Was Mesopotamian Tuning Diatonic? A Parsimonious Answer

Abstract

On the basis of assumptions and conclusions first advanced in 1968 concerning tuning instructions that were originally written down ca. 1800 BCE, Assyriologists have agreed that Mesopotamian tuning was diatonic. Nonetheless, Sam Mirelman (2013) has recently suggested that this consensus view is “uncomfortably familiar and Eurocentric.” As a follow-up to Mirelman’s misgiving, the present report begins by identifying flaws in the reasoning concerning Mesopotamian tuning that was disseminated more than half a century ago and have remained uncontested. The starting point of the present study is information directly recorded in Mesopotamian documents, as opposed to concepts dating from Greek Antiquity and beyond. This information includes the spatial ordering of strings and the relative fundamental frequencies of two pairs of strings on thesammû, a harp or lyre that is explicitly identified in cuneiform tablets, as well as the tuning instructions’ recursive and symmetrical patterning of prescriptions concerning the alterations of this instrument’s strings. At each step, this patterning involves loosening or tightening a string that is three or four strings away from the string that had just been tightened or loosened. Added to these observations are acoustical features of the harmonics produced by plucked strings, and the auditory roughness and smoothness produced by pairs of plucked strings that psychoacoustical studies have established as universally audible. On these bases, one can conclude that Mesopotamian tuning can be interpreted as diatonic in structure without assuming such notions as octave identity, scale degrees, and consonance, all concepts for which there is no known testimony until much later in the history of music theory.