Preheat the oven to 400°F.
Wrap the beets in aluminum foil, place them on a baking sheet, and roast for 50 minutes, being sure to check them once or twice. The beets are ready when a knife slides into them easily. Remove from the oven, open the foil packet, and let cool. Peel and chop the beets and set aside.
Prepare the barley according to the package directions. You should end up with about 4 cups barley.
Place 1 cup of the beets, ¼ cup water, the salt, some pepper, and the sugar in a blender and purée. Transfer the beet purée and the barley to a large bowl and combine thoroughly.
Reserve some pecans and tarragon for garnishing. Mix in the remaining beets, cranberries, grapes, pecans, and tarragon. Taste for seasoning and add more salt and pepper if necessary.
Heat a pan over medium-high heat and add the vinegar, being mindful of any fumes. When the vinegar starts boiling, reduce the heat to medium-low and simmer until the vinegar has reduced by more than half and has a thick, syrupy consistency. Remove from the heat.
To serve, divide the salad among eight bowls. Drizzle each with the balsamic reduction and top with a sprinkle of tarragon and pecans.