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My fudge uses regular granulated sugar, but if it doesn't reach the proper temperature and stay there for a full 5 minutes it results in a grainy texture.  Your choice of sugar is probaby fine, but you may want to check the temperature.  If the recipes calles for it to boil, it usually has to maintain a rolling boil for about 5 minutes while being stirred.  A lack of evaporated milk(or cream) or butter can also mess up the texture.
I agree but I also say that, sorry for the cheesieness and spoiled rotteness of me, but, the cheaper versions of sugar make a grainer texture.  C&H sugar is my choice, SMOOTH!!!  It just melts better than the cheaper versions.  There are a lot of generics that are great but Sugar and Campbell's soup are 2 of my peeves!  Gotta have them no matter what! LOL