A Symmetry Based Approach for Musical Tonality Analysis

We present a geometric approach for tonality analysis called symmetry model. To derive the symmetry model, Carol L.Krumhansl andE.J.Kessler’s toroidal Multi Dimensional Scaling (MDS) solution is separated into a key spanning and a key related component. While the key spanning component represents relationships betweendifferent keys, the key related component is suitable for the analysis of inner relationships of diatonic keys, for example tension or resolution tendencies, or functional relationships. These features are directly related to the symmetric organisation of tones around the tonal center, which is particularly visualized by the key related component.