As part of research on artificial intelligence music, Topological Data Analysis of traditional Korean music is being conducted, and new analytical methods are being developed. In this regard, we examined the application of a new analysis method that assigns additional weights to sigimsae and grace notes of in addition to the existing ‘pitch’ and ‘rhythm’ information, and explored its significance. First and foremost, the application result of the additional weight value of 1 shows the musical structure through the cycles and the overlap matrix and the melodic characteristics of Gyemyeonjo through the node configuration in the cycles. Moreover, according to the weight change of the sigimsae and grace notes, the number of cycles and the overlap matrix of each instrument change, and these aspects are different across instruments. Therefore, it becomes possible to examine the differences in the role and characteristics of sigimsae and grace note through the analysis with the weight function, in each musical piece or instrument.