Toroidal Models in Tonal Theory and Pitch - Class Analysis
نویسندگان
چکیده
The doubly circular relations of the major and minor keys based on all twelve pitchclasses 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. Tonal Theory for the Digital Age (Computing in Musicology 15, 2007), 73–98.
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