Clarity, Impurity, and Discant Structure in Mesopotamian Music

According to a widely accepted interpretation, the “unclear” (la-zakû) intervals of Mesopotamian tuning were tritones, which became “clear” (zakû) intervals—in modern terms, perfect 5ths or 4ths—by tightening or loosening a particular string on a harp or lyre. Nonetheless, Sam Mirelman has recently cautioned (2013) that we cannot be sure such an interpretation is correct. Meanwhile, Yitzhaq Feder’s (2014) survey of contexts for “zakû” in Mesopotamian texts has shown that it referred to things that were “pure” not only in the sense that they were “not impure,” but in the even more precise sense that they had been “purified” insofar as their impurity had been removed. Such a construal of the contrast between “zakû” and “la-zakû” is consistent with the view that Mesopotamian tuning comprised a process in which the psychoacoustical impurity of a la-zakû interval, namely, its beating or roughness, was removed by tightening or loosening a string, resulting in a purified, zakû interval. Further, if one assumes that the modular interval of Mesopotamian tuning corresponded to the perfect octave (an assumption that has never been disputed), one can reduce the possible ways in which a harp or lyre was tuned from twelve to two. Further still, close reading of a recently published transliteration and photograph of a cuneiform tablet reduces these two ways to one. Finally, applying the tuning process to the well-known Hurrian notations results in music that is cognate with a musical framework Patricia Carpenter characterized as “discant structure.”