In a medium mixing bowl, stir together the unbleached flour, whole-wheat flour, sugar, baking powder, cream of tartar, and salt. Cut the shortening into the dry ingredients until the mixture resembles coarse crumbs.
Make a well in the center. Combine egg and milk; add all at once to flour mixture. Stir mixture until dough just clings together.
On a lightly floured surface, knead gently for 10 to 12 strokes. Roll or pat to 1/2-inch thickness. Cut with a 2-1/2-inch biscuit cutter, dipping cutter into flour between cuts. Transfer to a baking sheet.
Bake in a 375 degree F oven for 15 to 18 minutes or until golden brown. Serve warm. Makes about 10 biscuits.