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

Abstract

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.

Keywords:

• Korean music
• Jeongganbo music
• topological data analysis
• persistent homology
• cycles
• cyclic music

Classification codes:

• AMS 00A65
• 55N31

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 https://www.youtube.com/watch?v=_DKo8FjL7Mg&t = 461s. Readers can listen to Suyeonjang played by Haegeum instrument with the link from 0:24–5:24.

2 https://www.youtube.com/watch?v=_DKo8FjL7Mg&t = 461s. Readers can listen to Suyeonjang played by Haegeum instrument with the link from 0:24–5:24. The rest of the pieces in the link are the variations of Suyeonjang composed with the technique of artificial intelligence.

3 M. Tran, D. Lee, J.-H. Jung, Machine composition of Korean music via topological data analysis and artificial neural network, arXiv:2203.15468, 2022.

Additional information

Funding

This work was supported by the National Research Foundation under Grant No. 2018R1D1A1A02086097 and 2021R1A2C3009648.