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The ideal soil acidity for the majority of temperate plants is 6.5. Some will happily tolerate lower acidities, like potatoes while a few will actually require it like blueberries. This has to do with the nutrients required by the plant and their roots only being able to absorb those nutrients at lower levels.
I don't recommended this but I knew a soil scientist who could pretty accurately tell you the pH by tasting the soil.
In addition, hardwood ash is high in potassium which is an important addition for fruit crops like tomatoes.
I saw the charcoal heap on TV but have never done it. Anything you remember of it? I will try to hunt down an infographic, there must be one.