did open string have its own notes?

Not sure if I understand your question completely... Open strings "have its notes", depending on how they are tuned. For instance a guitar is commonly tuned (open strings): E, A, D, G, B and E (low to high), a violin (and mandolin) is tuned (open strings): G, D, A and E (low to high). Other stringed instruments, like bass, dobro, ukulele, banjo, sitar etc. can be tuned in a number of ways. You can also have a guitar tuned many ways, something which will change the open string notes.

If you're thinking of something else all together regarding "its own notes", you will need to supply more information :-)