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We explore the formal foundations of recent studies comparining aural pattern recognition capabilities of populations of human and non-human animals. To date, these experiments have focused on the boundary between the Regular and Context-Free stringsets. We argue that experiments directed at distinguishing capabilities with respect to the Subregular Hierarchy, which subdivides the class of Regular stringsets, are likely to provide better evidence about the distinctions between the cognitive mechanisms of humans and those of other species. Moreover, the classes of the Subregular Hierarchy have the advantage of fully abstract descriptive (model-theoretic) characterizations in addition to characterizations in more familiar grammar-and automata-theoretic terms. Because the descriptive characterizations make no assumptions about implementation, they provide a sound basis for drawing conclusions about potential cognitive mechanisms from the experimental results. We review the Subregular Hierarchy and provide a concrete set of principles for the design and interpretation of these experiments.