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Correspondence analysis for visualizing interplay of pitch class, key, and composer

Title Correspondence analysis for visualizing interplay of pitch class, key, and composer
Publication Type Book Chapter
Year of Publication 2004
Authors Purwins, H. , Graepel T. , Blankertz B. , & Obermayer K.
Editor Mazzola, G. , Noll T. , & Luis-Puebla E.
Book Title Perspectives in Mathematical and Computational Music Theory
Publisher Osnabrück Series on Music and Computation
Pages 432-454
Abstract 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 projects keys on a planar “keyscape”. Vice versa, on “pitchscapes” pitch 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 co- occurrence 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.
preprint/postprint document files/publications/e11e89-PerspMathMu03-PurwinsGraepelBlankertzObermayer.pdf