Preheat oven to 400 degrees. Line baking sheets with parchment paper; set aside. Whisk together flour, cream of tartar, baking soda, and salt in a medium bowl. Cream butter, shortening, and granulated sugar on medium- high speed in the bowl of a mixer with the paddle until pale and fluffy, about 3 minutes. Mix in eggs and zest. Mix in flour mixture, scraping down sides of bowl as needed. Refrigerate dough 15 minutes.
Roll teaspoonfuls of dough into balls; roll in colored sugar. Place 2 inches apart on lined sheets. Bake until edges are set but centers are soft, 7 to 8 minutes. Cool on sheets 2 minutes; transfer to wire racks.
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