Getting rid of the soap scum by adding more washing soda

I'm making my own laundry soap, and information is hard to come by on formulas. The base formula is soap flakes, washing soda (known by many other names, disodium carbonate, soda ash), and borax.

I thought soap scum was just what you had to suffer through, but no more. By increasing the washing soda, by a tablespoon or doubling it, until the scum disappears. It's the water hardness that determines how much you need to add. The water contains calcium and magnesium atoms, "hardness", and these positive ions are "neutralized" by the negatively charged sodium atoms in the washing soda. If you do not add the cheaper washing soda (than soap flakes) for this purpose, then you need more flakes to get the same cleaning power, as it uses the negative ions in the soap flakes to neutralize the hardness. The atoms used to neutralize are not available for cleaning.

Now, when my clothes come out of the washing machine, there is no scum accumulated on the sewn seams and buttons, and I do not have to use a brush to remove the scum.