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.

翻译：Jeongganbo 是一个独特的音乐代言人, 由Sejong大帝所发明。 与西方的音符相反, 每张音符的音调是加密的, 长度是直接在Jeongganbo以矩阵形式呈现的。 我们使用地形数据分析(TDA)来分析韩国音乐在Jeongganbo为Suyeonjang、Songuyeo和Taryong撰写的, 这些在宫殿和高尚社区中播放的著名作品。 我们特别感兴趣的是循环结构。 我们首先定义和确定每种音乐的节点元素, 以其音调和长度为独特特征。 然后我们将音乐转换成图表, 并将节点之间的距离定义为相邻的频率。 我们使用该图表作为点云, 通过测量每个层面的洞结构来调查其同系结构。 我们确定每种音乐的周期, 与在Jeongganbo 播放的曲目相匹配, 并展示这些循环是如何相互联系的。 我们发现这项工作的主要发现是苏yeonjang 和Songuyeo的周期, 被归类为一种特殊的周期, 被称为Dodeuri, 在出现音乐的周期中, 属于 Doderi 属于单项的周期, 属于单项。