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Fowler, Michael D. (2019): An analysis of pitch-class segmentation in John Cage's Ryoanji for oboe using morphological image analysis and formal concept analysis. In: Journal of Mathematics and Music
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Abstract

In 1983, John Cage used the traditional stone garden, or karesansui at the Zen temple, Ryoan-ji in Kyoto as a model to generate a series of visual and musical works that utilized tracings of a collection of his own rocks. In this article, I analyze the first of the musical works, Ryoanji for oboe, using mixed methods drawn from morphological image analysis and formal concept analysis (FCA). I introduce the aesthetics of the karesansui and then examine the previous work of van Tonder and Lyons regarding the medial axis transform (MAT) of the garden at Ryoan-ji. This leads to the use of the distance transform, local maxima, and Voronoi diagram in order to decompose the two-dimensional image plane of Cage's Ryoanji for oboe. Finally, using the technique of FCA for constructing a number of formal concept lattices, the pitch-class segmentation of Ryoanji for oboe is investigated in regard to the sound gardens and the classes of Voronoi regions found across sound gardens.