Place a nonstick silicone baking mat or parchment paper on a baking sheet. (See notes below.) This recipe will make enough macarons to use several baking sheets.
Add the almond flour and confectioners' sugar to a food processor and process until the mixture is finely ground. Then, sift the mixture, discarding any large pieces if necessary. Use a kitchen scale to divide the dry ingredients into 2 bowls, or measure it to divide it.
Using a mixing bowl and the whisk attachment, beat 6 egg whites and cream of tartar until foamy. Add 1/3 of the sugar and beat 1 minute until the sugar dissolves. Add half of the remaining sugar and beat for 1 more minute. Then add the rest of the sugar and beat until firm, glossy peaks form, about a minute or two.
Use a kitchen scale (for accuracy) to divide the meringue between two mixing bowls. To the first bowl, add the red gel food coloring and mix. Add the royal blue and violet colorings to the second bowl and mix. Add a substantial amount to give the macarons a vibrant color. Use less coloring for softer colors.
Use a spatula to gently fold one bowl of the almond meal mixture into the red-tinted meringue. Add more food coloring if needed. Mix well. The batter will be thick. Divide the leftover 1/2 egg white into 2 bowls and beat with a hand whisk until frothy. Stir it into the red batter to soften it and moisten it.
Repeat the process for the other bowl of meringue containing the blue food coloring by adding the divided dry ingredients and fold until well mixed. Add the remaining 1/2 egg white to moisten the batter.
Cut off the end of each ex-large piping bag and add a round tip to each. Add the red batter to one bag and the blue batter to the other bag. Fold over the top of the piping bags and then roll them under. Hold the top so none of the batter can escape.
Position the red batter bag over the prepared baking sheet, holding it straight vertically. Then, pipe 1 to 1 1/2-inch circles onto the pan. Leave room between each circle for the batter to expand.
Repeat with the blue batter.
Tap each baking sheet on the counter when filled with macaron batter. (Tap before they start forming a skin.) Tapping will spread the macaron batter and also help remove air bubbles. Use a toothpick to burst any bubbles in the macarons. Let the macarons sit for 30 minutes or until they form a dried skin on top. You can test for the skins with your fingertip. If the macaron batter sticks to your finger, dry it longer. If none sticks to your finger, the macarons are ready to bake.
Preheat oven to 300 degrees F. Bake for 14-15 minutes. Keep a check on the cookies so they do not brown or they will lose their vibrant colors.
Cool cookie shells completely on the pan. Then remove them very gently.