Interpretation methods constitute a foundation of the termination analysis of term rewriting. From time to time, remarkable instances of interpretation methods appeared, such as polynomial interpretations, matrix interpretations, arctic interpretations, and their variants. In this paper, we introduce a general framework, the tuple interpretation method, that subsumes these variants as well as many previously unknown interpretation methods as instances. Employing the notion of derivers, we prove the soundness of the proposed method in an elegant way. We implement the proposed method in the termination prover NaTT and verify its significance through experiments.