Topological data analysis of Korean music in Jeongganbo: a cycle structure

Jeongganbo is a unique music representation invented by Sejong the Great. Contrary to the Western music notation, the pitch of each note is encrypted and the length is visualized directly in a matrix form. We use topological data analysis (TDA) to analyze the Korean music written in Jeongganbo for Suyeonjang, Songuyeo, and Taryong, those well-known pieces played among noble community. We define the nodes of each music with pitch and length and transform the music into a graph with the distance between the nodes defined as their adjacent occurrence rate. The graph homology is investigated by TDA. We identify cycles of each music and show how those cycles are interconnected. We found that the cycles of Suyeonjang and Songuyeo, categorized as a special type of cyclic music, frequently overlap each other in the music, while those of Taryong, which does not belong to the same class, appear only individually.