Tennessee falls into the "transitional zone," where neither cool-season grasses nor warm-season grasses consistently thrive. American Lawns recommends cool-season grasses like fescue, zoysia and bluegrass as being the most consistent throughout the state, but also notes that warm-season grasses like Bahia and Bermuda grass may do well in the lower elevations.
Sow cool-season grass seeds from late August to mid-October so they have the advantage of two cool growing cycles before the next summer sets in. Warm-season grasses are best grown from sprigs or plugs, which should be planted in May or June to give them the benefit of the full summer to become established.
Use a soil test kit to determine the pH and nutrient content of your soil. If you pH is below 6.0, work lime into the soil before planting seed. If your nitrogen balance is off, apply a starter fertilizer to the soil before planting, then again about six weeks after germination.