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Toroidal Models in Tonal Theory
Citation key Purwins2008
Author Purwins, H. and Blankertz, B. and Obermayer, K.
Title of Book Tonal Theory for the Digital Age - Computing in Musicology
Pages 73 – 98
Year 2008
Publisher Stanford University
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.
Bibtex Type of Publication Selected:music
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