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"Vinegar is product that has been used for dental hygiene for many years. A
half strength solution of vinegar (apple cider for taste) will pickle most
of the motile bacteria and it will help to dissolve deposits of calculus.
For persons whose dental hygiene does not reduce the buildup of bacterial
plaques adequately, some of this buildup may harden into calculus.  Brushing
several time a week with a vinegar solution can help to prevent calculus
formation.
Regards,
Dr. Paul H. Keyes

Dr. Keyes is the founder of  the International Dental Health Foundation
Education: D.D.S., University of Pennsylvania School of Dental Medicine
(1941); B.A., University of Rochester (1944); M.S. in Anatomy, University of
Rochester (1945); Fellowship in Orthodontics, Harvard University School of
Dental Medicine (1948).

Research Interests: anti-infective periodontal therapy."

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I tried vinegar full strength and it removed more calculus than any other
things I tried.
Right after I used baking soda to remove the taste.  I'm going to do this
once a day until my excess calculus is nil.
After which I'll cut back to once or twice a week.

The only other effective method is scaling which takes too much time and
effort.
It's too much headache to find a good hygienist , after trying three in a
row with all thumbs.

Jamffer