Rahn

AAWM JOURNAL VOL. 1 NO. 2 (2011)

The Hurrian Pieces, ca. 1350 BCE:
Part Two—From Numbered Strings to Tuned Strings

Jay Rahn

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Abstract:

The first part of this study concluded that on the basis of numbered strings and their pairwise ordering (from left to right and top to bottom) on cuneiform tablets, one can identify within h.6, the earliest known piece of music that is notated from beginning to end, structural relationships of similarity, adjacency, and analogy as well as statistical tendencies. Further, most of these tendencies appear throughout the other 34 earliest pieces, which are highly fragmentary, and these tendencies can be understood in terms of the structural relationships identified in h.6. Moreover, structural and statistical anomalies in h.6 are cognate with the features that tend to be shared by all 35 Hurrian pieces.

This, the second part of the study, shows how the numbered strings were tuned and how relationships of similarity, adjacency and analogy can be understood in terms of Gestalt Grouping Principles, i.e., as relationships perceived among the sounds produced by the tuned strings. Decisive in narrowing the possibilities of Mesopotmian tuning to 12 general cases is its well-formed (WF), specifically ‘2-Gap,’ structure. Consequences of 2 of the 12 kinds of 2-Gap structure include parallels with later music of ancient Greece and Europe as well as eastern and southeastern Asia. In both of these kinds of 2-Gap structure, the number of steps in the generating interval is (dm±1)/2, where dm is the number of steps in the modular interval.

These 2-Gap structures comprise a distinction between generic and specific intervals that amplifies relationships of sameness, analogy, and adjacency considered in the first part of the study. These relationships are further interpreted in terms of the Gestalt Grouping Principles of Similarity, Proximity, and Common Fate. In particular, Common Fate accounts for ‘motion’ among the string-pairs of h.6.

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Contributor Information:

Jay Rahn is Professor of Music in the Humanities Department and Faculty of Graduate Studies, York University (Toronto). Best known for his first book, A Theory for All Music, Dr. Rahn has published extensively on topics in systematic musicology, including music theory, comparative musicology, and music cognition.

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