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Toroidal Models in Tonal Theory and Pitch-Class Analysis

Title Toroidal Models in Tonal Theory and Pitch-Class Analysis
Publication Type Journal Article
Year of Publication 2007
Authors Purwins, H. , Blankertz B. , & Obermayer K.
Journal Title Computing in Musicology (Tonal Theory for the Digital Age )
Volume 15
Pages 73–98
Abstract The doubly circular relations of the major and minor keys based on all twelve pitch- classes can be depicted in toroidal models. We demonstrate a convergence of derivations from the different bases of conventional harmonic theory and recent experiments in music psychology. We present a formalization of the music-theoretical derivation from Gottfried Weber’s 1817 chart of tone-centers by using a topographic ordering map. We find the results to be consistent with Krumhansl and Kessler’s 1982 visualization of perceptual ratings.