I've heard that there are 3 parts to the vocal cords: the true vocal cords, and the "false" vestibular folds and ventricular ligament. I read that the vestibular serves some function in chanting and such but was not clear what purpose the ventricular is used for.
I think you may have misunderstood your informational source. The terms vestibular folds and ventricular folds respectively refer to the same anatomical structures. They are synonyms. See the Wikipedia article on vestibular folds.