tumbled stone mosaic tiles - help!

Hi everyone, I'm new here and would love to have some help. I am making a 3' diameter mosaic of stone tiles.
The tiles are 3/8" and tumbled. Being new at this too, I bought tumbled stone tiles but they didn't have all the colors of stone I need. I'd like to make my own by cutting stone to size and tumbling. I know how to cut, but not the tumbling.
Is this possible? Do I need a large tumbler? Does it take a long time?
I don't want a polish - only softened edges ..... sort of so it looks old.
Thanks for any help you can give!