We present a method where Luttinger-like parameters extracted from first-principles calculations on small prototype systems are used to calculate near-band-gap states of much larger semiconductor heterostructures. The method can be used for small- and large-scale heterostructures with equal first-principles accuracy and it illustrates approximations that are implicit in the Luttinger model. GaAs - AlAs(001) superlattices are used to illustrate the method.