Abstract
The ethnic names associated with the diatonic modes (e.g., Dorian, Lydian, et al.) were assigned in one way by the ancient Greeks and in a different way in the anonymous medieval treatise Alia musica. Music historians usually say that this renaming was the result of a confusion, and leave it at that, but Edward Gollin showed that there was a logic here that could be captured in transformational terms. In this paper we add/uncover another layer to the palimpsest with the observation that the respective Greek and medieval nomenclatures are correlated with one of the fundamental distinctions in mathematical scale theory/word theory, the distinction between plain and twisted adjoint folding patterns of modes, as represented by conjugacy classes of Christoffel words.
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References
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Clampitt, D., Shafer, J. (2015). Greek Ethnic Modal Names vs. Alia Musica’s Nomenclature. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham. https://doi.org/10.1007/978-3-319-20603-5_38
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DOI: https://doi.org/10.1007/978-3-319-20603-5_38
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