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Many computing environments are heterogeneous, i.e., they consist of a number of different machines that vary in their computational capabilities. These machines are used to execute task types that vary in their computational requirements. Characterizing heterogeneous computing environments and quantifying their heterogeneity is important for many applications. In previous research, we have proposed preliminary measures for machine performance homogeneity and task-machine affinity. In this paper, we build on our previous work by introducing a complementary measure called the task difficulty homogeneity. Furthermore, we refine our measure of task-machine affinity to be independent of the task type difficulty measure and the machine performance homogeneity measure. We also give examples of how the measures can be used to characterize heterogeneous computing environments that are based on real world task types and machines extracted from the SPEC benchmark data.