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Gongchepu, one of the popular ancient Chinese musical scores, is hard to interpret due to the incomplete rhythmic rules, which only present a general rhythmic structure while the duration of each note within a beat is missing. Knowledge of determining the duration of each note is passed down via oral tradition. Since there are few experts who can master such musical score now, lots of effort has been taken to translate gongchepu into staff, making it much easier to learn. In this paper, we describe an instance-based method called KNN-based bootstrapping to annotate rhythm of Gongchepu automatically. Measurement of distance between two beats is one of the key challenges in this task. Our results demonstrate that the instance-based models significantly improve the accuracy of annotation. As an attempt to solve the rhythmic immeasurability problem in the study of musical score with the application of statistical models, this work is conducive to the preservation of Chinese traditional cultural heritage.