Hendrik Purwins, Thore Graepel, Benjamin Blankertz, and Klaus Obermayer
We apply correspondence analysis for visualization of interdependence of pitch class & key and key & composer. A co-occurrence matrix of key & pitch class frequencies is extracted from score (Bach's WTC). Keys are represented as high-dimensional pitch class vectors. Correspondence analysis then projectskeys on a planarkeyscape. Vice versa, on pitchscapespitch classes can also be embedded in the key space. In both scenarios a homogenous circle of fifths emerges in the scapes. We employ biplots to embed keys and pitch classes in the keyscape to visualize their interdependence. After a change of co-ordinates the four-dimensional biplots can be interpreted as a configuration on a torus, closely resembling results from music theory and experiments in listener models. In conjunction with spectral analysis, correspondence analysis constitutes a cognitive auditory model. Correspondence analysis of the co-occurrence table of intensities of keys and pitch classes lets the circle of fifths evolve in the pitchscape. This model works on digitized recorded music, does not require averaging or normalization of the data, and does not implicitly use circularity inherent in the model. Statistics on key preference in composers yields a composer & key cooccurrence matrix. Then stylescapes visualize relations between musical styles of particular composers and schools. The Biplotting technique links stylistic characteristics to favored keys. Interdependence of composers and schools is meaningfully visualized according to their key preferences.
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