Greek Ethnic Modal Names vs. Alia Musica's Nomenclature

摘要

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.