Wash the apples. Line a colander with a thin cotton dish towel or a triple thickness of cheesecloth. Place the lined colander over a bowl. Using the large holes of a box grater, grate the apples, including the skin, into the lined colander. Grate the apples down to the core. Or peel, core, and quarter the apples and grate them in the food processor, then dump them into the cheesecloth-lined colander. Juice will start dripping through the dish towel into the bowl below. This is good. Add 1/4 cup (65 ml) of the sugar, the cinnamon, nutmeg, and cloves on top of the grated apples and toss gently.
Gather up the dish towel and squeeze the juice out of the apples. You don't have to squeeze out every drop. This will produce about 3 cups (750 ml) of juice. Set aside. You will have about 8 cups of apples.
Bring 2 cups (500 ml) of water and the remaining 1/2 cup (125 ml) sugar to a boil in a medium pot over medium high heat. Stir to dissolve the sugar. Add the apples and boil them in the syrup for 3 to 5 minutes.
Have ready 4 scalded pint (500 ml) jars and their bands. (To scald, simply dip the jars in boiling water. You don't need to sterilize the jars, as you will be processing them for over 10 minutes.) Simmer new lids in a small pan of hot water to soften the rubberized flange. Place 1/2 teaspoon of the citric acid in the bottom of each jar, then add the apples, leaving 1/2 to 3/4 inch of headspace. Wipe the rims, set on the lids, and screw on the bands fingertip tight.
Place the jars on a rack in a big pot and add enough water to cover the jars by 3 inches. Cover the pot and bring to a boil over high heat, then lower the heat to medium and gently boil the jars for 25 minutes. Remove the cover and then, after about 5 minutes, remove the jars. Allow the jars to cool, untouched, for 4 to 6 hours. Check the seals and store in a cool, dark place for up to a year. Refrigerate after opening.
In the meantime, pour the juice into a sterilized quart (1 L) jar (to sterilize, boil the jar, its lid, and its band for 10 minutes) and refrigerate until you are ready to make the granita. The juice will hold in the refrigerator for about 3 days.