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For an up-to-date list of publications from the Music Technology Group see the
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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. |
