Wash, stone, and cut the nectarines into small pieces. Place in a saucepan with the water and half of the simple syrup. Bring to a boil and cook, stirring occasionally, until the fruit falls apart, about 10 minutes. Remove from the heat and force through a fine mesh strainer.
Let cool to room temperature. Add enough of the remaining simple syrup to bring the mixture to between 16° and 20° Baumé. Add the tartaric acid or lemon juice.
Process in an ice cream freezer according to the manufacturer’s directions. Transfer the finished sorbet to a chilled container, cover, and store in the freezer.