  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.
