Topological Data Analysis of Korean Music in Jeongganbo: A Cycle Structure

TL;DR

This paper applies topological data analysis to Korean Jeongganbo music notation, revealing distinct cycle structures and overlaps in Dodeuri music compared to non-Dodeuri pieces.

Contribution

It introduces a novel TDA-based method to analyze Jeongganbo music, identifying cycle patterns and their interconnections in traditional Korean compositions.

Findings

Cycles in Dodeuri music often overlap

Taryong cycles appear individually

Homological analysis reveals structural differences

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 in Jeongganbo. We use topological data analysis (TDA) to analyze the Korean music written in Jeongganbo for Suyeonjang, Songuyeo, and Taryong, those well-known pieces played at the palace and among noble community. We are particularly interested in the cycle structure. We first define and determine the node elements of each music, characterized uniquely with its pitch and length. Then we transform the music into a graph and define the distance between the nodes as their adjacent occurrence rate. The graph is used as a point cloud whose homological structure is investigated by measuring the hole structure in each dimension. We identify cycles of each music, match those in Jeongganbo, and show how those cycles are interconnected. The main discovery of this work is that the cycles of Suyeonjang and Songuyeo, categorized as a special type of cyclic music known as Dodeuri, frequently overlap each other when appearing in the music while the cycles found in Taryong, which does not belong to Dodeuri class, appear individually.