Make the salad: Bring a large pot of water to a boil. Add the barley and cook for 15 minutes. Using a sieve, remove barley from the water and transfer to a bowl.
Bring the water back to a boil and salt, to taste. Add the barley and rye and wheat berries and cook, stirring occasionally, until tender, about 30 to 40 minutes. Drain, transfer to a bowl, and cool.
When cool, combine with the remaining ingredients.
Meanwhile, make the Dressing: Whisk together the vinegar, dill, and garlic. While whisking, drizzle in the oil to make a smooth dressing. Season with salt and pepper, to taste.
Toss the salad with the dressing and serve.
Recipe courtesy of Chef Jon-Paul Hutchins, Scottsdale Culinary Institute