches. So for example the pitch 工 (Gong1) would correspond to the 3rd pitch of the scale. The dots next to the notes determine length/beats. The purpose of this notation, as I mentioned, was just to aid memorization. Embellishment and performance practice were a mix of literate and oral. You would probably be taught the piece by ear via your teacher if you played an instrument, maybe with a little bit of gongche as an aid. The pieces that were disseminated in this oral+literate tradition definitely had some warp (as games of telephone are ought to do), so these notations may be an example of one specific tradition of playing a piece, within a smaller subset tradition of general chinese music.

This has "evolved" in a more recent time to a similar system using Arabic numerals and the such.Here is my personal example of a piece by Lou Harrison written in this newer form of notation There are some additions to this example that I believe to be entirely his (and not at all common in the literate part of this tradition). As you can see, the number of lines correspond to Western 8th, 16th, and 32nd notes, and the pitches in this piece to the members of the western diatonic scale diatonic scale. The transcription into western notation is my own. The dots below or above the pitch numbers indicate up or down an octave (2 dots indicating 2 octaves). My transcription is written for vibraphone, so not entirely note for note.

I'm uncertain of how common the traditional and newer forms of tablature are nowadays. I know I've seen a couple of pieces for traditional instruments written in western notation, and haven't really seen any tablature in my admittedly limited interaction with modern concert music for traditional chinese instruments.

These are just two examples of notation from the large chinese tradition, which is a lot more diverse than what I've provided, and more than a generalist book could feasibly provide. If a fellow historian who specializes in this would like to chime in on other forms of notation, I'd definitely appreciate.

Some Sources:

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Lau, Frederick. *Music in China: Experiencing Music, Expressing Culture.*Oxford University Press, Oxford: 2008.

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Harrison, Lou. Garden at One and One Quarter Moons. Frogpeak Press.