Preheat the oven to 425 degrees F (220 C).
In a large mixing bowl, whisk together the flour, baking powder, cream of tartar, baking soda, and salt. Work in the butter with the fingertips until the mixture has the consistency of large, flaky crumbs. Make a well in the center, and add milk. Stir using a spatula until the dough is soft.
On a floured surface, roll out the dough to a 1/2-inch (1.25 cm) thickness. Use a pastry cutter 2 to 2 1/2 inches (5 to 6.5 cm) in diameter or a water glass, press out rounds. (Do not twist when pressing out, or the scones are likely to bake unevenly).
Lightly grease a baking sheet with butter or line with parchment paper. Arrange the rounds on the sheet. Lightly dust their faces with flour.
Bake until they have risen and turned golden, 10 to 15 minutes. Remove from the oven. Serve warm.