I'm going to link to a previous answer I've done on this as well: https://www.reddit.com/r/AskHistorians/comments/4j8ltr/when_did_music_begin_to_be_written_like_it_was/
Yes, there have been other forms of musical notation:
There are some notations from India
A different notation was developed in the East for chanting
Some symbols were added to texts in Cantillation
And Western musical notation has not always been exactly the same
There have been tablatures for different instruments (Lute, organ) and shorthand notations (figured bass)
To be honest, there have been additions to Western notation and even new proposals