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The balance between sweet and sour is crucial to the majority of cocktails and consistently producing balanced cocktails is made easier when using sugar...
But I think maybe I have to vote down my own comment! I didn't take into account that 2:1 doesn't automatically mean the concentration is twice as great! I bet 2 cups sugar + 1 of water gives greater volume than 1 cup sugar + 1 of water, so you have to add less 1:1 to get the same sweetness as you would think. If "brix" is actually a direct measure of sugar concentration, then the 13.57 ml equivalency would make sense!