In this study, we extract the pitch transition patterns from traditional Japanese, Chinese and German folk songs, and examine the characteristics of their respective schema. We sample 1,794 works from Nihon Min-yo Taikan for Japanese folk songs, 1,984 and 2,286 works from a website providing virtual musical scores for both Chinese and German folk songs, respectively. Our main method of extracting pitch transition patterns is to fit variable-length Markov chains (VLMCs) from musical data. A variable-length Markov chain model is a Markovian process having a sparse memory structure with some states that closely cohere. The structure can be characterized by a parsimonious number of transition probabilities for stationary categorical time series. The results indicate that the minimal structures of Japanese folk songs tend to create a longer schema than other two folk songs, while the minimal structures of both Chinese and German folk songs tend to create a shorter schema.