Place the blueberries and water in a saucepan and cook over medium heat for about 10
minutes or until the blueberries pop open and begin to fall apart. Strain, pressing firmly on the contents of the strainer; discard the pulp.
Add enough simple syrup to the blueberry juice to bring the mixture to between 16° and 20° Baumé. Add the tartaric acid or lemon juice.
Process in an ice cream freezer following the manufacturer’s instructions. Transfer to a chilled bowl and store, covered, in the freezer.