Preheat the oven to 350°. Butter and flour a 9-inch springform pan. In a bowl, sift the flour, baking soda, cream of tartar and salt. In a large bowl, using an electric mixer, beat the butter with 1/2 cup of the sugar at medium speed until fluffy. Add the vanilla, then the eggs, 1 at a time; beat well between additions. At low speed, beat in the dry ingredients in 3 batches, alternating with the milk.